diff --git "a/data/track_pure_gps/splits/task5_bearing_computation_dev.json" "b/data/track_pure_gps/splits/task5_bearing_computation_dev.json" new file mode 100644--- /dev/null +++ "b/data/track_pure_gps/splits/task5_bearing_computation_dev.json" @@ -0,0 +1,10882 @@ +[ + { + "task": "bearing_computation", + "point_a": { + "lat": 31.72888, + "lon": 34.74632, + "name": "Qiryat Mal’akhi" + }, + "point_b": { + "lat": 53.73953, + "lon": 78.04387, + "name": "Karasuk" + }, + "ground_truth": { + "initial_bearing_deg": 41.44, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Qiryat Mal’akhi at (31.72888°, 34.74632°)", + " To: Karasuk at (53.73953°, 78.04387°)", + "Step 2: Calculate longitude difference", + " Δlon = 78.04387 - 34.74632 = 43.2976°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 41.44°", + "Step 5: Determine cardinal direction", + " 41.4° → NE", + "FINAL ANSWER: 41.44° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 16.70836, + "lon": 95.9336, + "name": "Twante" + }, + "point_b": { + "lat": -22.36611, + "lon": -48.38028, + "name": "Dois Córregos" + }, + "ground_truth": { + "initial_bearing_deg": 254.61, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Twante at (16.70836°, 95.9336°)", + " To: Dois Córregos at (-22.36611°, -48.38028°)", + "Step 2: Calculate longitude difference", + " Δlon = -48.38028 - 95.9336 = -144.3139°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 254.61°", + "Step 5: Determine cardinal direction", + " 254.6° → W", + "FINAL ANSWER: 254.61° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 29.86632, + "lon": 77.89118, + "name": "Roorkee" + }, + "point_b": { + "lat": -37.84205, + "lon": 145.0694, + "name": "Camberwell" + }, + "ground_truth": { + "initial_bearing_deg": 133.24, + "cardinal_direction": "SE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Roorkee at (29.86632°, 77.89118°)", + " To: Camberwell at (-37.84205°, 145.0694°)", + "Step 2: Calculate longitude difference", + " Δlon = 145.0694 - 77.89118 = 67.1782°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 133.24°", + "Step 5: Determine cardinal direction", + " 133.2° → SE", + "FINAL ANSWER: 133.24° (SE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 30.20942, + "lon": -9.37922, + "name": "Tine Biougra" + }, + "point_b": { + "lat": 45.63873, + "lon": -122.66149, + "name": "Vancouver" + }, + "ground_truth": { + "initial_bearing_deg": 319.68, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Tine Biougra at (30.20942°, -9.37922°)", + " To: Vancouver at (45.63873°, -122.66149°)", + "Step 2: Calculate longitude difference", + " Δlon = -122.66149 - -9.37922 = -113.2823°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 319.68°", + "Step 5: Determine cardinal direction", + " 319.7° → NW", + "FINAL ANSWER: 319.68° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -18.14307, + "lon": 177.50691, + "name": "Sigatoka" + }, + "point_b": { + "lat": 12.24922, + "lon": -0.61527, + "name": "Zorgo" + }, + "ground_truth": { + "initial_bearing_deg": 197.35, + "cardinal_direction": "S", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Sigatoka at (-18.14307°, 177.50691°)", + " To: Zorgo at (12.24922°, -0.61527°)", + "Step 2: Calculate longitude difference", + " Δlon = -0.61527 - 177.50691 = -178.1222°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 197.35°", + "Step 5: Determine cardinal direction", + " 197.3° → S", + "FINAL ANSWER: 197.35° (S)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 26.13421, + "lon": -80.23184, + "name": "Plantation" + }, + "point_b": { + "lat": 40.68496, + "lon": -80.10714, + "name": "Cranberry Township" + }, + "ground_truth": { + "initial_bearing_deg": 0.38, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Plantation at (26.13421°, -80.23184°)", + " To: Cranberry Township at (40.68496°, -80.10714°)", + "Step 2: Calculate longitude difference", + " Δlon = -80.10714 - -80.23184 = 0.1247°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 0.38°", + "Step 5: Determine cardinal direction", + " 0.4° → N", + "FINAL ANSWER: 0.38° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -23.55108, + "lon": -46.53829, + "name": "Carrao" + }, + "point_b": { + "lat": -5.04098, + "lon": 18.81619, + "name": "Kikwit" + }, + "ground_truth": { + "initial_bearing_deg": 84.61, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Carrao at (-23.55108°, -46.53829°)", + " To: Kikwit at (-5.04098°, 18.81619°)", + "Step 2: Calculate longitude difference", + " Δlon = 18.81619 - -46.53829 = 65.3545°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 84.61°", + "Step 5: Determine cardinal direction", + " 84.6° → E", + "FINAL ANSWER: 84.61° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 13.95, + "lon": 40.66667, + "name": "Arerti" + }, + "point_b": { + "lat": 24.47979, + "lon": 118.08187, + "name": "Xiamen" + }, + "ground_truth": { + "initial_bearing_deg": 68.25, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Arerti at (13.95°, 40.66667°)", + " To: Xiamen at (24.47979°, 118.08187°)", + "Step 2: Calculate longitude difference", + " Δlon = 118.08187 - 40.66667 = 77.4152°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 68.25°", + "Step 5: Determine cardinal direction", + " 68.2° → E", + "FINAL ANSWER: 68.25° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 43.98333, + "lon": 25.33333, + "name": "Alexandria" + }, + "point_b": { + "lat": 54.66079, + "lon": -5.66802, + "name": "Bangor" + }, + "ground_truth": { + "initial_bearing_deg": 309.16, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Alexandria at (43.98333°, 25.33333°)", + " To: Bangor at (54.66079°, -5.66802°)", + "Step 2: Calculate longitude difference", + " Δlon = -5.66802 - 25.33333 = -31.0014°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 309.16°", + "Step 5: Determine cardinal direction", + " 309.2° → NW", + "FINAL ANSWER: 309.16° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -28.72472, + "lon": -52.84972, + "name": "Espumoso" + }, + "point_b": { + "lat": 50.90395, + "lon": -1.40428, + "name": "Southampton" + }, + "ground_truth": { + "initial_bearing_deg": 29.56, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Espumoso at (-28.72472°, -52.84972°)", + " To: Southampton at (50.90395°, -1.40428°)", + "Step 2: Calculate longitude difference", + " Δlon = -1.40428 - -52.84972 = 51.4454°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 29.56°", + "Step 5: Determine cardinal direction", + " 29.6° → NE", + "FINAL ANSWER: 29.56° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 10.38542, + "lon": -9.30568, + "name": "Kankan" + }, + "point_b": { + "lat": 24.74745, + "lon": 67.92353, + "name": "Thatta" + }, + "ground_truth": { + "initial_bearing_deg": 67.02, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Kankan at (10.38542°, -9.30568°)", + " To: Thatta at (24.74745°, 67.92353°)", + "Step 2: Calculate longitude difference", + " Δlon = 67.92353 - -9.30568 = 77.2292°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 67.02°", + "Step 5: Determine cardinal direction", + " 67.0° → NE", + "FINAL ANSWER: 67.02° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -33.28397, + "lon": 149.10018, + "name": "Orange" + }, + "point_b": { + "lat": -37.87709, + "lon": 145.12939, + "name": "Mount Waverley" + }, + "ground_truth": { + "initial_bearing_deg": 213.97, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Orange at (-33.28397°, 149.10018°)", + " To: Mount Waverley at (-37.87709°, 145.12939°)", + "Step 2: Calculate longitude difference", + " Δlon = 145.12939 - 149.10018 = -3.9708°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 213.97°", + "Step 5: Determine cardinal direction", + " 214.0° → SW", + "FINAL ANSWER: 213.97° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 28.92313, + "lon": -13.66579, + "name": "Puerto del Carmen" + }, + "point_b": { + "lat": 46.61667, + "lon": 14.28333, + "name": "Sankt Martin" + }, + "ground_truth": { + "initial_bearing_deg": 43.21, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Puerto del Carmen at (28.92313°, -13.66579°)", + " To: Sankt Martin at (46.61667°, 14.28333°)", + "Step 2: Calculate longitude difference", + " Δlon = 14.28333 - -13.66579 = 27.9491°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 43.21°", + "Step 5: Determine cardinal direction", + " 43.2° → NE", + "FINAL ANSWER: 43.21° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 37.57444, + "lon": 43.74083, + "name": "Hakkâri" + }, + "point_b": { + "lat": 32.12722, + "lon": 112.75417, + "name": "Zaoyang" + }, + "ground_truth": { + "initial_bearing_deg": 73.35, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Hakkâri at (37.57444°, 43.74083°)", + " To: Zaoyang at (32.12722°, 112.75417°)", + "Step 2: Calculate longitude difference", + " Δlon = 112.75417 - 43.74083 = 69.0133°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 73.35°", + "Step 5: Determine cardinal direction", + " 73.3° → E", + "FINAL ANSWER: 73.35° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 9.86142, + "lon": -84.09266, + "name": "Aserrí" + }, + "point_b": { + "lat": -4.04167, + "lon": -44.475, + "name": "São Mateus do Maranhão" + }, + "ground_truth": { + "initial_bearing_deg": 107.54, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Aserrí at (9.86142°, -84.09266°)", + " To: São Mateus do Maranhão at (-4.04167°, -44.475°)", + "Step 2: Calculate longitude difference", + " Δlon = -44.475 - -84.09266 = 39.6177°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 107.54°", + "Step 5: Determine cardinal direction", + " 107.5° → E", + "FINAL ANSWER: 107.54° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 30.0362, + "lon": 47.91951, + "name": "Umm Qaşr" + }, + "point_b": { + "lat": 38.99817, + "lon": -77.28832, + "name": "Great Falls" + }, + "ground_truth": { + "initial_bearing_deg": 320.45, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Umm Qaşr at (30.0362°, 47.91951°)", + " To: Great Falls at (38.99817°, -77.28832°)", + "Step 2: Calculate longitude difference", + " Δlon = -77.28832 - 47.91951 = -125.2078°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 320.45°", + "Step 5: Determine cardinal direction", + " 320.4° → NW", + "FINAL ANSWER: 320.45° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 43.18944, + "lon": 141.00222, + "name": "Otaru" + }, + "point_b": { + "lat": -25.76972, + "lon": -49.71583, + "name": "Lapa" + }, + "ground_truth": { + "initial_bearing_deg": 30.13, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Otaru at (43.18944°, 141.00222°)", + " To: Lapa at (-25.76972°, -49.71583°)", + "Step 2: Calculate longitude difference", + " Δlon = -49.71583 - 141.00222 = -190.7181°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 30.13°", + "Step 5: Determine cardinal direction", + " 30.1° → NE", + "FINAL ANSWER: 30.13° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 35.93333, + "lon": 140.55, + "name": "Itako" + }, + "point_b": { + "lat": -1.04576, + "lon": -80.65889, + "name": "Montecristi" + }, + "ground_truth": { + "initial_bearing_deg": 57.07, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Itako at (35.93333°, 140.55°)", + " To: Montecristi at (-1.04576°, -80.65889°)", + "Step 2: Calculate longitude difference", + " Δlon = -80.65889 - 140.55 = -221.2089°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 57.07°", + "Step 5: Determine cardinal direction", + " 57.1° → NE", + "FINAL ANSWER: 57.07° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -33.85, + "lon": 151.03333, + "name": "Auburn" + }, + "point_b": { + "lat": -28.29917, + "lon": -54.26306, + "name": "Santo Ângelo" + }, + "ground_truth": { + "initial_bearing_deg": 155.8, + "cardinal_direction": "SE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Auburn at (-33.85°, 151.03333°)", + " To: Santo Ângelo at (-28.29917°, -54.26306°)", + "Step 2: Calculate longitude difference", + " Δlon = -54.26306 - 151.03333 = -205.2964°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 155.80°", + "Step 5: Determine cardinal direction", + " 155.8° → SE", + "FINAL ANSWER: 155.80° (SE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 43.93064, + "lon": 10.92365, + "name": "Pistoia" + }, + "point_b": { + "lat": 39.34474, + "lon": 16.23802, + "name": "Quattromiglia" + }, + "ground_truth": { + "initial_bearing_deg": 137.31, + "cardinal_direction": "SE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Pistoia at (43.93064°, 10.92365°)", + " To: Quattromiglia at (39.34474°, 16.23802°)", + "Step 2: Calculate longitude difference", + " Δlon = 16.23802 - 10.92365 = 5.3144°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 137.31°", + "Step 5: Determine cardinal direction", + " 137.3° → SE", + "FINAL ANSWER: 137.31° (SE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 32.65236, + "lon": -8.42769, + "name": "Sidi Bennour" + }, + "point_b": { + "lat": 11.70611, + "lon": 122.36444, + "name": "Kalibo (poblacion)" + }, + "ground_truth": { + "initial_bearing_deg": 55.16, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Sidi Bennour at (32.65236°, -8.42769°)", + " To: Kalibo (poblacion) at (11.70611°, 122.36444°)", + "Step 2: Calculate longitude difference", + " Δlon = 122.36444 - -8.42769 = 130.7921°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 55.16°", + "Step 5: Determine cardinal direction", + " 55.2° → NE", + "FINAL ANSWER: 55.16° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 11.52134, + "lon": 13.68952, + "name": "Bama" + }, + "point_b": { + "lat": 36.72016, + "lon": -4.42034, + "name": "Málaga" + }, + "ground_truth": { + "initial_bearing_deg": 330.12, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Bama at (11.52134°, 13.68952°)", + " To: Málaga at (36.72016°, -4.42034°)", + "Step 2: Calculate longitude difference", + " Δlon = -4.42034 - 13.68952 = -18.1099°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 330.12°", + "Step 5: Determine cardinal direction", + " 330.1° → NW", + "FINAL ANSWER: 330.12° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -22.54861, + "lon": -47.91389, + "name": "São Pedro" + }, + "point_b": { + "lat": -34.49459, + "lon": -58.62729, + "name": "Don Torcuato" + }, + "ground_truth": { + "initial_bearing_deg": 215.79, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: São Pedro at (-22.54861°, -47.91389°)", + " To: Don Torcuato at (-34.49459°, -58.62729°)", + "Step 2: Calculate longitude difference", + " Δlon = -58.62729 - -47.91389 = -10.7134°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 215.79°", + "Step 5: Determine cardinal direction", + " 215.8° → SW", + "FINAL ANSWER: 215.79° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 35.70915, + "lon": 10.67397, + "name": "Ouardenine" + }, + "point_b": { + "lat": 48.7606, + "lon": 8.23975, + "name": "Baden-Baden" + }, + "ground_truth": { + "initial_bearing_deg": 352.94, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Ouardenine at (35.70915°, 10.67397°)", + " To: Baden-Baden at (48.7606°, 8.23975°)", + "Step 2: Calculate longitude difference", + " Δlon = 8.23975 - 10.67397 = -2.4342°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 352.94°", + "Step 5: Determine cardinal direction", + " 352.9° → N", + "FINAL ANSWER: 352.94° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 52.20667, + "lon": 104.2177, + "name": "Markova" + }, + "point_b": { + "lat": 24.55524, + "lon": -81.78163, + "name": "Key West" + }, + "ground_truth": { + "initial_bearing_deg": 5.6, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Markova at (52.20667°, 104.2177°)", + " To: Key West at (24.55524°, -81.78163°)", + "Step 2: Calculate longitude difference", + " Δlon = -81.78163 - 104.2177 = -185.9993°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 5.60°", + "Step 5: Determine cardinal direction", + " 5.6° → N", + "FINAL ANSWER: 5.60° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 37.16911, + "lon": 10.03478, + "name": "El Alia" + }, + "point_b": { + "lat": 7.90303, + "lon": 4.31364, + "name": "Ejigbo" + }, + "ground_truth": { + "initial_bearing_deg": 191.49, + "cardinal_direction": "S", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: El Alia at (37.16911°, 10.03478°)", + " To: Ejigbo at (7.90303°, 4.31364°)", + "Step 2: Calculate longitude difference", + " Δlon = 4.31364 - 10.03478 = -5.7211°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 191.49°", + "Step 5: Determine cardinal direction", + " 191.5° → S", + "FINAL ANSWER: 191.49° (S)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 17.67178, + "lon": 74.01289, + "name": "Godoli" + }, + "point_b": { + "lat": 56.56699, + "lon": 9.02707, + "name": "Skive" + }, + "ground_truth": { + "initial_bearing_deg": 325.43, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Godoli at (17.67178°, 74.01289°)", + " To: Skive at (56.56699°, 9.02707°)", + "Step 2: Calculate longitude difference", + " Δlon = 9.02707 - 74.01289 = -64.9858°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 325.43°", + "Step 5: Determine cardinal direction", + " 325.4° → NW", + "FINAL ANSWER: 325.43° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 19.6031, + "lon": 74.19356, + "name": "Ghulewadi" + }, + "point_b": { + "lat": -37.71893, + "lon": -72.24099, + "name": "Mulchén" + }, + "ground_truth": { + "initial_bearing_deg": 230.92, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Ghulewadi at (19.6031°, 74.19356°)", + " To: Mulchén at (-37.71893°, -72.24099°)", + "Step 2: Calculate longitude difference", + " Δlon = -72.24099 - 74.19356 = -146.4346°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 230.92°", + "Step 5: Determine cardinal direction", + " 230.9° → SW", + "FINAL ANSWER: 230.92° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 14.10594, + "lon": -15.5508, + "name": "Kaffrine" + }, + "point_b": { + "lat": 31.18352, + "lon": 30.52448, + "name": "Al Maḩmūdīyah" + }, + "ground_truth": { + "initial_bearing_deg": 59.88, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Kaffrine at (14.10594°, -15.5508°)", + " To: Al Maḩmūdīyah at (31.18352°, 30.52448°)", + "Step 2: Calculate longitude difference", + " Δlon = 30.52448 - -15.5508 = 46.0753°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 59.88°", + "Step 5: Determine cardinal direction", + " 59.9° → NE", + "FINAL ANSWER: 59.88° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 57.7584, + "lon": 16.63733, + "name": "Västervik" + }, + "point_b": { + "lat": -31.44957, + "lon": -60.93153, + "name": "Esperanza" + }, + "ground_truth": { + "initial_bearing_deg": 242.5, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Västervik at (57.7584°, 16.63733°)", + " To: Esperanza at (-31.44957°, -60.93153°)", + "Step 2: Calculate longitude difference", + " Δlon = -60.93153 - 16.63733 = -77.5689°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 242.50°", + "Step 5: Determine cardinal direction", + " 242.5° → SW", + "FINAL ANSWER: 242.50° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 36.84666, + "lon": 136.98355, + "name": "Himi" + }, + "point_b": { + "lat": 30.36846, + "lon": 75.86791, + "name": "Dhūri" + }, + "ground_truth": { + "initial_bearing_deg": 281.57, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Himi at (36.84666°, 136.98355°)", + " To: Dhūri at (30.36846°, 75.86791°)", + "Step 2: Calculate longitude difference", + " Δlon = 75.86791 - 136.98355 = -61.1156°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 281.57°", + "Step 5: Determine cardinal direction", + " 281.6° → W", + "FINAL ANSWER: 281.57° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 60.45148, + "lon": 22.26869, + "name": "Turku" + }, + "point_b": { + "lat": 33.41477, + "lon": -111.90931, + "name": "Tempe" + }, + "ground_truth": { + "initial_bearing_deg": 322.41, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Turku at (60.45148°, 22.26869°)", + " To: Tempe at (33.41477°, -111.90931°)", + "Step 2: Calculate longitude difference", + " Δlon = -111.90931 - 22.26869 = -134.1780°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 322.41°", + "Step 5: Determine cardinal direction", + " 322.4° → NW", + "FINAL ANSWER: 322.41° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -20.83778, + "lon": -40.72194, + "name": "Piúma" + }, + "point_b": { + "lat": 48.78421, + "lon": 1.9552, + "name": "Élancourt" + }, + "ground_truth": { + "initial_bearing_deg": 27.03, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Piúma at (-20.83778°, -40.72194°)", + " To: Élancourt at (48.78421°, 1.9552°)", + "Step 2: Calculate longitude difference", + " Δlon = 1.9552 - -40.72194 = 42.6771°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 27.03°", + "Step 5: Determine cardinal direction", + " 27.0° → NE", + "FINAL ANSWER: 27.03° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -4.36667, + "lon": 35.08333, + "name": "Basotu" + }, + "point_b": { + "lat": -0.40306, + "lon": 31.15722, + "name": "Lyantonde" + }, + "ground_truth": { + "initial_bearing_deg": 315.2, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Basotu at (-4.36667°, 35.08333°)", + " To: Lyantonde at (-0.40306°, 31.15722°)", + "Step 2: Calculate longitude difference", + " Δlon = 31.15722 - 35.08333 = -3.9261°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 315.20°", + "Step 5: Determine cardinal direction", + " 315.2° → NW", + "FINAL ANSWER: 315.20° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -22.98436, + "lon": -43.20285, + "name": "Ipanema" + }, + "point_b": { + "lat": 45.81516, + "lon": 19.6318, + "name": "Bačka Topola" + }, + "ground_truth": { + "initial_bearing_deg": 38.33, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Ipanema at (-22.98436°, -43.20285°)", + " To: Bačka Topola at (45.81516°, 19.6318°)", + "Step 2: Calculate longitude difference", + " Δlon = 19.6318 - -43.20285 = 62.8346°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 38.33°", + "Step 5: Determine cardinal direction", + " 38.3° → NE", + "FINAL ANSWER: 38.33° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 38.24719, + "lon": 125.79476, + "name": "Ayang-ni" + }, + "point_b": { + "lat": -19.9, + "lon": 47.23333, + "name": "Soanindrariny" + }, + "ground_truth": { + "initial_bearing_deg": 247.45, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Ayang-ni at (38.24719°, 125.79476°)", + " To: Soanindrariny at (-19.9°, 47.23333°)", + "Step 2: Calculate longitude difference", + " Δlon = 47.23333 - 125.79476 = -78.5614°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 247.45°", + "Step 5: Determine cardinal direction", + " 247.4° → SW", + "FINAL ANSWER: 247.45° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 27.06193, + "lon": -101.54891, + "name": "San Buenaventura" + }, + "point_b": { + "lat": 38.50839, + "lon": -90.32289, + "name": "Mehlville" + }, + "ground_truth": { + "initial_bearing_deg": 36.58, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: San Buenaventura at (27.06193°, -101.54891°)", + " To: Mehlville at (38.50839°, -90.32289°)", + "Step 2: Calculate longitude difference", + " Δlon = -90.32289 - -101.54891 = 11.2260°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 36.58°", + "Step 5: Determine cardinal direction", + " 36.6° → NE", + "FINAL ANSWER: 36.58° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 21.68216, + "lon": -78.62567, + "name": "Baraguá" + }, + "point_b": { + "lat": 20.66667, + "lon": -88.56667, + "name": "Chichén-Itzá" + }, + "ground_truth": { + "initial_bearing_deg": 265.56, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Baraguá at (21.68216°, -78.62567°)", + " To: Chichén-Itzá at (20.66667°, -88.56667°)", + "Step 2: Calculate longitude difference", + " Δlon = -88.56667 - -78.62567 = -9.9410°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 265.56°", + "Step 5: Determine cardinal direction", + " 265.6° → W", + "FINAL ANSWER: 265.56° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -5.04098, + "lon": 18.81619, + "name": "Kikwit" + }, + "point_b": { + "lat": -27.18871, + "lon": 25.32931, + "name": "Schweizer-Reneke" + }, + "ground_truth": { + "initial_bearing_deg": 165.04, + "cardinal_direction": "S", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Kikwit at (-5.04098°, 18.81619°)", + " To: Schweizer-Reneke at (-27.18871°, 25.32931°)", + "Step 2: Calculate longitude difference", + " Δlon = 25.32931 - 18.81619 = 6.5131°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 165.04°", + "Step 5: Determine cardinal direction", + " 165.0° → S", + "FINAL ANSWER: 165.04° (S)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 34.67139, + "lon": 70.20944, + "name": "Mehtar Lām" + }, + "point_b": { + "lat": -7.31473, + "lon": 16.0024, + "name": "Sanza Pombo" + }, + "ground_truth": { + "initial_bearing_deg": 241.62, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Mehtar Lām at (34.67139°, 70.20944°)", + " To: Sanza Pombo at (-7.31473°, 16.0024°)", + "Step 2: Calculate longitude difference", + " Δlon = 16.0024 - 70.20944 = -54.2070°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 241.62°", + "Step 5: Determine cardinal direction", + " 241.6° → SW", + "FINAL ANSWER: 241.62° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 9.8, + "lon": 38.73333, + "name": "Fichē" + }, + "point_b": { + "lat": 7.15571, + "lon": 3.34509, + "name": "Abeokuta" + }, + "ground_truth": { + "initial_bearing_deg": 268.51, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Fichē at (9.8°, 38.73333°)", + " To: Abeokuta at (7.15571°, 3.34509°)", + "Step 2: Calculate longitude difference", + " Δlon = 3.34509 - 38.73333 = -35.3882°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 268.51°", + "Step 5: Determine cardinal direction", + " 268.5° → W", + "FINAL ANSWER: 268.51° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 50.965, + "lon": 5.50082, + "name": "Genk" + }, + "point_b": { + "lat": 10.35028, + "lon": 39.93626, + "name": "Āt’aye" + }, + "ground_truth": { + "initial_bearing_deg": 132.91, + "cardinal_direction": "SE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Genk at (50.965°, 5.50082°)", + " To: Āt’aye at (10.35028°, 39.93626°)", + "Step 2: Calculate longitude difference", + " Δlon = 39.93626 - 5.50082 = 34.4354°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 132.91°", + "Step 5: Determine cardinal direction", + " 132.9° → SE", + "FINAL ANSWER: 132.91° (SE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -3.49167, + "lon": -45.25111, + "name": "Monção" + }, + "point_b": { + "lat": 13.4556, + "lon": 109.22348, + "name": "Sông Cầu" + }, + "ground_truth": { + "initial_bearing_deg": 66.89, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Monção at (-3.49167°, -45.25111°)", + " To: Sông Cầu at (13.4556°, 109.22348°)", + "Step 2: Calculate longitude difference", + " Δlon = 109.22348 - -45.25111 = 154.4746°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 66.89°", + "Step 5: Determine cardinal direction", + " 66.9° → NE", + "FINAL ANSWER: 66.89° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 41.17289, + "lon": -8.59931, + "name": "Paranhos" + }, + "point_b": { + "lat": -27.3171, + "lon": 153.03097, + "name": "Bracken Ridge" + }, + "ground_truth": { + "initial_bearing_deg": 53.17, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Paranhos at (41.17289°, -8.59931°)", + " To: Bracken Ridge at (-27.3171°, 153.03097°)", + "Step 2: Calculate longitude difference", + " Δlon = 153.03097 - -8.59931 = 161.6303°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 53.17°", + "Step 5: Determine cardinal direction", + " 53.2° → NE", + "FINAL ANSWER: 53.17° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -11.72917, + "lon": -49.06861, + "name": "Gurupi" + }, + "point_b": { + "lat": 22.75923, + "lon": 113.79452, + "name": "Gongheyong" + }, + "ground_truth": { + "initial_bearing_deg": 53.69, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Gurupi at (-11.72917°, -49.06861°)", + " To: Gongheyong at (22.75923°, 113.79452°)", + "Step 2: Calculate longitude difference", + " Δlon = 113.79452 - -49.06861 = 162.8631°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 53.69°", + "Step 5: Determine cardinal direction", + " 53.7° → NE", + "FINAL ANSWER: 53.69° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 34.11849, + "lon": -6.7389, + "name": "Bouknadel" + }, + "point_b": { + "lat": 59.34, + "lon": 17.94, + "name": "Bromma" + }, + "ground_truth": { + "initial_bearing_deg": 25.21, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Bouknadel at (34.11849°, -6.7389°)", + " To: Bromma at (59.34°, 17.94°)", + "Step 2: Calculate longitude difference", + " Δlon = 17.94 - -6.7389 = 24.6789°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 25.21°", + "Step 5: Determine cardinal direction", + " 25.2° → NE", + "FINAL ANSWER: 25.21° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 32.7236, + "lon": -5.1025, + "name": "Boumia" + }, + "point_b": { + "lat": 39.07195, + "lon": -0.26623, + "name": "Tavernes de la Valldigna" + }, + "ground_truth": { + "initial_bearing_deg": 30.29, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Boumia at (32.7236°, -5.1025°)", + " To: Tavernes de la Valldigna at (39.07195°, -0.26623°)", + "Step 2: Calculate longitude difference", + " Δlon = -0.26623 - -5.1025 = 4.8363°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 30.29°", + "Step 5: Determine cardinal direction", + " 30.3° → NE", + "FINAL ANSWER: 30.29° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 39.76282, + "lon": -86.39972, + "name": "Avon" + }, + "point_b": { + "lat": 3.6746, + "lon": 100.9867, + "name": "Sungai Besar" + }, + "ground_truth": { + "initial_bearing_deg": 349.35, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Avon at (39.76282°, -86.39972°)", + " To: Sungai Besar at (3.6746°, 100.9867°)", + "Step 2: Calculate longitude difference", + " Δlon = 100.9867 - -86.39972 = 187.3864°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 349.35°", + "Step 5: Determine cardinal direction", + " 349.4° → N", + "FINAL ANSWER: 349.35° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -21.13361, + "lon": -51.10167, + "name": "Mirandópolis" + }, + "point_b": { + "lat": 6.19041, + "lon": -67.48391, + "name": "Puerto Carreño" + }, + "ground_truth": { + "initial_bearing_deg": 327.75, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Mirandópolis at (-21.13361°, -51.10167°)", + " To: Puerto Carreño at (6.19041°, -67.48391°)", + "Step 2: Calculate longitude difference", + " Δlon = -67.48391 - -51.10167 = -16.3822°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 327.75°", + "Step 5: Determine cardinal direction", + " 327.8° → NW", + "FINAL ANSWER: 327.75° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 20.71373, + "lon": 77.02639, + "name": "Umbri" + }, + "point_b": { + "lat": -43.89834, + "lon": 171.73011, + "name": "Ashburton" + }, + "ground_truth": { + "initial_bearing_deg": 131.15, + "cardinal_direction": "SE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Umbri at (20.71373°, 77.02639°)", + " To: Ashburton at (-43.89834°, 171.73011°)", + "Step 2: Calculate longitude difference", + " Δlon = 171.73011 - 77.02639 = 94.7037°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 131.15°", + "Step 5: Determine cardinal direction", + " 131.2° → SE", + "FINAL ANSWER: 131.15° (SE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -9.53694, + "lon": -36.63361, + "name": "Igaci" + }, + "point_b": { + "lat": -20.87222, + "lon": -51.4875, + "name": "Castilho" + }, + "ground_truth": { + "initial_bearing_deg": 229.9, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Igaci at (-9.53694°, -36.63361°)", + " To: Castilho at (-20.87222°, -51.4875°)", + "Step 2: Calculate longitude difference", + " Δlon = -51.4875 - -36.63361 = -14.8539°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 229.90°", + "Step 5: Determine cardinal direction", + " 229.9° → SW", + "FINAL ANSWER: 229.90° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 40.84394, + "lon": 14.0952, + "name": "Pozzuoli" + }, + "point_b": { + "lat": 9.56667, + "lon": 37.1, + "name": "Shambu" + }, + "ground_truth": { + "initial_bearing_deg": 140.52, + "cardinal_direction": "SE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Pozzuoli at (40.84394°, 14.0952°)", + " To: Shambu at (9.56667°, 37.1°)", + "Step 2: Calculate longitude difference", + " Δlon = 37.1 - 14.0952 = 23.0048°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 140.52°", + "Step 5: Determine cardinal direction", + " 140.5° → SE", + "FINAL ANSWER: 140.52° (SE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 49.19884, + "lon": 9.5072, + "name": "Öhringen" + }, + "point_b": { + "lat": 78.22334, + "lon": 15.64689, + "name": "Longyearbyen" + }, + "ground_truth": { + "initial_bearing_deg": 2.57, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Öhringen at (49.19884°, 9.5072°)", + " To: Longyearbyen at (78.22334°, 15.64689°)", + "Step 2: Calculate longitude difference", + " Δlon = 15.64689 - 9.5072 = 6.1397°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 2.57°", + "Step 5: Determine cardinal direction", + " 2.6° → N", + "FINAL ANSWER: 2.57° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -33.71028, + "lon": 150.95095, + "name": "Kellyville" + }, + "point_b": { + "lat": 43.70313, + "lon": 7.26608, + "name": "Nice" + }, + "ground_truth": { + "initial_bearing_deg": 300.43, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Kellyville at (-33.71028°, 150.95095°)", + " To: Nice at (43.70313°, 7.26608°)", + "Step 2: Calculate longitude difference", + " Δlon = 7.26608 - 150.95095 = -143.6849°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 300.43°", + "Step 5: Determine cardinal direction", + " 300.4° → NW", + "FINAL ANSWER: 300.43° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -2.94722, + "lon": -48.95306, + "name": "Tailândia" + }, + "point_b": { + "lat": 17.66709, + "lon": 82.61245, + "name": "Narsīpatnam" + }, + "ground_truth": { + "initial_bearing_deg": 69.22, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Tailândia at (-2.94722°, -48.95306°)", + " To: Narsīpatnam at (17.66709°, 82.61245°)", + "Step 2: Calculate longitude difference", + " Δlon = 82.61245 - -48.95306 = 131.5655°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 69.22°", + "Step 5: Determine cardinal direction", + " 69.2° → E", + "FINAL ANSWER: 69.22° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 49.26667, + "lon": 6.78333, + "name": "Wadgassen" + }, + "point_b": { + "lat": 11.46009, + "lon": 78.18635, + "name": "Rasipuram" + }, + "ground_truth": { + "initial_bearing_deg": 96.58, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Wadgassen at (49.26667°, 6.78333°)", + " To: Rasipuram at (11.46009°, 78.18635°)", + "Step 2: Calculate longitude difference", + " Δlon = 78.18635 - 6.78333 = 71.4030°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 96.58°", + "Step 5: Determine cardinal direction", + " 96.6° → E", + "FINAL ANSWER: 96.58° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 25.84341, + "lon": 93.43116, + "name": "Diphu" + }, + "point_b": { + "lat": -35.41647, + "lon": 149.06954, + "name": "Tuggeranong Administrative District" + }, + "ground_truth": { + "initial_bearing_deg": 137.03, + "cardinal_direction": "SE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Diphu at (25.84341°, 93.43116°)", + " To: Tuggeranong Administrative District at (-35.41647°, 149.06954°)", + "Step 2: Calculate longitude difference", + " Δlon = 149.06954 - 93.43116 = 55.6384°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 137.03°", + "Step 5: Determine cardinal direction", + " 137.0° → SE", + "FINAL ANSWER: 137.03° (SE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 4.08466, + "lon": -76.19536, + "name": "Tuluá" + }, + "point_b": { + "lat": 27.31667, + "lon": 103.71667, + "name": "Zhaotong" + }, + "ground_truth": { + "initial_bearing_deg": 0.15, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Tuluá at (4.08466°, -76.19536°)", + " To: Zhaotong at (27.31667°, 103.71667°)", + "Step 2: Calculate longitude difference", + " Δlon = 103.71667 - -76.19536 = 179.9120°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 0.15°", + "Step 5: Determine cardinal direction", + " 0.1° → N", + "FINAL ANSWER: 0.15° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -34.424, + "lon": 150.89345, + "name": "Wollongong" + }, + "point_b": { + "lat": 54.69981, + "lon": 25.18393, + "name": "Pilaitė" + }, + "ground_truth": { + "initial_bearing_deg": 315.8, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Wollongong at (-34.424°, 150.89345°)", + " To: Pilaitė at (54.69981°, 25.18393°)", + "Step 2: Calculate longitude difference", + " Δlon = 25.18393 - 150.89345 = -125.7095°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 315.80°", + "Step 5: Determine cardinal direction", + " 315.8° → NW", + "FINAL ANSWER: 315.80° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -37.0646, + "lon": 174.94212, + "name": "Papakura" + }, + "point_b": { + "lat": 41.20917, + "lon": 36.97389, + "name": "Terme" + }, + "ground_truth": { + "initial_bearing_deg": 290.56, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Papakura at (-37.0646°, 174.94212°)", + " To: Terme at (41.20917°, 36.97389°)", + "Step 2: Calculate longitude difference", + " Δlon = 36.97389 - 174.94212 = -137.9682°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 290.56°", + "Step 5: Determine cardinal direction", + " 290.6° → W", + "FINAL ANSWER: 290.56° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 14.1951, + "lon": 43.31518, + "name": "Zabīd" + }, + "point_b": { + "lat": -22.84278, + "lon": -45.25139, + "name": "Potim" + }, + "ground_truth": { + "initial_bearing_deg": 247.48, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Zabīd at (14.1951°, 43.31518°)", + " To: Potim at (-22.84278°, -45.25139°)", + "Step 2: Calculate longitude difference", + " Δlon = -45.25139 - 43.31518 = -88.5666°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 247.48°", + "Step 5: Determine cardinal direction", + " 247.5° → SW", + "FINAL ANSWER: 247.48° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 25.27143, + "lon": 55.30207, + "name": "Dayrah" + }, + "point_b": { + "lat": 39.75895, + "lon": -84.19161, + "name": "Dayton" + }, + "ground_truth": { + "initial_bearing_deg": 328.9, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Dayrah at (25.27143°, 55.30207°)", + " To: Dayton at (39.75895°, -84.19161°)", + "Step 2: Calculate longitude difference", + " Δlon = -84.19161 - 55.30207 = -139.4937°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 328.90°", + "Step 5: Determine cardinal direction", + " 328.9° → NW", + "FINAL ANSWER: 328.90° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 1.23889, + "lon": 35.11194, + "name": "Kapenguria" + }, + "point_b": { + "lat": 41.74115, + "lon": -87.61255, + "name": "Chatham" + }, + "ground_truth": { + "initial_bearing_deg": 317.05, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Kapenguria at (1.23889°, 35.11194°)", + " To: Chatham at (41.74115°, -87.61255°)", + "Step 2: Calculate longitude difference", + " Δlon = -87.61255 - 35.11194 = -122.7245°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 317.05°", + "Step 5: Determine cardinal direction", + " 317.1° → NW", + "FINAL ANSWER: 317.05° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -3.20333, + "lon": -52.20639, + "name": "Altamira" + }, + "point_b": { + "lat": 51.09242, + "lon": 4.3717, + "name": "Boom" + }, + "ground_truth": { + "initial_bearing_deg": 33.36, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Altamira at (-3.20333°, -52.20639°)", + " To: Boom at (51.09242°, 4.3717°)", + "Step 2: Calculate longitude difference", + " Δlon = 4.3717 - -52.20639 = 56.5781°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 33.36°", + "Step 5: Determine cardinal direction", + " 33.4° → NE", + "FINAL ANSWER: 33.36° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -11.83268, + "lon": 16.23613, + "name": "Mungo" + }, + "point_b": { + "lat": -11.26833, + "lon": -37.43833, + "name": "Estância" + }, + "ground_truth": { + "initial_bearing_deg": 264.78, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Mungo at (-11.83268°, 16.23613°)", + " To: Estância at (-11.26833°, -37.43833°)", + "Step 2: Calculate longitude difference", + " Δlon = -37.43833 - 16.23613 = -53.6745°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 264.78°", + "Step 5: Determine cardinal direction", + " 264.8° → W", + "FINAL ANSWER: 264.78° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 43.17124, + "lon": -2.6338, + "name": "Durango" + }, + "point_b": { + "lat": 20.38983, + "lon": 78.09027, + "name": "Lohāra" + }, + "ground_truth": { + "initial_bearing_deg": 80.75, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Durango at (43.17124°, -2.6338°)", + " To: Lohāra at (20.38983°, 78.09027°)", + "Step 2: Calculate longitude difference", + " Δlon = 78.09027 - -2.6338 = 80.7241°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 80.75°", + "Step 5: Determine cardinal direction", + " 80.8° → E", + "FINAL ANSWER: 80.75° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 40.15669, + "lon": 43.13424, + "name": "Kağızman" + }, + "point_b": { + "lat": 12.99809, + "lon": 15.73195, + "name": "Massakory" + }, + "ground_truth": { + "initial_bearing_deg": 229.28, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Kağızman at (40.15669°, 43.13424°)", + " To: Massakory at (12.99809°, 15.73195°)", + "Step 2: Calculate longitude difference", + " Δlon = 15.73195 - 43.13424 = -27.4023°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 229.28°", + "Step 5: Determine cardinal direction", + " 229.3° → SW", + "FINAL ANSWER: 229.28° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -27.31472, + "lon": -48.55917, + "name": "Governador Celso Ramos" + }, + "point_b": { + "lat": -38.82225, + "lon": -68.06293, + "name": "Cinco Saltos" + }, + "ground_truth": { + "initial_bearing_deg": 229.77, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Governador Celso Ramos at (-27.31472°, -48.55917°)", + " To: Cinco Saltos at (-38.82225°, -68.06293°)", + "Step 2: Calculate longitude difference", + " Δlon = -68.06293 - -48.55917 = -19.5038°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 229.77°", + "Step 5: Determine cardinal direction", + " 229.8° → SW", + "FINAL ANSWER: 229.77° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 13.737, + "lon": 100.512, + "name": "Samphanthawong" + }, + "point_b": { + "lat": 19.26028, + "lon": -99.59083, + "name": "San Salvador Tizatlalli" + }, + "ground_truth": { + "initial_bearing_deg": 31.43, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Samphanthawong at (13.737°, 100.512°)", + " To: San Salvador Tizatlalli at (19.26028°, -99.59083°)", + "Step 2: Calculate longitude difference", + " Δlon = -99.59083 - 100.512 = -200.1028°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 31.43°", + "Step 5: Determine cardinal direction", + " 31.4° → NE", + "FINAL ANSWER: 31.43° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 26.96667, + "lon": 1.08333, + "name": "Aoulef" + }, + "point_b": { + "lat": 14.0775, + "lon": -3.51594, + "name": "Bankass" + }, + "ground_truth": { + "initial_bearing_deg": 199.34, + "cardinal_direction": "S", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Aoulef at (26.96667°, 1.08333°)", + " To: Bankass at (14.0775°, -3.51594°)", + "Step 2: Calculate longitude difference", + " Δlon = -3.51594 - 1.08333 = -4.5993°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 199.34°", + "Step 5: Determine cardinal direction", + " 199.3° → S", + "FINAL ANSWER: 199.34° (S)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 5.62611, + "lon": 10.25421, + "name": "Mbouda" + }, + "point_b": { + "lat": 38.6703, + "lon": 26.75656, + "name": "Foça" + }, + "ground_truth": { + "initial_bearing_deg": 22.02, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Mbouda at (5.62611°, 10.25421°)", + " To: Foça at (38.6703°, 26.75656°)", + "Step 2: Calculate longitude difference", + " Δlon = 26.75656 - 10.25421 = 16.5023°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 22.02°", + "Step 5: Determine cardinal direction", + " 22.0° → N", + "FINAL ANSWER: 22.02° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -26.49155, + "lon": 29.22878, + "name": "Trichardt" + }, + "point_b": { + "lat": 20.62268, + "lon": -103.06813, + "name": "Zapotlanejo" + }, + "ground_truth": { + "initial_bearing_deg": 272.83, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Trichardt at (-26.49155°, 29.22878°)", + " To: Zapotlanejo at (20.62268°, -103.06813°)", + "Step 2: Calculate longitude difference", + " Δlon = -103.06813 - 29.22878 = -132.2969°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 272.83°", + "Step 5: Determine cardinal direction", + " 272.8° → W", + "FINAL ANSWER: 272.83° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 41.2, + "lon": -8.63333, + "name": "São Tiago de Custoias" + }, + "point_b": { + "lat": 45.46005, + "lon": -73.57058, + "name": "Verdun" + }, + "ground_truth": { + "initial_bearing_deg": 298.19, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: São Tiago de Custoias at (41.2°, -8.63333°)", + " To: Verdun at (45.46005°, -73.57058°)", + "Step 2: Calculate longitude difference", + " Δlon = -73.57058 - -8.63333 = -64.9373°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 298.19°", + "Step 5: Determine cardinal direction", + " 298.2° → NW", + "FINAL ANSWER: 298.19° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -21.15345, + "lon": 149.16554, + "name": "Mackay" + }, + "point_b": { + "lat": -24.95911, + "lon": 31.17025, + "name": "Hlanganani" + }, + "ground_truth": { + "initial_bearing_deg": 235.65, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Mackay at (-21.15345°, 149.16554°)", + " To: Hlanganani at (-24.95911°, 31.17025°)", + "Step 2: Calculate longitude difference", + " Δlon = 31.17025 - 149.16554 = -117.9953°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 235.65°", + "Step 5: Determine cardinal direction", + " 235.7° → SW", + "FINAL ANSWER: 235.65° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -27.03424, + "lon": -65.30196, + "name": "Bella Vista" + }, + "point_b": { + "lat": 29.14816, + "lon": 31.12733, + "name": "Būsh" + }, + "ground_truth": { + "initial_bearing_deg": 65.84, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Bella Vista at (-27.03424°, -65.30196°)", + " To: Būsh at (29.14816°, 31.12733°)", + "Step 2: Calculate longitude difference", + " Δlon = 31.12733 - -65.30196 = 96.4293°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 65.84°", + "Step 5: Determine cardinal direction", + " 65.8° → NE", + "FINAL ANSWER: 65.84° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 52.92343, + "lon": 9.23491, + "name": "Verden" + }, + "point_b": { + "lat": -33.89743, + "lon": 150.93446, + "name": "Cabramatta" + }, + "ground_truth": { + "initial_bearing_deg": 70.37, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Verden at (52.92343°, 9.23491°)", + " To: Cabramatta at (-33.89743°, 150.93446°)", + "Step 2: Calculate longitude difference", + " Δlon = 150.93446 - 9.23491 = 141.6995°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 70.37°", + "Step 5: Determine cardinal direction", + " 70.4° → E", + "FINAL ANSWER: 70.37° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 20.27465, + "lon": -76.95132, + "name": "Yara" + }, + "point_b": { + "lat": 47.79494, + "lon": 124.45773, + "name": "Fuyu" + }, + "ground_truth": { + "initial_bearing_deg": 344.94, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Yara at (20.27465°, -76.95132°)", + " To: Fuyu at (47.79494°, 124.45773°)", + "Step 2: Calculate longitude difference", + " Δlon = 124.45773 - -76.95132 = 201.4090°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 344.94°", + "Step 5: Determine cardinal direction", + " 344.9° → N", + "FINAL ANSWER: 344.94° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -17.29972, + "lon": -48.27944, + "name": "Pires do Rio" + }, + "point_b": { + "lat": 1.3375, + "lon": 103.90917, + "name": "Kaki Bukit Estate" + }, + "ground_truth": { + "initial_bearing_deg": 117.29, + "cardinal_direction": "SE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Pires do Rio at (-17.29972°, -48.27944°)", + " To: Kaki Bukit Estate at (1.3375°, 103.90917°)", + "Step 2: Calculate longitude difference", + " Δlon = 103.90917 - -48.27944 = 152.1886°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 117.29°", + "Step 5: Determine cardinal direction", + " 117.3° → SE", + "FINAL ANSWER: 117.29° (SE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -32.27682, + "lon": 115.72978, + "name": "Rockingham" + }, + "point_b": { + "lat": 44.36548, + "lon": 20.95885, + "name": "Smederevska Palanka" + }, + "ground_truth": { + "initial_bearing_deg": 308.14, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Rockingham at (-32.27682°, 115.72978°)", + " To: Smederevska Palanka at (44.36548°, 20.95885°)", + "Step 2: Calculate longitude difference", + " Δlon = 20.95885 - 115.72978 = -94.7709°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 308.14°", + "Step 5: Determine cardinal direction", + " 308.1° → NW", + "FINAL ANSWER: 308.14° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 42.34593, + "lon": -71.55229, + "name": "Marlborough" + }, + "point_b": { + "lat": -3.50306, + "lon": -80.27306, + "name": "Zarumilla" + }, + "ground_truth": { + "initial_bearing_deg": 192.04, + "cardinal_direction": "S", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Marlborough at (42.34593°, -71.55229°)", + " To: Zarumilla at (-3.50306°, -80.27306°)", + "Step 2: Calculate longitude difference", + " Δlon = -80.27306 - -71.55229 = -8.7208°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 192.04°", + "Step 5: Determine cardinal direction", + " 192.0° → S", + "FINAL ANSWER: 192.04° (S)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -23.65094, + "lon": -70.39752, + "name": "Antofagasta" + }, + "point_b": { + "lat": 12.95479, + "lon": 36.15549, + "name": "Metemma" + }, + "ground_truth": { + "initial_bearing_deg": 84.26, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Antofagasta at (-23.65094°, -70.39752°)", + " To: Metemma at (12.95479°, 36.15549°)", + "Step 2: Calculate longitude difference", + " Δlon = 36.15549 - -70.39752 = 106.5530°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 84.26°", + "Step 5: Determine cardinal direction", + " 84.3° → E", + "FINAL ANSWER: 84.26° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 36.50861, + "lon": 32.08278, + "name": "Kestel" + }, + "point_b": { + "lat": 34.09205, + "lon": 134.28452, + "name": "Awa" + }, + "ground_truth": { + "initial_bearing_deg": 55.58, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Kestel at (36.50861°, 32.08278°)", + " To: Awa at (34.09205°, 134.28452°)", + "Step 2: Calculate longitude difference", + " Δlon = 134.28452 - 32.08278 = 102.2017°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 55.58°", + "Step 5: Determine cardinal direction", + " 55.6° → NE", + "FINAL ANSWER: 55.58° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 2.2618, + "lon": 102.2317, + "name": "Kawasan Perindustrian Cheng" + }, + "point_b": { + "lat": 31.31146, + "lon": 31.14766, + "name": "Al Ḩāmūl" + }, + "ground_truth": { + "initial_bearing_deg": 302.17, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Kawasan Perindustrian Cheng at (2.2618°, 102.2317°)", + " To: Al Ḩāmūl at (31.31146°, 31.14766°)", + "Step 2: Calculate longitude difference", + " Δlon = 31.14766 - 102.2317 = -71.0840°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 302.17°", + "Step 5: Determine cardinal direction", + " 302.2° → NW", + "FINAL ANSWER: 302.17° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 40.42122, + "lon": -3.61759, + "name": "Arcos" + }, + "point_b": { + "lat": 50.93331, + "lon": 6.95954, + "name": "Altstadt Sud" + }, + "ground_truth": { + "initial_bearing_deg": 31.42, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Arcos at (40.42122°, -3.61759°)", + " To: Altstadt Sud at (50.93331°, 6.95954°)", + "Step 2: Calculate longitude difference", + " Δlon = 6.95954 - -3.61759 = 10.5771°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 31.42°", + "Step 5: Determine cardinal direction", + " 31.4° → NE", + "FINAL ANSWER: 31.42° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 27.61987, + "lon": 80.20343, + "name": "Pihānī" + }, + "point_b": { + "lat": 40.41189, + "lon": -3.65682, + "name": "Media Legua" + }, + "ground_truth": { + "initial_bearing_deg": 305.33, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Pihānī at (27.61987°, 80.20343°)", + " To: Media Legua at (40.41189°, -3.65682°)", + "Step 2: Calculate longitude difference", + " Δlon = -3.65682 - 80.20343 = -83.8602°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 305.33°", + "Step 5: Determine cardinal direction", + " 305.3° → NW", + "FINAL ANSWER: 305.33° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 48.53695, + "lon": 9.2833, + "name": "Metzingen" + }, + "point_b": { + "lat": 10.47027, + "lon": -66.61934, + "name": "Guarenas" + }, + "ground_truth": { + "initial_bearing_deg": 266.45, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Metzingen at (48.53695°, 9.2833°)", + " To: Guarenas at (10.47027°, -66.61934°)", + "Step 2: Calculate longitude difference", + " Δlon = -66.61934 - 9.2833 = -75.9026°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 266.45°", + "Step 5: Determine cardinal direction", + " 266.4° → W", + "FINAL ANSWER: 266.45° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 43.80306, + "lon": 143.89083, + "name": "Kitami" + }, + "point_b": { + "lat": -19.05294, + "lon": -169.91957, + "name": "Alofi" + }, + "ground_truth": { + "initial_bearing_deg": 135.27, + "cardinal_direction": "SE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Kitami at (43.80306°, 143.89083°)", + " To: Alofi at (-19.05294°, -169.91957°)", + "Step 2: Calculate longitude difference", + " Δlon = -169.91957 - 143.89083 = -313.8104°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 135.27°", + "Step 5: Determine cardinal direction", + " 135.3° → SE", + "FINAL ANSWER: 135.27° (SE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -17.36667, + "lon": 30.2, + "name": "Chinhoyi" + }, + "point_b": { + "lat": 48.92426, + "lon": 2.2128, + "name": "Bezons" + }, + "ground_truth": { + "initial_bearing_deg": 340.94, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Chinhoyi at (-17.36667°, 30.2°)", + " To: Bezons at (48.92426°, 2.2128°)", + "Step 2: Calculate longitude difference", + " Δlon = 2.2128 - 30.2 = -27.9872°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 340.94°", + "Step 5: Determine cardinal direction", + " 340.9° → N", + "FINAL ANSWER: 340.94° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 38.83861, + "lon": 105.66861, + "name": "Bayan Hot" + }, + "point_b": { + "lat": 38.90524, + "lon": -77.04362, + "name": "Golden Triangle" + }, + "ground_truth": { + "initial_bearing_deg": 2.16, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Bayan Hot at (38.83861°, 105.66861°)", + " To: Golden Triangle at (38.90524°, -77.04362°)", + "Step 2: Calculate longitude difference", + " Δlon = -77.04362 - 105.66861 = -182.7122°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 2.16°", + "Step 5: Determine cardinal direction", + " 2.2° → N", + "FINAL ANSWER: 2.16° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -10.68333, + "lon": 39.83333, + "name": "Nanyamba" + }, + "point_b": { + "lat": 1.94468, + "lon": 30.03861, + "name": "Mangbwalu" + }, + "ground_truth": { + "initial_bearing_deg": 321.78, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Nanyamba at (-10.68333°, 39.83333°)", + " To: Mangbwalu at (1.94468°, 30.03861°)", + "Step 2: Calculate longitude difference", + " Δlon = 30.03861 - 39.83333 = -9.7947°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 321.78°", + "Step 5: Determine cardinal direction", + " 321.8° → NW", + "FINAL ANSWER: 321.78° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 51.90006, + "lon": -2.07972, + "name": "Cheltenham" + }, + "point_b": { + "lat": 54.67501, + "lon": 20.13473, + "name": "Svetlyy" + }, + "ground_truth": { + "initial_bearing_deg": 69.4, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Cheltenham at (51.90006°, -2.07972°)", + " To: Svetlyy at (54.67501°, 20.13473°)", + "Step 2: Calculate longitude difference", + " Δlon = 20.13473 - -2.07972 = 22.2144°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 69.40°", + "Step 5: Determine cardinal direction", + " 69.4° → E", + "FINAL ANSWER: 69.40° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 44.103, + "lon": 9.82375, + "name": "La Spezia" + }, + "point_b": { + "lat": 1.61549, + "lon": -75.60412, + "name": "Florencia" + }, + "ground_truth": { + "initial_bearing_deg": 267.98, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: La Spezia at (44.103°, 9.82375°)", + " To: Florencia at (1.61549°, -75.60412°)", + "Step 2: Calculate longitude difference", + " Δlon = -75.60412 - 9.82375 = -85.4279°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 267.98°", + "Step 5: Determine cardinal direction", + " 268.0° → W", + "FINAL ANSWER: 267.98° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 8.05861, + "lon": -6.18972, + "name": "Mankono" + }, + "point_b": { + "lat": 41.97263, + "lon": -71.32474, + "name": "North Attleborough Center" + }, + "ground_truth": { + "initial_bearing_deg": 312.51, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Mankono at (8.05861°, -6.18972°)", + " To: North Attleborough Center at (41.97263°, -71.32474°)", + "Step 2: Calculate longitude difference", + " Δlon = -71.32474 - -6.18972 = -65.1350°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 312.51°", + "Step 5: Determine cardinal direction", + " 312.5° → NW", + "FINAL ANSWER: 312.51° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 22.06566, + "lon": 81.68543, + "name": "Mungeli" + }, + "point_b": { + "lat": 44.53889, + "lon": 10.81166, + "name": "Fiorano" + }, + "ground_truth": { + "initial_bearing_deg": 309.86, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Mungeli at (22.06566°, 81.68543°)", + " To: Fiorano at (44.53889°, 10.81166°)", + "Step 2: Calculate longitude difference", + " Δlon = 10.81166 - 81.68543 = -70.8738°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 309.86°", + "Step 5: Determine cardinal direction", + " 309.9° → NW", + "FINAL ANSWER: 309.86° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 25.00827, + "lon": 55.15682, + "name": "Dubai Investments Park" + }, + "point_b": { + "lat": 55.75, + "lon": -4.03333, + "name": "Meikle Earnock" + }, + "ground_truth": { + "initial_bearing_deg": 322.38, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Dubai Investments Park at (25.00827°, 55.15682°)", + " To: Meikle Earnock at (55.75°, -4.03333°)", + "Step 2: Calculate longitude difference", + " Δlon = -4.03333 - 55.15682 = -59.1902°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 322.38°", + "Step 5: Determine cardinal direction", + " 322.4° → NW", + "FINAL ANSWER: 322.38° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 28.3769, + "lon": 129.49379, + "name": "Amami" + }, + "point_b": { + "lat": 11.21266, + "lon": 79.36369, + "name": "Jayamkondacholapuram" + }, + "ground_truth": { + "initial_bearing_deg": 260.37, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Amami at (28.3769°, 129.49379°)", + " To: Jayamkondacholapuram at (11.21266°, 79.36369°)", + "Step 2: Calculate longitude difference", + " Δlon = 79.36369 - 129.49379 = -50.1301°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 260.37°", + "Step 5: Determine cardinal direction", + " 260.4° → W", + "FINAL ANSWER: 260.37° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 32.91851, + "lon": -80.02203, + "name": "Hanahan" + }, + "point_b": { + "lat": -4.32861, + "lon": -38.88472, + "name": "Baturité" + }, + "ground_truth": { + "initial_bearing_deg": 125.71, + "cardinal_direction": "SE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Hanahan at (32.91851°, -80.02203°)", + " To: Baturité at (-4.32861°, -38.88472°)", + "Step 2: Calculate longitude difference", + " Δlon = -38.88472 - -80.02203 = 41.1373°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 125.71°", + "Step 5: Determine cardinal direction", + " 125.7° → SE", + "FINAL ANSWER: 125.71° (SE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 29.2699, + "lon": 51.2188, + "name": "Borāzjān" + }, + "point_b": { + "lat": 47.29722, + "lon": -1.4921, + "name": "Carquefou" + }, + "ground_truth": { + "initial_bearing_deg": 309.21, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Borāzjān at (29.2699°, 51.2188°)", + " To: Carquefou at (47.29722°, -1.4921°)", + "Step 2: Calculate longitude difference", + " Δlon = -1.4921 - 51.2188 = -52.7109°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 309.21°", + "Step 5: Determine cardinal direction", + " 309.2° → NW", + "FINAL ANSWER: 309.21° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 22.24126, + "lon": -80.3911, + "name": "Palmira" + }, + "point_b": { + "lat": 35.73289, + "lon": 139.82085, + "name": "Sumida" + }, + "ground_truth": { + "initial_bearing_deg": 325.94, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Palmira at (22.24126°, -80.3911°)", + " To: Sumida at (35.73289°, 139.82085°)", + "Step 2: Calculate longitude difference", + " Δlon = 139.82085 - -80.3911 = 220.2120°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 325.94°", + "Step 5: Determine cardinal direction", + " 325.9° → NW", + "FINAL ANSWER: 325.94° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 46.87719, + "lon": -96.7898, + "name": "Fargo" + }, + "point_b": { + "lat": -31.76737, + "lon": 115.96936, + "name": "Ellenbrook" + }, + "ground_truth": { + "initial_bearing_deg": 289.4, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Fargo at (46.87719°, -96.7898°)", + " To: Ellenbrook at (-31.76737°, 115.96936°)", + "Step 2: Calculate longitude difference", + " Δlon = 115.96936 - -96.7898 = 212.7592°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 289.40°", + "Step 5: Determine cardinal direction", + " 289.4° → W", + "FINAL ANSWER: 289.40° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 11.08155, + "lon": 39.74339, + "name": "Kombolcha" + }, + "point_b": { + "lat": 41.66394, + "lon": -83.55521, + "name": "Toledo" + }, + "ground_truth": { + "initial_bearing_deg": 319.5, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Kombolcha at (11.08155°, 39.74339°)", + " To: Toledo at (41.66394°, -83.55521°)", + "Step 2: Calculate longitude difference", + " Δlon = -83.55521 - 39.74339 = -123.2986°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 319.50°", + "Step 5: Determine cardinal direction", + " 319.5° → NW", + "FINAL ANSWER: 319.50° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 8.01714, + "lon": 4.90421, + "name": "Ila Orangun" + }, + "point_b": { + "lat": 39.95373, + "lon": -74.19792, + "name": "Toms River" + }, + "ground_truth": { + "initial_bearing_deg": 309.28, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Ila Orangun at (8.01714°, 4.90421°)", + " To: Toms River at (39.95373°, -74.19792°)", + "Step 2: Calculate longitude difference", + " Δlon = -74.19792 - 4.90421 = -79.1021°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 309.28°", + "Step 5: Determine cardinal direction", + " 309.3° → NW", + "FINAL ANSWER: 309.28° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 30.96187, + "lon": 108.24327, + "name": "Nanmen" + }, + "point_b": { + "lat": 21.46002, + "lon": 95.3884, + "name": "Myingyan" + }, + "ground_truth": { + "initial_bearing_deg": 233.52, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Nanmen at (30.96187°, 108.24327°)", + " To: Myingyan at (21.46002°, 95.3884°)", + "Step 2: Calculate longitude difference", + " Δlon = 95.3884 - 108.24327 = -12.8549°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 233.52°", + "Step 5: Determine cardinal direction", + " 233.5° → SW", + "FINAL ANSWER: 233.52° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 10.31028, + "lon": 123.94944, + "name": "Lapu-Lapu City" + }, + "point_b": { + "lat": -0.41611, + "lon": 31.40806, + "name": "Lwengo" + }, + "ground_truth": { + "initial_bearing_deg": 270.05, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Lapu-Lapu City at (10.31028°, 123.94944°)", + " To: Lwengo at (-0.41611°, 31.40806°)", + "Step 2: Calculate longitude difference", + " Δlon = 31.40806 - 123.94944 = -92.5414°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 270.05°", + "Step 5: Determine cardinal direction", + " 270.1° → W", + "FINAL ANSWER: 270.05° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 18.91614, + "lon": -103.87713, + "name": "Tecomán" + }, + "point_b": { + "lat": -36.99282, + "lon": 174.87986, + "name": "Manukau City" + }, + "ground_truth": { + "initial_bearing_deg": 232.37, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Tecomán at (18.91614°, -103.87713°)", + " To: Manukau City at (-36.99282°, 174.87986°)", + "Step 2: Calculate longitude difference", + " Δlon = 174.87986 - -103.87713 = 278.7570°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 232.37°", + "Step 5: Determine cardinal direction", + " 232.4° → SW", + "FINAL ANSWER: 232.37° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -17.345, + "lon": -44.94194, + "name": "Pirapora" + }, + "point_b": { + "lat": 4.29005, + "lon": -74.81612, + "name": "Flandes" + }, + "ground_truth": { + "initial_bearing_deg": 303.53, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Pirapora at (-17.345°, -44.94194°)", + " To: Flandes at (4.29005°, -74.81612°)", + "Step 2: Calculate longitude difference", + " Δlon = -74.81612 - -44.94194 = -29.8742°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 303.53°", + "Step 5: Determine cardinal direction", + " 303.5° → NW", + "FINAL ANSWER: 303.53° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 43.50092, + "lon": -70.44283, + "name": "Saco" + }, + "point_b": { + "lat": 11.22191, + "lon": -4.64423, + "name": "Karankasso" + }, + "ground_truth": { + "initial_bearing_deg": 98.62, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Saco at (43.50092°, -70.44283°)", + " To: Karankasso at (11.22191°, -4.64423°)", + "Step 2: Calculate longitude difference", + " Δlon = -4.64423 - -70.44283 = 65.7986°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 98.62°", + "Step 5: Determine cardinal direction", + " 98.6° → E", + "FINAL ANSWER: 98.62° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -33.30422, + "lon": 26.53276, + "name": "Grahamstown" + }, + "point_b": { + "lat": 7.6685, + "lon": 5.12627, + "name": "Igede-Ekiti" + }, + "ground_truth": { + "initial_bearing_deg": 329.67, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Grahamstown at (-33.30422°, 26.53276°)", + " To: Igede-Ekiti at (7.6685°, 5.12627°)", + "Step 2: Calculate longitude difference", + " Δlon = 5.12627 - 26.53276 = -21.4065°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 329.67°", + "Step 5: Determine cardinal direction", + " 329.7° → NW", + "FINAL ANSWER: 329.67° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 47.05893, + "lon": -0.87974, + "name": "Cholet" + }, + "point_b": { + "lat": -19.93167, + "lon": -44.05361, + "name": "Contagem" + }, + "ground_truth": { + "initial_bearing_deg": 221.22, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Cholet at (47.05893°, -0.87974°)", + " To: Contagem at (-19.93167°, -44.05361°)", + "Step 2: Calculate longitude difference", + " Δlon = -44.05361 - -0.87974 = -43.1739°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 221.22°", + "Step 5: Determine cardinal direction", + " 221.2° → SW", + "FINAL ANSWER: 221.22° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 35.65087, + "lon": 139.79163, + "name": "Toyosu" + }, + "point_b": { + "lat": 38.67727, + "lon": -87.52863, + "name": "Vincennes" + }, + "ground_truth": { + "initial_bearing_deg": 35.11, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Toyosu at (35.65087°, 139.79163°)", + " To: Vincennes at (38.67727°, -87.52863°)", + "Step 2: Calculate longitude difference", + " Δlon = -87.52863 - 139.79163 = -227.3203°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 35.11°", + "Step 5: Determine cardinal direction", + " 35.1° → NE", + "FINAL ANSWER: 35.11° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -13.08333, + "lon": 48.85, + "name": "Antsohimbondrona" + }, + "point_b": { + "lat": -30.60106, + "lon": -71.19901, + "name": "Ovalle" + }, + "ground_truth": { + "initial_bearing_deg": 231.46, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Antsohimbondrona at (-13.08333°, 48.85°)", + " To: Ovalle at (-30.60106°, -71.19901°)", + "Step 2: Calculate longitude difference", + " Δlon = -71.19901 - 48.85 = -120.0490°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 231.46°", + "Step 5: Determine cardinal direction", + " 231.5° → SW", + "FINAL ANSWER: 231.46° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 35.818, + "lon": 139.368, + "name": "Iruma" + }, + "point_b": { + "lat": 9.45149, + "lon": 18.94493, + "name": "Kyabé" + }, + "ground_truth": { + "initial_bearing_deg": 296.57, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Iruma at (35.818°, 139.368°)", + " To: Kyabé at (9.45149°, 18.94493°)", + "Step 2: Calculate longitude difference", + " Δlon = 18.94493 - 139.368 = -120.4231°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 296.57°", + "Step 5: Determine cardinal direction", + " 296.6° → NW", + "FINAL ANSWER: 296.57° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 42.37649, + "lon": -71.23561, + "name": "Waltham" + }, + "point_b": { + "lat": -37.73333, + "lon": 145.15, + "name": "Eltham" + }, + "ground_truth": { + "initial_bearing_deg": 267.2, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Waltham at (42.37649°, -71.23561°)", + " To: Eltham at (-37.73333°, 145.15°)", + "Step 2: Calculate longitude difference", + " Δlon = 145.15 - -71.23561 = 216.3856°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 267.20°", + "Step 5: Determine cardinal direction", + " 267.2° → W", + "FINAL ANSWER: 267.20° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 53.85713, + "lon": -2.16851, + "name": "Colne" + }, + "point_b": { + "lat": 38.91667, + "lon": 141.13333, + "name": "Ichinoseki" + }, + "ground_truth": { + "initial_bearing_deg": 28.01, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Colne at (53.85713°, -2.16851°)", + " To: Ichinoseki at (38.91667°, 141.13333°)", + "Step 2: Calculate longitude difference", + " Δlon = 141.13333 - -2.16851 = 143.3018°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 28.01°", + "Step 5: Determine cardinal direction", + " 28.0° → NE", + "FINAL ANSWER: 28.01° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 31.09311, + "lon": 30.31418, + "name": "Abū Ḩummuş" + }, + "point_b": { + "lat": -29.57366, + "lon": 31.11552, + "name": "Tongaat" + }, + "ground_truth": { + "initial_bearing_deg": 179.2, + "cardinal_direction": "S", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Abū Ḩummuş at (31.09311°, 30.31418°)", + " To: Tongaat at (-29.57366°, 31.11552°)", + "Step 2: Calculate longitude difference", + " Δlon = 31.11552 - 30.31418 = 0.8013°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 179.20°", + "Step 5: Determine cardinal direction", + " 179.2° → S", + "FINAL ANSWER: 179.20° (S)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 12.77972, + "lon": 101.64831, + "name": "Klaeng" + }, + "point_b": { + "lat": -15.48211, + "lon": 28.35099, + "name": "Chisankane" + }, + "ground_truth": { + "initial_bearing_deg": 250.79, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Klaeng at (12.77972°, 101.64831°)", + " To: Chisankane at (-15.48211°, 28.35099°)", + "Step 2: Calculate longitude difference", + " Δlon = 28.35099 - 101.64831 = -73.2973°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 250.79°", + "Step 5: Determine cardinal direction", + " 250.8° → W", + "FINAL ANSWER: 250.79° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 53.20271, + "lon": 5.80973, + "name": "Leeuwarden" + }, + "point_b": { + "lat": -4.52483, + "lon": 35.3849, + "name": "Katesh" + }, + "ground_truth": { + "initial_bearing_deg": 146.43, + "cardinal_direction": "SE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Leeuwarden at (53.20271°, 5.80973°)", + " To: Katesh at (-4.52483°, 35.3849°)", + "Step 2: Calculate longitude difference", + " Δlon = 35.3849 - 5.80973 = 29.5752°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 146.43°", + "Step 5: Determine cardinal direction", + " 146.4° → SE", + "FINAL ANSWER: 146.43° (SE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -17.54234, + "lon": -65.83472, + "name": "Punata" + }, + "point_b": { + "lat": 40.45245, + "lon": -3.70763, + "name": "Bellas Vistas" + }, + "ground_truth": { + "initial_bearing_deg": 42.82, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Punata at (-17.54234°, -65.83472°)", + " To: Bellas Vistas at (40.45245°, -3.70763°)", + "Step 2: Calculate longitude difference", + " Δlon = -3.70763 - -65.83472 = 62.1271°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 42.82°", + "Step 5: Determine cardinal direction", + " 42.8° → NE", + "FINAL ANSWER: 42.82° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -33.9049, + "lon": 151.01996, + "name": "Yagoona" + }, + "point_b": { + "lat": 14.33236, + "lon": -16.40513, + "name": "Fatick" + }, + "ground_truth": { + "initial_bearing_deg": 213.23, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Yagoona at (-33.9049°, 151.01996°)", + " To: Fatick at (14.33236°, -16.40513°)", + "Step 2: Calculate longitude difference", + " Δlon = -16.40513 - 151.01996 = -167.4251°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 213.23°", + "Step 5: Determine cardinal direction", + " 213.2° → SW", + "FINAL ANSWER: 213.23° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 48.6511, + "lon": 2.41406, + "name": "Ris-Orangis" + }, + "point_b": { + "lat": -25.96222, + "lon": 32.45889, + "name": "Matola" + }, + "ground_truth": { + "initial_bearing_deg": 152.74, + "cardinal_direction": "SE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Ris-Orangis at (48.6511°, 2.41406°)", + " To: Matola at (-25.96222°, 32.45889°)", + "Step 2: Calculate longitude difference", + " Δlon = 32.45889 - 2.41406 = 30.0448°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 152.74°", + "Step 5: Determine cardinal direction", + " 152.7° → SE", + "FINAL ANSWER: 152.74° (SE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 24.42244, + "lon": 88.25238, + "name": "Lālgola" + }, + "point_b": { + "lat": -2.5964, + "lon": 140.6324, + "name": "Abepura" + }, + "ground_truth": { + "initial_bearing_deg": 110.34, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Lālgola at (24.42244°, 88.25238°)", + " To: Abepura at (-2.5964°, 140.6324°)", + "Step 2: Calculate longitude difference", + " Δlon = 140.6324 - 88.25238 = 52.3800°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 110.34°", + "Step 5: Determine cardinal direction", + " 110.3° → E", + "FINAL ANSWER: 110.34° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -0.24849, + "lon": 35.73194, + "name": "Molo" + }, + "point_b": { + "lat": -22.67842, + "lon": 14.52663, + "name": "Swakopmund" + }, + "ground_truth": { + "initial_bearing_deg": 221.16, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Molo at (-0.24849°, 35.73194°)", + " To: Swakopmund at (-22.67842°, 14.52663°)", + "Step 2: Calculate longitude difference", + " Δlon = 14.52663 - 35.73194 = -21.2053°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 221.16°", + "Step 5: Determine cardinal direction", + " 221.2° → SW", + "FINAL ANSWER: 221.16° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -2.85, + "lon": 33.08333, + "name": "Misungwi" + }, + "point_b": { + "lat": 45.82972, + "lon": 20.46528, + "name": "Kikinda" + }, + "ground_truth": { + "initial_bearing_deg": 348.53, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Misungwi at (-2.85°, 33.08333°)", + " To: Kikinda at (45.82972°, 20.46528°)", + "Step 2: Calculate longitude difference", + " Δlon = 20.46528 - 33.08333 = -12.6180°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 348.53°", + "Step 5: Determine cardinal direction", + " 348.5° → N", + "FINAL ANSWER: 348.53° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 23.6303, + "lon": 85.52156, + "name": "Rāmgarh" + }, + "point_b": { + "lat": 40.65642, + "lon": 17.70814, + "name": "San Vito dei Normanni" + }, + "ground_truth": { + "initial_bearing_deg": 304.46, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Rāmgarh at (23.6303°, 85.52156°)", + " To: San Vito dei Normanni at (40.65642°, 17.70814°)", + "Step 2: Calculate longitude difference", + " Δlon = 17.70814 - 85.52156 = -67.8134°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 304.46°", + "Step 5: Determine cardinal direction", + " 304.5° → NW", + "FINAL ANSWER: 304.46° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -5.22152, + "lon": 145.78695, + "name": "Madang" + }, + "point_b": { + "lat": 33.19973, + "lon": 120.4578, + "name": "Dazhong" + }, + "ground_truth": { + "initial_bearing_deg": 329.76, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Madang at (-5.22152°, 145.78695°)", + " To: Dazhong at (33.19973°, 120.4578°)", + "Step 2: Calculate longitude difference", + " Δlon = 120.4578 - 145.78695 = -25.3291°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 329.76°", + "Step 5: Determine cardinal direction", + " 329.8° → NW", + "FINAL ANSWER: 329.76° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 36.64997, + "lon": 3.3308, + "name": "Khemis el Khechna" + }, + "point_b": { + "lat": 0.55667, + "lon": 31.80222, + "name": "Kasanda" + }, + "ground_truth": { + "initial_bearing_deg": 137.32, + "cardinal_direction": "SE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Khemis el Khechna at (36.64997°, 3.3308°)", + " To: Kasanda at (0.55667°, 31.80222°)", + "Step 2: Calculate longitude difference", + " Δlon = 31.80222 - 3.3308 = 28.4714°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 137.32°", + "Step 5: Determine cardinal direction", + " 137.3° → SE", + "FINAL ANSWER: 137.32° (SE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -26.14095, + "lon": 28.15247, + "name": "Edenvale" + }, + "point_b": { + "lat": 36.01393, + "lon": -5.60695, + "name": "Tarifa" + }, + "ground_truth": { + "initial_bearing_deg": 331.39, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Edenvale at (-26.14095°, 28.15247°)", + " To: Tarifa at (36.01393°, -5.60695°)", + "Step 2: Calculate longitude difference", + " Δlon = -5.60695 - 28.15247 = -33.7594°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 331.39°", + "Step 5: Determine cardinal direction", + " 331.4° → NW", + "FINAL ANSWER: 331.39° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 28.3091, + "lon": 70.12652, + "name": "Saddiqabad" + }, + "point_b": { + "lat": 29.41369, + "lon": 112.16435, + "name": "Shenliu" + }, + "ground_truth": { + "initial_bearing_deg": 77.85, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Saddiqabad at (28.3091°, 70.12652°)", + " To: Shenliu at (29.41369°, 112.16435°)", + "Step 2: Calculate longitude difference", + " Δlon = 112.16435 - 70.12652 = 42.0378°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 77.85°", + "Step 5: Determine cardinal direction", + " 77.8° → E", + "FINAL ANSWER: 77.85° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 50.50301, + "lon": 13.63617, + "name": "Most" + }, + "point_b": { + "lat": 19.30023, + "lon": 73.05881, + "name": "Bhiwandi" + }, + "ground_truth": { + "initial_bearing_deg": 101.16, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Most at (50.50301°, 13.63617°)", + " To: Bhiwandi at (19.30023°, 73.05881°)", + "Step 2: Calculate longitude difference", + " Δlon = 73.05881 - 13.63617 = 59.4226°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 101.16°", + "Step 5: Determine cardinal direction", + " 101.2° → E", + "FINAL ANSWER: 101.16° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 20.4925, + "lon": -103.4175, + "name": "Lomas del Sur" + }, + "point_b": { + "lat": 42.96336, + "lon": -85.66809, + "name": "Grand Rapids" + }, + "ground_truth": { + "initial_bearing_deg": 29.49, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Lomas del Sur at (20.4925°, -103.4175°)", + " To: Grand Rapids at (42.96336°, -85.66809°)", + "Step 2: Calculate longitude difference", + " Δlon = -85.66809 - -103.4175 = 17.7494°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 29.49°", + "Step 5: Determine cardinal direction", + " 29.5° → NE", + "FINAL ANSWER: 29.49° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 40.80028, + "lon": 19.91667, + "name": "Kuçovë" + }, + "point_b": { + "lat": -8.94111, + "lon": -72.79167, + "name": "Marechal Thaumaturgo" + }, + "ground_truth": { + "initial_bearing_deg": 264.95, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Kuçovë at (40.80028°, 19.91667°)", + " To: Marechal Thaumaturgo at (-8.94111°, -72.79167°)", + "Step 2: Calculate longitude difference", + " Δlon = -72.79167 - 19.91667 = -92.7083°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 264.95°", + "Step 5: Determine cardinal direction", + " 264.9° → W", + "FINAL ANSWER: 264.95° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 41.49167, + "lon": 20.22194, + "name": "Bulqizë" + }, + "point_b": { + "lat": 20.22627, + "lon": -103.56981, + "name": "Zacoalco de Torres" + }, + "ground_truth": { + "initial_bearing_deg": 307.79, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Bulqizë at (41.49167°, 20.22194°)", + " To: Zacoalco de Torres at (20.22627°, -103.56981°)", + "Step 2: Calculate longitude difference", + " Δlon = -103.56981 - 20.22194 = -123.7918°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 307.79°", + "Step 5: Determine cardinal direction", + " 307.8° → NW", + "FINAL ANSWER: 307.79° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -25.5036, + "lon": -54.65067, + "name": "Ciudad del Este" + }, + "point_b": { + "lat": 11.89494, + "lon": 75.43959, + "name": "Chelora" + }, + "ground_truth": { + "initial_bearing_deg": 96.5, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Ciudad del Este at (-25.5036°, -54.65067°)", + " To: Chelora at (11.89494°, 75.43959°)", + "Step 2: Calculate longitude difference", + " Δlon = 75.43959 - -54.65067 = 130.0903°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 96.50°", + "Step 5: Determine cardinal direction", + " 96.5° → E", + "FINAL ANSWER: 96.50° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 35.07465, + "lon": -1.22431, + "name": "Bensekrane" + }, + "point_b": { + "lat": 47.42346, + "lon": -120.31035, + "name": "Wenatchee" + }, + "ground_truth": { + "initial_bearing_deg": 323.25, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Bensekrane at (35.07465°, -1.22431°)", + " To: Wenatchee at (47.42346°, -120.31035°)", + "Step 2: Calculate longitude difference", + " Δlon = -120.31035 - -1.22431 = -119.0860°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 323.25°", + "Step 5: Determine cardinal direction", + " 323.2° → NW", + "FINAL ANSWER: 323.25° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 49.48056, + "lon": 6.0875, + "name": "Dudelange" + }, + "point_b": { + "lat": 46.23175, + "lon": 27.66907, + "name": "Bârlad" + }, + "ground_truth": { + "initial_bearing_deg": 94.45, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Dudelange at (49.48056°, 6.0875°)", + " To: Bârlad at (46.23175°, 27.66907°)", + "Step 2: Calculate longitude difference", + " Δlon = 27.66907 - 6.0875 = 21.5816°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 94.45°", + "Step 5: Determine cardinal direction", + " 94.5° → E", + "FINAL ANSWER: 94.45° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 17.64944, + "lon": 95.45705, + "name": "Hinthada" + }, + "point_b": { + "lat": -22.94564, + "lon": 30.48497, + "name": "Thohoyandou" + }, + "ground_truth": { + "initial_bearing_deg": 239.6, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Hinthada at (17.64944°, 95.45705°)", + " To: Thohoyandou at (-22.94564°, 30.48497°)", + "Step 2: Calculate longitude difference", + " Δlon = 30.48497 - 95.45705 = -64.9721°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 239.60°", + "Step 5: Determine cardinal direction", + " 239.6° → SW", + "FINAL ANSWER: 239.60° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 33.72835, + "lon": -117.14642, + "name": "Menifee" + }, + "point_b": { + "lat": 15.40637, + "lon": 79.50702, + "name": "Kanigiri U" + }, + "ground_truth": { + "initial_bearing_deg": 339.37, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Menifee at (33.72835°, -117.14642°)", + " To: Kanigiri U at (15.40637°, 79.50702°)", + "Step 2: Calculate longitude difference", + " Δlon = 79.50702 - -117.14642 = 196.6534°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 339.37°", + "Step 5: Determine cardinal direction", + " 339.4° → N", + "FINAL ANSWER: 339.37° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 20.67738, + "lon": -103.34749, + "name": "Guadalajara" + }, + "point_b": { + "lat": -33.8406, + "lon": 151.00748, + "name": "Granville" + }, + "ground_truth": { + "initial_bearing_deg": 241.08, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Guadalajara at (20.67738°, -103.34749°)", + " To: Granville at (-33.8406°, 151.00748°)", + "Step 2: Calculate longitude difference", + " Δlon = 151.00748 - -103.34749 = 254.3550°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 241.08°", + "Step 5: Determine cardinal direction", + " 241.1° → SW", + "FINAL ANSWER: 241.08° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 40.31412, + "lon": -112.00688, + "name": "Eagle Mountain" + }, + "point_b": { + "lat": 5.31198, + "lon": -3.99363, + "name": "Marcory" + }, + "ground_truth": { + "initial_bearing_deg": 74.1, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Eagle Mountain at (40.31412°, -112.00688°)", + " To: Marcory at (5.31198°, -3.99363°)", + "Step 2: Calculate longitude difference", + " Δlon = -3.99363 - -112.00688 = 108.0132°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 74.10°", + "Step 5: Determine cardinal direction", + " 74.1° → E", + "FINAL ANSWER: 74.10° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 2.7389, + "lon": 102.2487, + "name": "Kuala Pilah" + }, + "point_b": { + "lat": 1.25881, + "lon": 35.09569, + "name": "Makutano" + }, + "ground_truth": { + "initial_bearing_deg": 270.21, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Kuala Pilah at (2.7389°, 102.2487°)", + " To: Makutano at (1.25881°, 35.09569°)", + "Step 2: Calculate longitude difference", + " Δlon = 35.09569 - 102.2487 = -67.1530°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 270.21°", + "Step 5: Determine cardinal direction", + " 270.2° → W", + "FINAL ANSWER: 270.21° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -8.39818, + "lon": -74.53774, + "name": "San Fernando" + }, + "point_b": { + "lat": 45.25167, + "lon": 19.83694, + "name": "Novi Sad" + }, + "ground_truth": { + "initial_bearing_deg": 45.3, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: San Fernando at (-8.39818°, -74.53774°)", + " To: Novi Sad at (45.25167°, 19.83694°)", + "Step 2: Calculate longitude difference", + " Δlon = 19.83694 - -74.53774 = 94.3747°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 45.30°", + "Step 5: Determine cardinal direction", + " 45.3° → NE", + "FINAL ANSWER: 45.30° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 7.50077, + "lon": 134.6238, + "name": "Ngerulmud" + }, + "point_b": { + "lat": -27.00805, + "lon": 27.3646, + "name": "Vredefort" + }, + "ground_truth": { + "initial_bearing_deg": 243.96, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Ngerulmud at (7.50077°, 134.6238°)", + " To: Vredefort at (-27.00805°, 27.3646°)", + "Step 2: Calculate longitude difference", + " Δlon = 27.3646 - 134.6238 = -107.2592°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 243.96°", + "Step 5: Determine cardinal direction", + " 244.0° → SW", + "FINAL ANSWER: 243.96° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 9.36238, + "lon": -73.60313, + "name": "Chiriguaná" + }, + "point_b": { + "lat": 4.95384, + "lon": -6.08531, + "name": "Sassandra" + }, + "ground_truth": { + "initial_bearing_deg": 88.55, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Chiriguaná at (9.36238°, -73.60313°)", + " To: Sassandra at (4.95384°, -6.08531°)", + "Step 2: Calculate longitude difference", + " Δlon = -6.08531 - -73.60313 = 67.5178°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 88.55°", + "Step 5: Determine cardinal direction", + " 88.5° → E", + "FINAL ANSWER: 88.55° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 38.76511, + "lon": -76.89831, + "name": "Clinton" + }, + "point_b": { + "lat": 36.52056, + "lon": 6.26111, + "name": "Sidi Mérouane" + }, + "ground_truth": { + "initial_bearing_deg": 63.14, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Clinton at (38.76511°, -76.89831°)", + " To: Sidi Mérouane at (36.52056°, 6.26111°)", + "Step 2: Calculate longitude difference", + " Δlon = 6.26111 - -76.89831 = 83.1594°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 63.14°", + "Step 5: Determine cardinal direction", + " 63.1° → NE", + "FINAL ANSWER: 63.14° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 14.87964, + "lon": -91.45699, + "name": "Salcajá" + }, + "point_b": { + "lat": 33.88474, + "lon": -118.41091, + "name": "Manhattan Beach" + }, + "ground_truth": { + "initial_bearing_deg": 312.83, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Salcajá at (14.87964°, -91.45699°)", + " To: Manhattan Beach at (33.88474°, -118.41091°)", + "Step 2: Calculate longitude difference", + " Δlon = -118.41091 - -91.45699 = -26.9539°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 312.83°", + "Step 5: Determine cardinal direction", + " 312.8° → NW", + "FINAL ANSWER: 312.83° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 18.54478, + "lon": -72.30036, + "name": "Delmas" + }, + "point_b": { + "lat": -21.03306, + "lon": -44.75806, + "name": "Bom Sucesso" + }, + "ground_truth": { + "initial_bearing_deg": 144.43, + "cardinal_direction": "SE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Delmas at (18.54478°, -72.30036°)", + " To: Bom Sucesso at (-21.03306°, -44.75806°)", + "Step 2: Calculate longitude difference", + " Δlon = -44.75806 - -72.30036 = 27.5423°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 144.43°", + "Step 5: Determine cardinal direction", + " 144.4° → SE", + "FINAL ANSWER: 144.43° (SE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 38.67351, + "lon": 29.4058, + "name": "Uşak" + }, + "point_b": { + "lat": -26.31401, + "lon": 26.82223, + "name": "Ventersdorp" + }, + "ground_truth": { + "initial_bearing_deg": 182.55, + "cardinal_direction": "S", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Uşak at (38.67351°, 29.4058°)", + " To: Ventersdorp at (-26.31401°, 26.82223°)", + "Step 2: Calculate longitude difference", + " Δlon = 26.82223 - 29.4058 = -2.5836°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 182.55°", + "Step 5: Determine cardinal direction", + " 182.6° → S", + "FINAL ANSWER: 182.55° (S)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -17.73111, + "lon": -49.09944, + "name": "Morrinhos" + }, + "point_b": { + "lat": -27.31472, + "lon": -48.55917, + "name": "Governador Celso Ramos" + }, + "ground_truth": { + "initial_bearing_deg": 177.12, + "cardinal_direction": "S", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Morrinhos at (-17.73111°, -49.09944°)", + " To: Governador Celso Ramos at (-27.31472°, -48.55917°)", + "Step 2: Calculate longitude difference", + " Δlon = -48.55917 - -49.09944 = 0.5403°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 177.12°", + "Step 5: Determine cardinal direction", + " 177.1° → S", + "FINAL ANSWER: 177.12° (S)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -7.31056, + "lon": -50.04833, + "name": "Rio Maria" + }, + "point_b": { + "lat": 14.79032, + "lon": -15.90803, + "name": "Mbaké" + }, + "ground_truth": { + "initial_bearing_deg": 56.8, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Rio Maria at (-7.31056°, -50.04833°)", + " To: Mbaké at (14.79032°, -15.90803°)", + "Step 2: Calculate longitude difference", + " Δlon = -15.90803 - -50.04833 = 34.1403°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 56.80°", + "Step 5: Determine cardinal direction", + " 56.8° → NE", + "FINAL ANSWER: 56.80° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -3.52278, + "lon": -40.34278, + "name": "Massapê" + }, + "point_b": { + "lat": 5.55221, + "lon": -0.33912, + "name": "Mandela" + }, + "ground_truth": { + "initial_bearing_deg": 77.37, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Massapê at (-3.52278°, -40.34278°)", + " To: Mandela at (5.55221°, -0.33912°)", + "Step 2: Calculate longitude difference", + " Δlon = -0.33912 - -40.34278 = 40.0037°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 77.37°", + "Step 5: Determine cardinal direction", + " 77.4° → E", + "FINAL ANSWER: 77.37° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 44.9483, + "lon": -93.34801, + "name": "Saint Louis Park" + }, + "point_b": { + "lat": 54.90973, + "lon": 64.4319, + "name": "Kurtamysh" + }, + "ground_truth": { + "initial_bearing_deg": 12.82, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Saint Louis Park at (44.9483°, -93.34801°)", + " To: Kurtamysh at (54.90973°, 64.4319°)", + "Step 2: Calculate longitude difference", + " Δlon = 64.4319 - -93.34801 = 157.7799°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 12.82°", + "Step 5: Determine cardinal direction", + " 12.8° → N", + "FINAL ANSWER: 12.82° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -33.01529, + "lon": 27.91162, + "name": "East London" + }, + "point_b": { + "lat": 43.67159, + "lon": -79.404, + "name": "Annex" + }, + "ground_truth": { + "initial_bearing_deg": 303.77, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: East London at (-33.01529°, 27.91162°)", + " To: Annex at (43.67159°, -79.404°)", + "Step 2: Calculate longitude difference", + " Δlon = -79.404 - 27.91162 = -107.3156°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 303.77°", + "Step 5: Determine cardinal direction", + " 303.8° → NW", + "FINAL ANSWER: 303.77° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 14.2, + "lon": 24.66667, + "name": "Kutum" + }, + "point_b": { + "lat": 51.66361, + "lon": 16.0845, + "name": "Głogów" + }, + "ground_truth": { + "initial_bearing_deg": 351.37, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Kutum at (14.2°, 24.66667°)", + " To: Głogów at (51.66361°, 16.0845°)", + "Step 2: Calculate longitude difference", + " Δlon = 16.0845 - 24.66667 = -8.5822°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 351.37°", + "Step 5: Determine cardinal direction", + " 351.4° → N", + "FINAL ANSWER: 351.37° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 54.61378, + "lon": 25.95537, + "name": "Astraviec" + }, + "point_b": { + "lat": 43.6475, + "lon": 111.97667, + "name": "Erenhot" + }, + "ground_truth": { + "initial_bearing_deg": 63.57, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Astraviec at (54.61378°, 25.95537°)", + " To: Erenhot at (43.6475°, 111.97667°)", + "Step 2: Calculate longitude difference", + " Δlon = 111.97667 - 25.95537 = 86.0213°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 63.57°", + "Step 5: Determine cardinal direction", + " 63.6° → NE", + "FINAL ANSWER: 63.57° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 33.88168, + "lon": -118.11701, + "name": "Bellflower" + }, + "point_b": { + "lat": -7.5817, + "lon": -39.28348, + "name": "Jardim" + }, + "ground_truth": { + "initial_bearing_deg": 102.55, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Bellflower at (33.88168°, -118.11701°)", + " To: Jardim at (-7.5817°, -39.28348°)", + "Step 2: Calculate longitude difference", + " Δlon = -39.28348 - -118.11701 = 78.8335°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 102.55°", + "Step 5: Determine cardinal direction", + " 102.5° → E", + "FINAL ANSWER: 102.55° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 48.59479, + "lon": 17.82591, + "name": "Piešťany" + }, + "point_b": { + "lat": 9.91861, + "lon": -68.30472, + "name": "Tinaquillo" + }, + "ground_truth": { + "initial_bearing_deg": 273.73, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Piešťany at (48.59479°, 17.82591°)", + " To: Tinaquillo at (9.91861°, -68.30472°)", + "Step 2: Calculate longitude difference", + " Δlon = -68.30472 - 17.82591 = -86.1306°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 273.73°", + "Step 5: Determine cardinal direction", + " 273.7° → W", + "FINAL ANSWER: 273.73° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -7.96556, + "lon": 110.60361, + "name": "Wonosari" + }, + "point_b": { + "lat": 46.56718, + "lon": 26.91384, + "name": "Bacău" + }, + "ground_truth": { + "initial_bearing_deg": 316.88, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Wonosari at (-7.96556°, 110.60361°)", + " To: Bacău at (46.56718°, 26.91384°)", + "Step 2: Calculate longitude difference", + " Δlon = 26.91384 - 110.60361 = -83.6898°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 316.88°", + "Step 5: Determine cardinal direction", + " 316.9° → NW", + "FINAL ANSWER: 316.88° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 10.1664, + "lon": 76.20179, + "name": "Vadakakarai" + }, + "point_b": { + "lat": 9.03333, + "lon": 38.15, + "name": "Gīnch’ī" + }, + "ground_truth": { + "initial_bearing_deg": 271.63, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Vadakakarai at (10.1664°, 76.20179°)", + " To: Gīnch’ī at (9.03333°, 38.15°)", + "Step 2: Calculate longitude difference", + " Δlon = 38.15 - 76.20179 = -38.0518°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 271.63°", + "Step 5: Determine cardinal direction", + " 271.6° → W", + "FINAL ANSWER: 271.63° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 46.25773, + "lon": 126.28065, + "name": "Lanxi" + }, + "point_b": { + "lat": -14.33611, + "lon": -43.77361, + "name": "Malhada" + }, + "ground_truth": { + "initial_bearing_deg": 342.1, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Lanxi at (46.25773°, 126.28065°)", + " To: Malhada at (-14.33611°, -43.77361°)", + "Step 2: Calculate longitude difference", + " Δlon = -43.77361 - 126.28065 = -170.0543°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 342.10°", + "Step 5: Determine cardinal direction", + " 342.1° → N", + "FINAL ANSWER: 342.10° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 50.70825, + "lon": -120.41337, + "name": "Brocklehurst" + }, + "point_b": { + "lat": 34.1463, + "lon": 73.21168, + "name": "Abbottabad" + }, + "ground_truth": { + "initial_bearing_deg": 348.73, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Brocklehurst at (50.70825°, -120.41337°)", + " To: Abbottabad at (34.1463°, 73.21168°)", + "Step 2: Calculate longitude difference", + " Δlon = 73.21168 - -120.41337 = 193.6250°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 348.73°", + "Step 5: Determine cardinal direction", + " 348.7° → N", + "FINAL ANSWER: 348.73° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 34.01325, + "lon": -6.83255, + "name": "Rabat" + }, + "point_b": { + "lat": 29.70885, + "lon": 73.62539, + "name": "Padampur" + }, + "ground_truth": { + "initial_bearing_deg": 68.91, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Rabat at (34.01325°, -6.83255°)", + " To: Padampur at (29.70885°, 73.62539°)", + "Step 2: Calculate longitude difference", + " Δlon = 73.62539 - -6.83255 = 80.4579°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 68.91°", + "Step 5: Determine cardinal direction", + " 68.9° → E", + "FINAL ANSWER: 68.91° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 13.2045, + "lon": 108.21029, + "name": "Ea Drăng" + }, + "point_b": { + "lat": 7.4839, + "lon": 80.3683, + "name": "Kurunegala" + }, + "ground_truth": { + "initial_bearing_deg": 260.99, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Ea Drăng at (13.2045°, 108.21029°)", + " To: Kurunegala at (7.4839°, 80.3683°)", + "Step 2: Calculate longitude difference", + " Δlon = 80.3683 - 108.21029 = -27.8420°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 260.99°", + "Step 5: Determine cardinal direction", + " 261.0° → W", + "FINAL ANSWER: 260.99° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -4.36667, + "lon": 35.08333, + "name": "Basotu" + }, + "point_b": { + "lat": 41.52614, + "lon": -87.88922, + "name": "Mokena" + }, + "ground_truth": { + "initial_bearing_deg": 315.09, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Basotu at (-4.36667°, 35.08333°)", + " To: Mokena at (41.52614°, -87.88922°)", + "Step 2: Calculate longitude difference", + " Δlon = -87.88922 - 35.08333 = -122.9725°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 315.09°", + "Step 5: Determine cardinal direction", + " 315.1° → NW", + "FINAL ANSWER: 315.09° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 28.01888, + "lon": -82.11469, + "name": "Plant City" + }, + "point_b": { + "lat": -37.84205, + "lon": 145.0694, + "name": "Camberwell" + }, + "ground_truth": { + "initial_bearing_deg": 243.45, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Plant City at (28.01888°, -82.11469°)", + " To: Camberwell at (-37.84205°, 145.0694°)", + "Step 2: Calculate longitude difference", + " Δlon = 145.0694 - -82.11469 = 227.1841°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 243.45°", + "Step 5: Determine cardinal direction", + " 243.4° → SW", + "FINAL ANSWER: 243.45° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -17.82772, + "lon": 31.05337, + "name": "Harare" + }, + "point_b": { + "lat": -22.66167, + "lon": -50.41222, + "name": "Assis" + }, + "ground_truth": { + "initial_bearing_deg": 250.41, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Harare at (-17.82772°, 31.05337°)", + " To: Assis at (-22.66167°, -50.41222°)", + "Step 2: Calculate longitude difference", + " Δlon = -50.41222 - 31.05337 = -81.4656°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 250.41°", + "Step 5: Determine cardinal direction", + " 250.4° → W", + "FINAL ANSWER: 250.41° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 30.73058, + "lon": 76.69368, + "name": "Balaungi" + }, + "point_b": { + "lat": 30.21754, + "lon": 105.7452, + "name": "Shuangjiang" + }, + "ground_truth": { + "initial_bearing_deg": 83.66, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Balaungi at (30.73058°, 76.69368°)", + " To: Shuangjiang at (30.21754°, 105.7452°)", + "Step 2: Calculate longitude difference", + " Δlon = 105.7452 - 76.69368 = 29.0515°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 83.66°", + "Step 5: Determine cardinal direction", + " 83.7° → E", + "FINAL ANSWER: 83.66° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -25.40222, + "lon": 32.80722, + "name": "Manhiça" + }, + "point_b": { + "lat": 36.18683, + "lon": 5.31347, + "name": "Aïn Arnat" + }, + "ground_truth": { + "initial_bearing_deg": 336.09, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Manhiça at (-25.40222°, 32.80722°)", + " To: Aïn Arnat at (36.18683°, 5.31347°)", + "Step 2: Calculate longitude difference", + " Δlon = 5.31347 - 32.80722 = -27.4938°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 336.09°", + "Step 5: Determine cardinal direction", + " 336.1° → NW", + "FINAL ANSWER: 336.09° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -7.86139, + "lon": -38.75972, + "name": "São José do Belmonte" + }, + "point_b": { + "lat": 29.16042, + "lon": 78.00762, + "name": "Hastināpur" + }, + "ground_truth": { + "initial_bearing_deg": 61.19, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: São José do Belmonte at (-7.86139°, -38.75972°)", + " To: Hastināpur at (29.16042°, 78.00762°)", + "Step 2: Calculate longitude difference", + " Δlon = 78.00762 - -38.75972 = 116.7673°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 61.19°", + "Step 5: Determine cardinal direction", + " 61.2° → NE", + "FINAL ANSWER: 61.19° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 35.49474, + "lon": 6.92492, + "name": "Kaïs" + }, + "point_b": { + "lat": 16.6614, + "lon": -9.6149, + "name": "Ayoun El Atrous" + }, + "ground_truth": { + "initial_bearing_deg": 222.29, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Kaïs at (35.49474°, 6.92492°)", + " To: Ayoun El Atrous at (16.6614°, -9.6149°)", + "Step 2: Calculate longitude difference", + " Δlon = -9.6149 - 6.92492 = -16.5398°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 222.29°", + "Step 5: Determine cardinal direction", + " 222.3° → SW", + "FINAL ANSWER: 222.29° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 48.44963, + "lon": -123.50261, + "name": "Langford" + }, + "point_b": { + "lat": 6.56913, + "lon": -8.00253, + "name": "Bloléquin" + }, + "ground_truth": { + "initial_bearing_deg": 66.17, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Langford at (48.44963°, -123.50261°)", + " To: Bloléquin at (6.56913°, -8.00253°)", + "Step 2: Calculate longitude difference", + " Δlon = -8.00253 - -123.50261 = 115.5001°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 66.17°", + "Step 5: Determine cardinal direction", + " 66.2° → NE", + "FINAL ANSWER: 66.17° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 10.86242, + "lon": 76.09218, + "name": "Irimbiliyam" + }, + "point_b": { + "lat": 22.91, + "lon": -81.85639, + "name": "Madruga" + }, + "ground_truth": { + "initial_bearing_deg": 327.52, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Irimbiliyam at (10.86242°, 76.09218°)", + " To: Madruga at (22.91°, -81.85639°)", + "Step 2: Calculate longitude difference", + " Δlon = -81.85639 - 76.09218 = -157.9486°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 327.52°", + "Step 5: Determine cardinal direction", + " 327.5° → NW", + "FINAL ANSWER: 327.52° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 5.7, + "lon": 101.83333, + "name": "Kampung Jeli" + }, + "point_b": { + "lat": 40.70788, + "lon": -73.7868, + "name": "Hillside" + }, + "ground_truth": { + "initial_bearing_deg": 355.43, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Kampung Jeli at (5.7°, 101.83333°)", + " To: Hillside at (40.70788°, -73.7868°)", + "Step 2: Calculate longitude difference", + " Δlon = -73.7868 - 101.83333 = -175.6201°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 355.43°", + "Step 5: Determine cardinal direction", + " 355.4° → N", + "FINAL ANSWER: 355.43° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 11.17151, + "lon": 75.80611, + "name": "Beypore" + }, + "point_b": { + "lat": 51.10821, + "lon": 6.94831, + "name": "Langenfeld" + }, + "ground_truth": { + "initial_bearing_deg": 320.87, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Beypore at (11.17151°, 75.80611°)", + " To: Langenfeld at (51.10821°, 6.94831°)", + "Step 2: Calculate longitude difference", + " Δlon = 6.94831 - 75.80611 = -68.8578°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 320.87°", + "Step 5: Determine cardinal direction", + " 320.9° → NW", + "FINAL ANSWER: 320.87° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 43.96667, + "lon": 116.03333, + "name": "Xilin Hot" + }, + "point_b": { + "lat": -2.51667, + "lon": 32.9, + "name": "Mwanza" + }, + "ground_truth": { + "initial_bearing_deg": 263.41, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Xilin Hot at (43.96667°, 116.03333°)", + " To: Mwanza at (-2.51667°, 32.9°)", + "Step 2: Calculate longitude difference", + " Δlon = 32.9 - 116.03333 = -83.1333°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 263.41°", + "Step 5: Determine cardinal direction", + " 263.4° → W", + "FINAL ANSWER: 263.41° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 40.98333, + "lon": 68.9, + "name": "Zafar" + }, + "point_b": { + "lat": -23.20083, + "lon": -47.28694, + "name": "Salto" + }, + "ground_truth": { + "initial_bearing_deg": 267.82, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Zafar at (40.98333°, 68.9°)", + " To: Salto at (-23.20083°, -47.28694°)", + "Step 2: Calculate longitude difference", + " Δlon = -47.28694 - 68.9 = -116.1869°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 267.82°", + "Step 5: Determine cardinal direction", + " 267.8° → W", + "FINAL ANSWER: 267.82° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 22.80667, + "lon": -80.07556, + "name": "Sagua la Grande" + }, + "point_b": { + "lat": 22.61892, + "lon": -83.70694, + "name": "Viñales" + }, + "ground_truth": { + "initial_bearing_deg": 267.49, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Sagua la Grande at (22.80667°, -80.07556°)", + " To: Viñales at (22.61892°, -83.70694°)", + "Step 2: Calculate longitude difference", + " Δlon = -83.70694 - -80.07556 = -3.6314°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 267.49°", + "Step 5: Determine cardinal direction", + " 267.5° → W", + "FINAL ANSWER: 267.49° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 6.26812, + "lon": 100.42167, + "name": "Jitra" + }, + "point_b": { + "lat": 41.60797, + "lon": 2.28773, + "name": "Granollers" + }, + "ground_truth": { + "initial_bearing_deg": 312.22, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Jitra at (6.26812°, 100.42167°)", + " To: Granollers at (41.60797°, 2.28773°)", + "Step 2: Calculate longitude difference", + " Δlon = 2.28773 - 100.42167 = -98.1339°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 312.22°", + "Step 5: Determine cardinal direction", + " 312.2° → NW", + "FINAL ANSWER: 312.22° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -7.18833, + "lon": -39.73694, + "name": "Santana do Cariri" + }, + "point_b": { + "lat": 4.0913, + "lon": 9.3144, + "name": "Mutengene" + }, + "ground_truth": { + "initial_bearing_deg": 78.55, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Santana do Cariri at (-7.18833°, -39.73694°)", + " To: Mutengene at (4.0913°, 9.3144°)", + "Step 2: Calculate longitude difference", + " Δlon = 9.3144 - -39.73694 = 49.0513°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 78.55°", + "Step 5: Determine cardinal direction", + " 78.5° → E", + "FINAL ANSWER: 78.55° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 47.67399, + "lon": -122.12151, + "name": "Redmond" + }, + "point_b": { + "lat": 13.44189, + "lon": 79.55314, + "name": "Puttūr" + }, + "ground_truth": { + "initial_bearing_deg": 336.46, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Redmond at (47.67399°, -122.12151°)", + " To: Puttūr at (13.44189°, 79.55314°)", + "Step 2: Calculate longitude difference", + " Δlon = 79.55314 - -122.12151 = 201.6746°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 336.46°", + "Step 5: Determine cardinal direction", + " 336.5° → NW", + "FINAL ANSWER: 336.46° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 28.0199, + "lon": -82.77323, + "name": "Dunedin" + }, + "point_b": { + "lat": -23.38032, + "lon": 150.50595, + "name": "Rockhampton" + }, + "ground_truth": { + "initial_bearing_deg": 262.83, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Dunedin at (28.0199°, -82.77323°)", + " To: Rockhampton at (-23.38032°, 150.50595°)", + "Step 2: Calculate longitude difference", + " Δlon = 150.50595 - -82.77323 = 233.2792°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 262.83°", + "Step 5: Determine cardinal direction", + " 262.8° → W", + "FINAL ANSWER: 262.83° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 19.30133, + "lon": 76.49735, + "name": "Manwath" + }, + "point_b": { + "lat": 55.84244, + "lon": 38.19362, + "name": "Monino" + }, + "ground_truth": { + "initial_bearing_deg": 331.29, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Manwath at (19.30133°, 76.49735°)", + " To: Monino at (55.84244°, 38.19362°)", + "Step 2: Calculate longitude difference", + " Δlon = 38.19362 - 76.49735 = -38.3037°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 331.29°", + "Step 5: Determine cardinal direction", + " 331.3° → NW", + "FINAL ANSWER: 331.29° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 37.49466, + "lon": -120.84659, + "name": "Turlock" + }, + "point_b": { + "lat": 22.02074, + "lon": 82.5666, + "name": "Nailā" + }, + "ground_truth": { + "initial_bearing_deg": 335.69, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Turlock at (37.49466°, -120.84659°)", + " To: Nailā at (22.02074°, 82.5666°)", + "Step 2: Calculate longitude difference", + " Δlon = 82.5666 - -120.84659 = 203.4132°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 335.69°", + "Step 5: Determine cardinal direction", + " 335.7° → NW", + "FINAL ANSWER: 335.69° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 51.7874, + "lon": 56.35987, + "name": "Saraktash" + }, + "point_b": { + "lat": 10.02798, + "lon": 39.8528, + "name": "Kobo" + }, + "ground_truth": { + "initial_bearing_deg": 203.81, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Saraktash at (51.7874°, 56.35987°)", + " To: Kobo at (10.02798°, 39.8528°)", + "Step 2: Calculate longitude difference", + " Δlon = 39.8528 - 56.35987 = -16.5071°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 203.81°", + "Step 5: Determine cardinal direction", + " 203.8° → SW", + "FINAL ANSWER: 203.81° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 42.96336, + "lon": -85.66809, + "name": "Grand Rapids" + }, + "point_b": { + "lat": -27.58333, + "lon": 153.1, + "name": "Eight Mile Plains" + }, + "ground_truth": { + "initial_bearing_deg": 268.06, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Grand Rapids at (42.96336°, -85.66809°)", + " To: Eight Mile Plains at (-27.58333°, 153.1°)", + "Step 2: Calculate longitude difference", + " Δlon = 153.1 - -85.66809 = 238.7681°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 268.06°", + "Step 5: Determine cardinal direction", + " 268.1° → W", + "FINAL ANSWER: 268.06° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -9.40611, + "lon": -38.21472, + "name": "Paulo Afonso" + }, + "point_b": { + "lat": 35.83333, + "lon": 140.23333, + "name": "Ajiki" + }, + "ground_truth": { + "initial_bearing_deg": 2.82, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Paulo Afonso at (-9.40611°, -38.21472°)", + " To: Ajiki at (35.83333°, 140.23333°)", + "Step 2: Calculate longitude difference", + " Δlon = 140.23333 - -38.21472 = 178.4480°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 2.82°", + "Step 5: Determine cardinal direction", + " 2.8° → N", + "FINAL ANSWER: 2.82° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 50.04862, + "lon": 14.5244, + "name": "Hostivař" + }, + "point_b": { + "lat": -25.9957, + "lon": 28.1971, + "name": "Ivory Park" + }, + "ground_truth": { + "initial_bearing_deg": 167.41, + "cardinal_direction": "S", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Hostivař at (50.04862°, 14.5244°)", + " To: Ivory Park at (-25.9957°, 28.1971°)", + "Step 2: Calculate longitude difference", + " Δlon = 28.1971 - 14.5244 = 13.6727°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 167.41°", + "Step 5: Determine cardinal direction", + " 167.4° → S", + "FINAL ANSWER: 167.41° (S)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 47.76977, + "lon": 9.17136, + "name": "Überlingen" + }, + "point_b": { + "lat": 47.23088, + "lon": 16.62155, + "name": "Szombathely" + }, + "ground_truth": { + "initial_bearing_deg": 93.35, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Überlingen at (47.76977°, 9.17136°)", + " To: Szombathely at (47.23088°, 16.62155°)", + "Step 2: Calculate longitude difference", + " Δlon = 16.62155 - 9.17136 = 7.4502°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 93.35°", + "Step 5: Determine cardinal direction", + " 93.3° → E", + "FINAL ANSWER: 93.35° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 51.61379, + "lon": 7.19738, + "name": "Recklinghausen" + }, + "point_b": { + "lat": -27.64613, + "lon": 152.85965, + "name": "Redbank Plains" + }, + "ground_truth": { + "initial_bearing_deg": 60.28, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Recklinghausen at (51.61379°, 7.19738°)", + " To: Redbank Plains at (-27.64613°, 152.85965°)", + "Step 2: Calculate longitude difference", + " Δlon = 152.85965 - 7.19738 = 145.6623°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 60.28°", + "Step 5: Determine cardinal direction", + " 60.3° → NE", + "FINAL ANSWER: 60.28° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 44.35012, + "lon": -78.73286, + "name": "Lindsay" + }, + "point_b": { + "lat": 24.33353, + "lon": 93.66999, + "name": "Churāchāndpur" + }, + "ground_truth": { + "initial_bearing_deg": 7.41, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Lindsay at (44.35012°, -78.73286°)", + " To: Churāchāndpur at (24.33353°, 93.66999°)", + "Step 2: Calculate longitude difference", + " Δlon = 93.66999 - -78.73286 = 172.4029°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 7.41°", + "Step 5: Determine cardinal direction", + " 7.4° → N", + "FINAL ANSWER: 7.41° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 42.00288, + "lon": -71.51478, + "name": "Woonsocket" + }, + "point_b": { + "lat": 27.59441, + "lon": 94.72402, + "name": "Silapathar" + }, + "ground_truth": { + "initial_bearing_deg": 12.9, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Woonsocket at (42.00288°, -71.51478°)", + " To: Silapathar at (27.59441°, 94.72402°)", + "Step 2: Calculate longitude difference", + " Δlon = 94.72402 - -71.51478 = 166.2388°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 12.90°", + "Step 5: Determine cardinal direction", + " 12.9° → N", + "FINAL ANSWER: 12.90° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 36.77667, + "lon": 121.15972, + "name": "Dongcun" + }, + "point_b": { + "lat": -9.13333, + "lon": -35.74833, + "name": "Joaquim Gomes" + }, + "ground_truth": { + "initial_bearing_deg": 317.09, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Dongcun at (36.77667°, 121.15972°)", + " To: Joaquim Gomes at (-9.13333°, -35.74833°)", + "Step 2: Calculate longitude difference", + " Δlon = -35.74833 - 121.15972 = -156.9081°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 317.09°", + "Step 5: Determine cardinal direction", + " 317.1° → NW", + "FINAL ANSWER: 317.09° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 13.73939, + "lon": 106.98727, + "name": "Banlung" + }, + "point_b": { + "lat": 51.44657, + "lon": 0.21423, + "name": "Dartford" + }, + "ground_truth": { + "initial_bearing_deg": 323.36, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Banlung at (13.73939°, 106.98727°)", + " To: Dartford at (51.44657°, 0.21423°)", + "Step 2: Calculate longitude difference", + " Δlon = 0.21423 - 106.98727 = -106.7730°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 323.36°", + "Step 5: Determine cardinal direction", + " 323.4° → NW", + "FINAL ANSWER: 323.36° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 31.54514, + "lon": 73.82891, + "name": "Chak Five Hundred Seventy-five" + }, + "point_b": { + "lat": 48.44248, + "lon": 22.718, + "name": "Mukachevo" + }, + "ground_truth": { + "initial_bearing_deg": 309.11, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Chak Five Hundred Seventy-five at (31.54514°, 73.82891°)", + " To: Mukachevo at (48.44248°, 22.718°)", + "Step 2: Calculate longitude difference", + " Δlon = 22.718 - 73.82891 = -51.1109°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 309.11°", + "Step 5: Determine cardinal direction", + " 309.1° → NW", + "FINAL ANSWER: 309.11° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -12.78234, + "lon": 45.22878, + "name": "Mamoudzou" + }, + "point_b": { + "lat": 43.93064, + "lon": 10.92365, + "name": "Pistoia" + }, + "ground_truth": { + "initial_bearing_deg": 333.33, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Mamoudzou at (-12.78234°, 45.22878°)", + " To: Pistoia at (43.93064°, 10.92365°)", + "Step 2: Calculate longitude difference", + " Δlon = 10.92365 - 45.22878 = -34.3051°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 333.33°", + "Step 5: Determine cardinal direction", + " 333.3° → NW", + "FINAL ANSWER: 333.33° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 51.78826, + "lon": 6.13865, + "name": "Kleve" + }, + "point_b": { + "lat": 54.42119, + "lon": 86.29907, + "name": "Belovo" + }, + "ground_truth": { + "initial_bearing_deg": 53.45, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Kleve at (51.78826°, 6.13865°)", + " To: Belovo at (54.42119°, 86.29907°)", + "Step 2: Calculate longitude difference", + " Δlon = 86.29907 - 6.13865 = 80.1604°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 53.45°", + "Step 5: Determine cardinal direction", + " 53.5° → NE", + "FINAL ANSWER: 53.45° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 46.05007, + "lon": -71.96579, + "name": "Victoriaville" + }, + "point_b": { + "lat": 32.55556, + "lon": 35.85, + "name": "Irbid" + }, + "ground_truth": { + "initial_bearing_deg": 55.13, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Victoriaville at (46.05007°, -71.96579°)", + " To: Irbid at (32.55556°, 35.85°)", + "Step 2: Calculate longitude difference", + " Δlon = 35.85 - -71.96579 = 107.8158°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 55.13°", + "Step 5: Determine cardinal direction", + " 55.1° → NE", + "FINAL ANSWER: 55.13° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 7.75624, + "lon": -8.8179, + "name": "Nzérékoré" + }, + "point_b": { + "lat": 45.82058, + "lon": 8.82511, + "name": "Varese" + }, + "ground_truth": { + "initial_bearing_deg": 18.79, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Nzérékoré at (7.75624°, -8.8179°)", + " To: Varese at (45.82058°, 8.82511°)", + "Step 2: Calculate longitude difference", + " Δlon = 8.82511 - -8.8179 = 17.6430°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 18.79°", + "Step 5: Determine cardinal direction", + " 18.8° → N", + "FINAL ANSWER: 18.79° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 55.78363, + "lon": 37.47137, + "name": "Khoroshëvo-Mnevniki" + }, + "point_b": { + "lat": 2.34464, + "lon": 42.27644, + "name": "Baardheere" + }, + "ground_truth": { + "initial_bearing_deg": 174.03, + "cardinal_direction": "S", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Khoroshëvo-Mnevniki at (55.78363°, 37.47137°)", + " To: Baardheere at (2.34464°, 42.27644°)", + "Step 2: Calculate longitude difference", + " Δlon = 42.27644 - 37.47137 = 4.8051°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 174.03°", + "Step 5: Determine cardinal direction", + " 174.0° → S", + "FINAL ANSWER: 174.03° (S)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 10.0477, + "lon": 78.74719, + "name": "Sankarapatti" + }, + "point_b": { + "lat": -12.3644, + "lon": 13.53601, + "name": "Lobito" + }, + "ground_truth": { + "initial_bearing_deg": 252.34, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Sankarapatti at (10.0477°, 78.74719°)", + " To: Lobito at (-12.3644°, 13.53601°)", + "Step 2: Calculate longitude difference", + " Δlon = 13.53601 - 78.74719 = -65.2112°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 252.34°", + "Step 5: Determine cardinal direction", + " 252.3° → W", + "FINAL ANSWER: 252.34° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 5.02208, + "lon": -74.00481, + "name": "Zipaquirá" + }, + "point_b": { + "lat": 25.78924, + "lon": 100.12279, + "name": "Wanqiao Zhen" + }, + "ground_truth": { + "initial_bearing_deg": 10.2, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Zipaquirá at (5.02208°, -74.00481°)", + " To: Wanqiao Zhen at (25.78924°, 100.12279°)", + "Step 2: Calculate longitude difference", + " Δlon = 100.12279 - -74.00481 = 174.1276°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 10.20°", + "Step 5: Determine cardinal direction", + " 10.2° → N", + "FINAL ANSWER: 10.20° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 9.02871, + "lon": 13.1848, + "name": "Tchéboa" + }, + "point_b": { + "lat": 54.12226, + "lon": 17.98119, + "name": "Kościerzyna" + }, + "ground_truth": { + "initial_bearing_deg": 3.96, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Tchéboa at (9.02871°, 13.1848°)", + " To: Kościerzyna at (54.12226°, 17.98119°)", + "Step 2: Calculate longitude difference", + " Δlon = 17.98119 - 13.1848 = 4.7964°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 3.96°", + "Step 5: Determine cardinal direction", + " 4.0° → N", + "FINAL ANSWER: 3.96° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 13.18421, + "lon": 30.21669, + "name": "El Obeid" + }, + "point_b": { + "lat": 52.30322, + "lon": 13.25405, + "name": "Ludwigsfelde" + }, + "ground_truth": { + "initial_bearing_deg": 344.35, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: El Obeid at (13.18421°, 30.21669°)", + " To: Ludwigsfelde at (52.30322°, 13.25405°)", + "Step 2: Calculate longitude difference", + " Δlon = 13.25405 - 30.21669 = -16.9626°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 344.35°", + "Step 5: Determine cardinal direction", + " 344.4° → N", + "FINAL ANSWER: 344.35° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 19.22031, + "lon": -70.53101, + "name": "La Vega" + }, + "point_b": { + "lat": 35.555, + "lon": 5.61056, + "name": "N’Gaous" + }, + "ground_truth": { + "initial_bearing_deg": 58.45, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: La Vega at (19.22031°, -70.53101°)", + " To: N’Gaous at (35.555°, 5.61056°)", + "Step 2: Calculate longitude difference", + " Δlon = 5.61056 - -70.53101 = 76.1416°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 58.45°", + "Step 5: Determine cardinal direction", + " 58.5° → NE", + "FINAL ANSWER: 58.45° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 9.59972, + "lon": 43.335, + "name": "Tog Wajaale" + }, + "point_b": { + "lat": 40.30428, + "lon": -74.10042, + "name": "Tinton Falls" + }, + "ground_truth": { + "initial_bearing_deg": 315.82, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Tog Wajaale at (9.59972°, 43.335°)", + " To: Tinton Falls at (40.30428°, -74.10042°)", + "Step 2: Calculate longitude difference", + " Δlon = -74.10042 - 43.335 = -117.4354°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 315.82°", + "Step 5: Determine cardinal direction", + " 315.8° → NW", + "FINAL ANSWER: 315.82° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 26.51393, + "lon": 85.29341, + "name": "Sheohar" + }, + "point_b": { + "lat": 33.85844, + "lon": -84.3402, + "name": "Brookhaven" + }, + "ground_truth": { + "initial_bearing_deg": 350.18, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Sheohar at (26.51393°, 85.29341°)", + " To: Brookhaven at (33.85844°, -84.3402°)", + "Step 2: Calculate longitude difference", + " Δlon = -84.3402 - 85.29341 = -169.6336°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 350.18°", + "Step 5: Determine cardinal direction", + " 350.2° → N", + "FINAL ANSWER: 350.18° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -13.77333, + "lon": -42.71417, + "name": "Igaporã" + }, + "point_b": { + "lat": 13.42722, + "lon": -16.68528, + "name": "Bununka Kunda" + }, + "ground_truth": { + "initial_bearing_deg": 44.55, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Igaporã at (-13.77333°, -42.71417°)", + " To: Bununka Kunda at (13.42722°, -16.68528°)", + "Step 2: Calculate longitude difference", + " Δlon = -16.68528 - -42.71417 = 26.0289°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 44.55°", + "Step 5: Determine cardinal direction", + " 44.5° → NE", + "FINAL ANSWER: 44.55° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 30.71877, + "lon": 31.56299, + "name": "Al Ibrāhīmīyah" + }, + "point_b": { + "lat": -2.51389, + "lon": -66.09167, + "name": "Fonte Boa" + }, + "ground_truth": { + "initial_bearing_deg": 271.75, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Al Ibrāhīmīyah at (30.71877°, 31.56299°)", + " To: Fonte Boa at (-2.51389°, -66.09167°)", + "Step 2: Calculate longitude difference", + " Δlon = -66.09167 - 31.56299 = -97.6547°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 271.75°", + "Step 5: Determine cardinal direction", + " 271.8° → W", + "FINAL ANSWER: 271.75° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 60.40338, + "lon": 25.105, + "name": "Kerava" + }, + "point_b": { + "lat": 29.35896, + "lon": 30.68061, + "name": "Ibshawāy" + }, + "ground_truth": { + "initial_bearing_deg": 170.61, + "cardinal_direction": "S", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Kerava at (60.40338°, 25.105°)", + " To: Ibshawāy at (29.35896°, 30.68061°)", + "Step 2: Calculate longitude difference", + " Δlon = 30.68061 - 25.105 = 5.5756°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 170.61°", + "Step 5: Determine cardinal direction", + " 170.6° → S", + "FINAL ANSWER: 170.61° (S)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 41.38555, + "lon": 60.36408, + "name": "Xiva" + }, + "point_b": { + "lat": -19.19694, + "lon": -40.09778, + "name": "Sooretama" + }, + "ground_truth": { + "initial_bearing_deg": 261.83, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Xiva at (41.38555°, 60.36408°)", + " To: Sooretama at (-19.19694°, -40.09778°)", + "Step 2: Calculate longitude difference", + " Δlon = -40.09778 - 60.36408 = -100.4619°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 261.83°", + "Step 5: Determine cardinal direction", + " 261.8° → W", + "FINAL ANSWER: 261.83° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 29.373, + "lon": 78.13636, + "name": "Bijnor" + }, + "point_b": { + "lat": 59.91273, + "lon": 10.74609, + "name": "Oslo" + }, + "ground_truth": { + "initial_bearing_deg": 324.94, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Bijnor at (29.373°, 78.13636°)", + " To: Oslo at (59.91273°, 10.74609°)", + "Step 2: Calculate longitude difference", + " Δlon = 10.74609 - 78.13636 = -67.3903°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 324.94°", + "Step 5: Determine cardinal direction", + " 324.9° → NW", + "FINAL ANSWER: 324.94° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 12.75975, + "lon": 75.20169, + "name": "Puttūr" + }, + "point_b": { + "lat": 11.8235, + "lon": -70.25637, + "name": "Santa Cruz de los Taques" + }, + "ground_truth": { + "initial_bearing_deg": 304.25, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Puttūr at (12.75975°, 75.20169°)", + " To: Santa Cruz de los Taques at (11.8235°, -70.25637°)", + "Step 2: Calculate longitude difference", + " Δlon = -70.25637 - 75.20169 = -145.4581°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 304.25°", + "Step 5: Determine cardinal direction", + " 304.2° → NW", + "FINAL ANSWER: 304.25° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 19.68006, + "lon": -103.2514, + "name": "Tamazula de Gordiano" + }, + "point_b": { + "lat": 12.37136, + "lon": -1.41468, + "name": "Saaba" + }, + "ground_truth": { + "initial_bearing_deg": 74.27, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Tamazula de Gordiano at (19.68006°, -103.2514°)", + " To: Saaba at (12.37136°, -1.41468°)", + "Step 2: Calculate longitude difference", + " Δlon = -1.41468 - -103.2514 = 101.8367°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 74.27°", + "Step 5: Determine cardinal direction", + " 74.3° → E", + "FINAL ANSWER: 74.27° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 5.26598, + "lon": -76.56487, + "name": "Tadó" + }, + "point_b": { + "lat": 28.31457, + "lon": 74.28952, + "name": "Bhādāsar" + }, + "ground_truth": { + "initial_bearing_deg": 38.3, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Tadó at (5.26598°, -76.56487°)", + " To: Bhādāsar at (28.31457°, 74.28952°)", + "Step 2: Calculate longitude difference", + " Δlon = 74.28952 - -76.56487 = 150.8544°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 38.30°", + "Step 5: Determine cardinal direction", + " 38.3° → NE", + "FINAL ANSWER: 38.30° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -6.98111, + "lon": -34.83389, + "name": "Cabedelo" + }, + "point_b": { + "lat": 35.72917, + "lon": 10.58082, + "name": "Msaken" + }, + "ground_truth": { + "initial_bearing_deg": 41.7, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Cabedelo at (-6.98111°, -34.83389°)", + " To: Msaken at (35.72917°, 10.58082°)", + "Step 2: Calculate longitude difference", + " Δlon = 10.58082 - -34.83389 = 45.4147°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 41.70°", + "Step 5: Determine cardinal direction", + " 41.7° → NE", + "FINAL ANSWER: 41.70° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 44.5432, + "lon": 10.7848, + "name": "Sassuolo" + }, + "point_b": { + "lat": 58.7002, + "lon": 59.4839, + "name": "Kachkanar" + }, + "ground_truth": { + "initial_bearing_deg": 46.65, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Sassuolo at (44.5432°, 10.7848°)", + " To: Kachkanar at (58.7002°, 59.4839°)", + "Step 2: Calculate longitude difference", + " Δlon = 59.4839 - 10.7848 = 48.6991°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 46.65°", + "Step 5: Determine cardinal direction", + " 46.6° → NE", + "FINAL ANSWER: 46.65° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 40.85843, + "lon": -74.16376, + "name": "Clifton" + }, + "point_b": { + "lat": -3.55, + "lon": 36.1, + "name": "Makuyuni" + }, + "ground_truth": { + "initial_bearing_deg": 79.16, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Clifton at (40.85843°, -74.16376°)", + " To: Makuyuni at (-3.55°, 36.1°)", + "Step 2: Calculate longitude difference", + " Δlon = 36.1 - -74.16376 = 110.2638°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 79.16°", + "Step 5: Determine cardinal direction", + " 79.2° → E", + "FINAL ANSWER: 79.16° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 32.68833, + "lon": 112.8275, + "name": "Binhe" + }, + "point_b": { + "lat": 60.81462, + "lon": 23.62146, + "name": "Forssa" + }, + "ground_truth": { + "initial_bearing_deg": 326.3, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Binhe at (32.68833°, 112.8275°)", + " To: Forssa at (60.81462°, 23.62146°)", + "Step 2: Calculate longitude difference", + " Δlon = 23.62146 - 112.8275 = -89.2060°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 326.30°", + "Step 5: Determine cardinal direction", + " 326.3° → NW", + "FINAL ANSWER: 326.30° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -34.71716, + "lon": -55.9584, + "name": "Pando" + }, + "point_b": { + "lat": 32.28034, + "lon": 119.16999, + "name": "Zhenzhou" + }, + "ground_truth": { + "initial_bearing_deg": 119.59, + "cardinal_direction": "SE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Pando at (-34.71716°, -55.9584°)", + " To: Zhenzhou at (32.28034°, 119.16999°)", + "Step 2: Calculate longitude difference", + " Δlon = 119.16999 - -55.9584 = 175.1284°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 119.59°", + "Step 5: Determine cardinal direction", + " 119.6° → SE", + "FINAL ANSWER: 119.59° (SE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 11.77554, + "lon": 79.67016, + "name": "Nellikkuppam" + }, + "point_b": { + "lat": 35.42146, + "lon": 133.24224, + "name": "Yasugichō" + }, + "ground_truth": { + "initial_bearing_deg": 54.45, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Nellikkuppam at (11.77554°, 79.67016°)", + " To: Yasugichō at (35.42146°, 133.24224°)", + "Step 2: Calculate longitude difference", + " Δlon = 133.24224 - 79.67016 = 53.5721°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 54.45°", + "Step 5: Determine cardinal direction", + " 54.5° → NE", + "FINAL ANSWER: 54.45° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -1.46771, + "lon": 34.52279, + "name": "Matongo" + }, + "point_b": { + "lat": 31.18065, + "lon": 31.86497, + "name": "Al Jammālīyah" + }, + "ground_truth": { + "initial_bearing_deg": 355.79, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Matongo at (-1.46771°, 34.52279°)", + " To: Al Jammālīyah at (31.18065°, 31.86497°)", + "Step 2: Calculate longitude difference", + " Δlon = 31.86497 - 34.52279 = -2.6578°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 355.79°", + "Step 5: Determine cardinal direction", + " 355.8° → N", + "FINAL ANSWER: 355.79° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -16.575, + "lon": -39.55333, + "name": "Itabela" + }, + "point_b": { + "lat": 6.27534, + "lon": -6.99704, + "name": "Buyo" + }, + "ground_truth": { + "initial_bearing_deg": 57.27, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Itabela at (-16.575°, -39.55333°)", + " To: Buyo at (6.27534°, -6.99704°)", + "Step 2: Calculate longitude difference", + " Δlon = -6.99704 - -39.55333 = 32.5563°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 57.27°", + "Step 5: Determine cardinal direction", + " 57.3° → NE", + "FINAL ANSWER: 57.27° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 25.67927, + "lon": -80.31727, + "name": "Kendall" + }, + "point_b": { + "lat": -28.21901, + "lon": 152.03438, + "name": "Warwick" + }, + "ground_truth": { + "initial_bearing_deg": 254.54, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Kendall at (25.67927°, -80.31727°)", + " To: Warwick at (-28.21901°, 152.03438°)", + "Step 2: Calculate longitude difference", + " Δlon = 152.03438 - -80.31727 = 232.3517°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 254.54°", + "Step 5: Determine cardinal direction", + " 254.5° → W", + "FINAL ANSWER: 254.54° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 42.9551, + "lon": -81.62232, + "name": "Strathroy" + }, + "point_b": { + "lat": 40.64175, + "lon": 15.80794, + "name": "Potenza" + }, + "ground_truth": { + "initial_bearing_deg": 54.16, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Strathroy at (42.9551°, -81.62232°)", + " To: Potenza at (40.64175°, 15.80794°)", + "Step 2: Calculate longitude difference", + " Δlon = 15.80794 - -81.62232 = 97.4303°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 54.16°", + "Step 5: Determine cardinal direction", + " 54.2° → NE", + "FINAL ANSWER: 54.16° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 25.10479, + "lon": 84.1162, + "name": "Nokha" + }, + "point_b": { + "lat": -28.07071, + "lon": 153.39329, + "name": "Robina" + }, + "ground_truth": { + "initial_bearing_deg": 124.09, + "cardinal_direction": "SE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Nokha at (25.10479°, 84.1162°)", + " To: Robina at (-28.07071°, 153.39329°)", + "Step 2: Calculate longitude difference", + " Δlon = 153.39329 - 84.1162 = 69.2771°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 124.09°", + "Step 5: Determine cardinal direction", + " 124.1° → SE", + "FINAL ANSWER: 124.09° (SE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 18.20107, + "lon": -67.13962, + "name": "Mayagüez" + }, + "point_b": { + "lat": 53.59398, + "lon": 142.95279, + "name": "Okha" + }, + "ground_truth": { + "initial_bearing_deg": 342.17, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Mayagüez at (18.20107°, -67.13962°)", + " To: Okha at (53.59398°, 142.95279°)", + "Step 2: Calculate longitude difference", + " Δlon = 142.95279 - -67.13962 = 210.0924°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 342.17°", + "Step 5: Determine cardinal direction", + " 342.2° → N", + "FINAL ANSWER: 342.17° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 6.42611, + "lon": 1.21333, + "name": "Tsévié" + }, + "point_b": { + "lat": 36.9, + "lon": 7.76667, + "name": "Annaba" + }, + "ground_truth": { + "initial_bearing_deg": 10.19, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Tsévié at (6.42611°, 1.21333°)", + " To: Annaba at (36.9°, 7.76667°)", + "Step 2: Calculate longitude difference", + " Δlon = 7.76667 - 1.21333 = 6.5533°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 10.19°", + "Step 5: Determine cardinal direction", + " 10.2° → N", + "FINAL ANSWER: 10.19° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 37.75018, + "lon": -122.43369, + "name": "Noe Valley" + }, + "point_b": { + "lat": 27.9378, + "lon": -82.28592, + "name": "Brandon" + }, + "ground_truth": { + "initial_bearing_deg": 94.32, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Noe Valley at (37.75018°, -122.43369°)", + " To: Brandon at (27.9378°, -82.28592°)", + "Step 2: Calculate longitude difference", + " Δlon = -82.28592 - -122.43369 = 40.1478°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 94.32°", + "Step 5: Determine cardinal direction", + " 94.3° → E", + "FINAL ANSWER: 94.32° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 19.64186, + "lon": 109.3545, + "name": "Guangcun" + }, + "point_b": { + "lat": 10.98133, + "lon": 8.05749, + "name": "Soba" + }, + "ground_truth": { + "initial_bearing_deg": 284.23, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Guangcun at (19.64186°, 109.3545°)", + " To: Soba at (10.98133°, 8.05749°)", + "Step 2: Calculate longitude difference", + " Δlon = 8.05749 - 109.3545 = -101.2970°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 284.23°", + "Step 5: Determine cardinal direction", + " 284.2° → W", + "FINAL ANSWER: 284.23° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 51.37281, + "lon": -2.14002, + "name": "Melksham" + }, + "point_b": { + "lat": 47.42642, + "lon": 9.65851, + "name": "Lustenau" + }, + "ground_truth": { + "initial_bearing_deg": 112.63, + "cardinal_direction": "SE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Melksham at (51.37281°, -2.14002°)", + " To: Lustenau at (47.42642°, 9.65851°)", + "Step 2: Calculate longitude difference", + " Δlon = 9.65851 - -2.14002 = 11.7985°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 112.63°", + "Step 5: Determine cardinal direction", + " 112.6° → SE", + "FINAL ANSWER: 112.63° (SE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 38.81144, + "lon": -90.85291, + "name": "Wentzville" + }, + "point_b": { + "lat": -34.09345, + "lon": 21.25725, + "name": "Riversdale" + }, + "ground_truth": { + "initial_bearing_deg": 107.47, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Wentzville at (38.81144°, -90.85291°)", + " To: Riversdale at (-34.09345°, 21.25725°)", + "Step 2: Calculate longitude difference", + " Δlon = 21.25725 - -90.85291 = 112.1102°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 107.47°", + "Step 5: Determine cardinal direction", + " 107.5° → E", + "FINAL ANSWER: 107.47° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 31.34038, + "lon": -110.93425, + "name": "Nogales" + }, + "point_b": { + "lat": 49.98037, + "lon": 18.95382, + "name": "Pszczyna" + }, + "ground_truth": { + "initial_bearing_deg": 29.6, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Nogales at (31.34038°, -110.93425°)", + " To: Pszczyna at (49.98037°, 18.95382°)", + "Step 2: Calculate longitude difference", + " Δlon = 18.95382 - -110.93425 = 129.8881°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 29.60°", + "Step 5: Determine cardinal direction", + " 29.6° → NE", + "FINAL ANSWER: 29.60° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 36.87617, + "lon": 6.90921, + "name": "Skikda" + }, + "point_b": { + "lat": -29.82068, + "lon": 30.88674, + "name": "Pinetown" + }, + "ground_truth": { + "initial_bearing_deg": 158.02, + "cardinal_direction": "S", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Skikda at (36.87617°, 6.90921°)", + " To: Pinetown at (-29.82068°, 30.88674°)", + "Step 2: Calculate longitude difference", + " Δlon = 30.88674 - 6.90921 = 23.9775°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 158.02°", + "Step 5: Determine cardinal direction", + " 158.0° → S", + "FINAL ANSWER: 158.02° (S)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -0.33316, + "lon": 37.64587, + "name": "Chuka" + }, + "point_b": { + "lat": -4.30028, + "lon": -38.49778, + "name": "Chorozinho" + }, + "ground_truth": { + "initial_bearing_deg": 265.65, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Chuka at (-0.33316°, 37.64587°)", + " To: Chorozinho at (-4.30028°, -38.49778°)", + "Step 2: Calculate longitude difference", + " Δlon = -38.49778 - 37.64587 = -76.1437°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 265.65°", + "Step 5: Determine cardinal direction", + " 265.6° → W", + "FINAL ANSWER: 265.65° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -32.25215, + "lon": 24.53075, + "name": "Graaff Reinet" + }, + "point_b": { + "lat": 35.75647, + "lon": -83.97046, + "name": "Maryville" + }, + "ground_truth": { + "initial_bearing_deg": 294.87, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Graaff Reinet at (-32.25215°, 24.53075°)", + " To: Maryville at (35.75647°, -83.97046°)", + "Step 2: Calculate longitude difference", + " Δlon = -83.97046 - 24.53075 = -108.5012°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 294.87°", + "Step 5: Determine cardinal direction", + " 294.9° → NW", + "FINAL ANSWER: 294.87° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -29.51694, + "lon": -50.77778, + "name": "Três Coroas" + }, + "point_b": { + "lat": 52.48419, + "lon": 13.53185, + "name": "Karlshorst" + }, + "ground_truth": { + "initial_bearing_deg": 33.78, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Três Coroas at (-29.51694°, -50.77778°)", + " To: Karlshorst at (52.48419°, 13.53185°)", + "Step 2: Calculate longitude difference", + " Δlon = 13.53185 - -50.77778 = 64.3096°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 33.78°", + "Step 5: Determine cardinal direction", + " 33.8° → NE", + "FINAL ANSWER: 33.78° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -12.48602, + "lon": 130.9833, + "name": "Palmerston" + }, + "point_b": { + "lat": -7.00667, + "lon": 39.29849, + "name": "Vikindu" + }, + "ground_truth": { + "initial_bearing_deg": 262.8, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Palmerston at (-12.48602°, 130.9833°)", + " To: Vikindu at (-7.00667°, 39.29849°)", + "Step 2: Calculate longitude difference", + " Δlon = 39.29849 - 130.9833 = -91.6848°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 262.80°", + "Step 5: Determine cardinal direction", + " 262.8° → W", + "FINAL ANSWER: 262.80° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 12.33042, + "lon": 76.60213, + "name": "Hinakallu" + }, + "point_b": { + "lat": 34.41639, + "lon": 117.36306, + "name": "Qingshanquan" + }, + "ground_truth": { + "initial_bearing_deg": 52.14, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Hinakallu at (12.33042°, 76.60213°)", + " To: Qingshanquan at (34.41639°, 117.36306°)", + "Step 2: Calculate longitude difference", + " Δlon = 117.36306 - 76.60213 = 40.7609°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 52.14°", + "Step 5: Determine cardinal direction", + " 52.1° → NE", + "FINAL ANSWER: 52.14° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 32.46367, + "lon": 44.41963, + "name": "Al Ḩillah" + }, + "point_b": { + "lat": 48.96833, + "lon": 89.9625, + "name": "Ölgii" + }, + "ground_truth": { + "initial_bearing_deg": 50.25, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Al Ḩillah at (32.46367°, 44.41963°)", + " To: Ölgii at (48.96833°, 89.9625°)", + "Step 2: Calculate longitude difference", + " Δlon = 89.9625 - 44.41963 = 45.5429°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 50.25°", + "Step 5: Determine cardinal direction", + " 50.2° → NE", + "FINAL ANSWER: 50.25° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 14.8888, + "lon": 5.2692, + "name": "Tahoua" + }, + "point_b": { + "lat": 25.7076, + "lon": -80.32561, + "name": "Glenvar Heights" + }, + "ground_truth": { + "initial_bearing_deg": 294.08, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Tahoua at (14.8888°, 5.2692°)", + " To: Glenvar Heights at (25.7076°, -80.32561°)", + "Step 2: Calculate longitude difference", + " Δlon = -80.32561 - 5.2692 = -85.5948°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 294.08°", + "Step 5: Determine cardinal direction", + " 294.1° → NW", + "FINAL ANSWER: 294.08° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 41.92208, + "lon": 21.53483, + "name": "Studeničani" + }, + "point_b": { + "lat": 7.43383, + "lon": 3.28788, + "name": "Igbo-Ora" + }, + "ground_truth": { + "initial_bearing_deg": 210.23, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Studeničani at (41.92208°, 21.53483°)", + " To: Igbo-Ora at (7.43383°, 3.28788°)", + "Step 2: Calculate longitude difference", + " Δlon = 3.28788 - 21.53483 = -18.2469°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 210.23°", + "Step 5: Determine cardinal direction", + " 210.2° → SW", + "FINAL ANSWER: 210.23° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 47.48919, + "lon": 19.07012, + "name": "Budapest VIII. kerület" + }, + "point_b": { + "lat": 20.21081, + "lon": -101.13212, + "name": "Yuriria" + }, + "ground_truth": { + "initial_bearing_deg": 305.64, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Budapest VIII. kerület at (47.48919°, 19.07012°)", + " To: Yuriria at (20.21081°, -101.13212°)", + "Step 2: Calculate longitude difference", + " Δlon = -101.13212 - 19.07012 = -120.2022°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 305.64°", + "Step 5: Determine cardinal direction", + " 305.6° → NW", + "FINAL ANSWER: 305.64° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 7.3, + "lon": 38.65, + "name": "Kuyera" + }, + "point_b": { + "lat": 1.99546, + "lon": 112.93254, + "name": "Kapit" + }, + "ground_truth": { + "initial_bearing_deg": 89.99, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Kuyera at (7.3°, 38.65°)", + " To: Kapit at (1.99546°, 112.93254°)", + "Step 2: Calculate longitude difference", + " Δlon = 112.93254 - 38.65 = 74.2825°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 89.99°", + "Step 5: Determine cardinal direction", + " 90.0° → E", + "FINAL ANSWER: 89.99° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 22.70256, + "lon": 77.93494, + "name": "Bābai" + }, + "point_b": { + "lat": 52.3475, + "lon": 5.98333, + "name": "Epe" + }, + "ground_truth": { + "initial_bearing_deg": 318.54, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Bābai at (22.70256°, 77.93494°)", + " To: Epe at (52.3475°, 5.98333°)", + "Step 2: Calculate longitude difference", + " Δlon = 5.98333 - 77.93494 = -71.9516°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 318.54°", + "Step 5: Determine cardinal direction", + " 318.5° → NW", + "FINAL ANSWER: 318.54° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 44.54394, + "lon": -73.14791, + "name": "Colchester" + }, + "point_b": { + "lat": 0.29517, + "lon": 32.50159, + "name": "Kyengera" + }, + "ground_truth": { + "initial_bearing_deg": 78.67, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Colchester at (44.54394°, -73.14791°)", + " To: Kyengera at (0.29517°, 32.50159°)", + "Step 2: Calculate longitude difference", + " Δlon = 32.50159 - -73.14791 = 105.6495°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 78.67°", + "Step 5: Determine cardinal direction", + " 78.7° → E", + "FINAL ANSWER: 78.67° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 14.76011, + "lon": 121.19993, + "name": "Rodriguez" + }, + "point_b": { + "lat": -37.78247, + "lon": 145.31682, + "name": "Mooroolbark" + }, + "ground_truth": { + "initial_bearing_deg": 157.41, + "cardinal_direction": "SE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Rodriguez at (14.76011°, 121.19993°)", + " To: Mooroolbark at (-37.78247°, 145.31682°)", + "Step 2: Calculate longitude difference", + " Δlon = 145.31682 - 121.19993 = 24.1169°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 157.41°", + "Step 5: Determine cardinal direction", + " 157.4° → SE", + "FINAL ANSWER: 157.41° (SE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 11.0517, + "lon": 124.0055, + "name": "Bogo" + }, + "point_b": { + "lat": 51.28087, + "lon": 4.41813, + "name": "Ekeren" + }, + "ground_truth": { + "initial_bearing_deg": 326.6, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Bogo at (11.0517°, 124.0055°)", + " To: Ekeren at (51.28087°, 4.41813°)", + "Step 2: Calculate longitude difference", + " Δlon = 4.41813 - 124.0055 = -119.5874°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 326.60°", + "Step 5: Determine cardinal direction", + " 326.6° → NW", + "FINAL ANSWER: 326.60° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 35.9132, + "lon": -79.05584, + "name": "Chapel Hill" + }, + "point_b": { + "lat": 38.96872, + "lon": -77.3411, + "name": "Reston" + }, + "ground_truth": { + "initial_bearing_deg": 23.5, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Chapel Hill at (35.9132°, -79.05584°)", + " To: Reston at (38.96872°, -77.3411°)", + "Step 2: Calculate longitude difference", + " Δlon = -77.3411 - -79.05584 = 1.7147°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 23.50°", + "Step 5: Determine cardinal direction", + " 23.5° → NE", + "FINAL ANSWER: 23.50° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 31.61667, + "lon": -2.21667, + "name": "Béchar" + }, + "point_b": { + "lat": -1.52823, + "lon": -45.07862, + "name": "Apicum-Açu" + }, + "ground_truth": { + "initial_bearing_deg": 239.11, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Béchar at (31.61667°, -2.21667°)", + " To: Apicum-Açu at (-1.52823°, -45.07862°)", + "Step 2: Calculate longitude difference", + " Δlon = -45.07862 - -2.21667 = -42.8620°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 239.11°", + "Step 5: Determine cardinal direction", + " 239.1° → SW", + "FINAL ANSWER: 239.11° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 31.50777, + "lon": 35.02929, + "name": "Dūrā" + }, + "point_b": { + "lat": 45.84806, + "lon": 62.15254, + "name": "Novokazalinsk" + }, + "ground_truth": { + "initial_bearing_deg": 47.82, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Dūrā at (31.50777°, 35.02929°)", + " To: Novokazalinsk at (45.84806°, 62.15254°)", + "Step 2: Calculate longitude difference", + " Δlon = 62.15254 - 35.02929 = 27.1232°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 47.82°", + "Step 5: Determine cardinal direction", + " 47.8° → NE", + "FINAL ANSWER: 47.82° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -20.03841, + "lon": 57.65055, + "name": "Goodlands" + }, + "point_b": { + "lat": 26.71194, + "lon": 107.81139, + "name": "Dafengdong" + }, + "ground_truth": { + "initial_bearing_deg": 47.96, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Goodlands at (-20.03841°, 57.65055°)", + " To: Dafengdong at (26.71194°, 107.81139°)", + "Step 2: Calculate longitude difference", + " Δlon = 107.81139 - 57.65055 = 50.1608°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 47.96°", + "Step 5: Determine cardinal direction", + " 48.0° → NE", + "FINAL ANSWER: 47.96° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -25.699, + "lon": 27.47475, + "name": "Marikana" + }, + "point_b": { + "lat": -19.57328, + "lon": 18.1003, + "name": "Grootfontein" + }, + "ground_truth": { + "initial_bearing_deg": 303.41, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Marikana at (-25.699°, 27.47475°)", + " To: Grootfontein at (-19.57328°, 18.1003°)", + "Step 2: Calculate longitude difference", + " Δlon = 18.1003 - 27.47475 = -9.3744°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 303.41°", + "Step 5: Determine cardinal direction", + " 303.4° → NW", + "FINAL ANSWER: 303.41° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 55.32058, + "lon": 42.17402, + "name": "Vyksa" + }, + "point_b": { + "lat": 1.30306, + "lon": 103.90778, + "name": "Marine Parade" + }, + "ground_truth": { + "initial_bearing_deg": 113.15, + "cardinal_direction": "SE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Vyksa at (55.32058°, 42.17402°)", + " To: Marine Parade at (1.30306°, 103.90778°)", + "Step 2: Calculate longitude difference", + " Δlon = 103.90778 - 42.17402 = 61.7338°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 113.15°", + "Step 5: Determine cardinal direction", + " 113.2° → SE", + "FINAL ANSWER: 113.15° (SE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 48.89452, + "lon": 18.04436, + "name": "Trenčín" + }, + "point_b": { + "lat": 16.455, + "lon": 120.5875, + "name": "La Trinidad" + }, + "ground_truth": { + "initial_bearing_deg": 69.87, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Trenčín at (48.89452°, 18.04436°)", + " To: La Trinidad at (16.455°, 120.5875°)", + "Step 2: Calculate longitude difference", + " Δlon = 120.5875 - 18.04436 = 102.5431°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 69.87°", + "Step 5: Determine cardinal direction", + " 69.9° → E", + "FINAL ANSWER: 69.87° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 19.15633, + "lon": 96.34593, + "name": "Yedashe" + }, + "point_b": { + "lat": 56.1, + "lon": 38.13333, + "name": "Krasnoarmeysk" + }, + "ground_truth": { + "initial_bearing_deg": 325.42, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Yedashe at (19.15633°, 96.34593°)", + " To: Krasnoarmeysk at (56.1°, 38.13333°)", + "Step 2: Calculate longitude difference", + " Δlon = 38.13333 - 96.34593 = -58.2126°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 325.42°", + "Step 5: Determine cardinal direction", + " 325.4° → NW", + "FINAL ANSWER: 325.42° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 41.11919, + "lon": 70.09406, + "name": "Yangiobod" + }, + "point_b": { + "lat": 15.42977, + "lon": 75.62971, + "name": "Gadag" + }, + "ground_truth": { + "initial_bearing_deg": 167.81, + "cardinal_direction": "S", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Yangiobod at (41.11919°, 70.09406°)", + " To: Gadag at (15.42977°, 75.62971°)", + "Step 2: Calculate longitude difference", + " Δlon = 75.62971 - 70.09406 = 5.5357°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 167.81°", + "Step 5: Determine cardinal direction", + " 167.8° → S", + "FINAL ANSWER: 167.81° (S)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -12.46113, + "lon": 130.84185, + "name": "Darwin" + }, + "point_b": { + "lat": 13.69889, + "lon": 100.51244, + "name": "Bang Khlo" + }, + "ground_truth": { + "initial_bearing_deg": 310.04, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Darwin at (-12.46113°, 130.84185°)", + " To: Bang Khlo at (13.69889°, 100.51244°)", + "Step 2: Calculate longitude difference", + " Δlon = 100.51244 - 130.84185 = -30.3294°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 310.04°", + "Step 5: Determine cardinal direction", + " 310.0° → NW", + "FINAL ANSWER: 310.04° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -37.8329, + "lon": 145.0367, + "name": "Hawthorn South" + }, + "point_b": { + "lat": 14.42196, + "lon": -16.96375, + "name": "Mbour" + }, + "ground_truth": { + "initial_bearing_deg": 219.1, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Hawthorn South at (-37.8329°, 145.0367°)", + " To: Mbour at (14.42196°, -16.96375°)", + "Step 2: Calculate longitude difference", + " Δlon = -16.96375 - 145.0367 = -162.0005°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 219.10°", + "Step 5: Determine cardinal direction", + " 219.1° → SW", + "FINAL ANSWER: 219.10° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 35.53227, + "lon": -97.95505, + "name": "El Reno" + }, + "point_b": { + "lat": -37.76722, + "lon": 144.76657, + "name": "Deer Park" + }, + "ground_truth": { + "initial_bearing_deg": 247.72, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: El Reno at (35.53227°, -97.95505°)", + " To: Deer Park at (-37.76722°, 144.76657°)", + "Step 2: Calculate longitude difference", + " Δlon = 144.76657 - -97.95505 = 242.7216°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 247.72°", + "Step 5: Determine cardinal direction", + " 247.7° → W", + "FINAL ANSWER: 247.72° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 53.14362, + "lon": 0.3363, + "name": "Skegness" + }, + "point_b": { + "lat": 8.13333, + "lon": 81.43333, + "name": "Vakarai" + }, + "ground_truth": { + "initial_bearing_deg": 92.21, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Skegness at (53.14362°, 0.3363°)", + " To: Vakarai at (8.13333°, 81.43333°)", + "Step 2: Calculate longitude difference", + " Δlon = 81.43333 - 0.3363 = 81.0970°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 92.21°", + "Step 5: Determine cardinal direction", + " 92.2° → E", + "FINAL ANSWER: 92.21° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 43.30491, + "lon": 13.72068, + "name": "Civitanova Marche" + }, + "point_b": { + "lat": 8.75225, + "lon": 38.97846, + "name": "Bishoftu" + }, + "ground_truth": { + "initial_bearing_deg": 139.99, + "cardinal_direction": "SE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Civitanova Marche at (43.30491°, 13.72068°)", + " To: Bishoftu at (8.75225°, 38.97846°)", + "Step 2: Calculate longitude difference", + " Δlon = 38.97846 - 13.72068 = 25.2578°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 139.99°", + "Step 5: Determine cardinal direction", + " 140.0° → SE", + "FINAL ANSWER: 139.99° (SE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -8.57472, + "lon": -36.87417, + "name": "Venturosa" + }, + "point_b": { + "lat": 12.24661, + "lon": -1.58402, + "name": "Zinguédéssé" + }, + "ground_truth": { + "initial_bearing_deg": 59.79, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Venturosa at (-8.57472°, -36.87417°)", + " To: Zinguédéssé at (12.24661°, -1.58402°)", + "Step 2: Calculate longitude difference", + " Δlon = -1.58402 - -36.87417 = 35.2901°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 59.79°", + "Step 5: Determine cardinal direction", + " 59.8° → NE", + "FINAL ANSWER: 59.79° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 34.50344, + "lon": -82.65013, + "name": "Anderson" + }, + "point_b": { + "lat": 35.33638, + "lon": 139.40434, + "name": "Chigasaki" + }, + "ground_truth": { + "initial_bearing_deg": 326.31, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Anderson at (34.50344°, -82.65013°)", + " To: Chigasaki at (35.33638°, 139.40434°)", + "Step 2: Calculate longitude difference", + " Δlon = 139.40434 - -82.65013 = 222.0545°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 326.31°", + "Step 5: Determine cardinal direction", + " 326.3° → NW", + "FINAL ANSWER: 326.31° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 9.95689, + "lon": -84.03209, + "name": "Purral" + }, + "point_b": { + "lat": 35.84509, + "lon": 127.14752, + "name": "Wanju" + }, + "ground_truth": { + "initial_bearing_deg": 328.94, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Purral at (9.95689°, -84.03209°)", + " To: Wanju at (35.84509°, 127.14752°)", + "Step 2: Calculate longitude difference", + " Δlon = 127.14752 - -84.03209 = 211.1796°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 328.94°", + "Step 5: Determine cardinal direction", + " 328.9° → NW", + "FINAL ANSWER: 328.94° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -25.85583, + "lon": -52.52333, + "name": "Chopinzinho" + }, + "point_b": { + "lat": 7.82719, + "lon": 6.07502, + "name": "Kabba" + }, + "ground_truth": { + "initial_bearing_deg": 67.65, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Chopinzinho at (-25.85583°, -52.52333°)", + " To: Kabba at (7.82719°, 6.07502°)", + "Step 2: Calculate longitude difference", + " Δlon = 6.07502 - -52.52333 = 58.5984°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 67.65°", + "Step 5: Determine cardinal direction", + " 67.7° → E", + "FINAL ANSWER: 67.65° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 8.91587, + "lon": 17.55046, + "name": "Koumra" + }, + "point_b": { + "lat": -17.345, + "lon": -44.94194, + "name": "Pirapora" + }, + "ground_truth": { + "initial_bearing_deg": 246.8, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Koumra at (8.91587°, 17.55046°)", + " To: Pirapora at (-17.345°, -44.94194°)", + "Step 2: Calculate longitude difference", + " Δlon = -44.94194 - 17.55046 = -62.4924°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 246.80°", + "Step 5: Determine cardinal direction", + " 246.8° → SW", + "FINAL ANSWER: 246.80° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 36.81058, + "lon": 10.13481, + "name": "Le Bardo" + }, + "point_b": { + "lat": -33.88834, + "lon": 151.12274, + "name": "Ashfield" + }, + "ground_truth": { + "initial_bearing_deg": 96.54, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Le Bardo at (36.81058°, 10.13481°)", + " To: Ashfield at (-33.88834°, 151.12274°)", + "Step 2: Calculate longitude difference", + " Δlon = 151.12274 - 10.13481 = 140.9879°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 96.54°", + "Step 5: Determine cardinal direction", + " 96.5° → E", + "FINAL ANSWER: 96.54° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 36.45833, + "lon": 7.51389, + "name": "Boumahra Ahmed" + }, + "point_b": { + "lat": 25.53852, + "lon": 87.57044, + "name": "Katihar" + }, + "ground_truth": { + "initial_bearing_deg": 74.04, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Boumahra Ahmed at (36.45833°, 7.51389°)", + " To: Katihar at (25.53852°, 87.57044°)", + "Step 2: Calculate longitude difference", + " Δlon = 87.57044 - 7.51389 = 80.0566°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 74.04°", + "Step 5: Determine cardinal direction", + " 74.0° → E", + "FINAL ANSWER: 74.04° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 42.07593, + "lon": 21.05179, + "name": "Tearce" + }, + "point_b": { + "lat": 36.76639, + "lon": 3.47717, + "name": "Boumerdas" + }, + "ground_truth": { + "initial_bearing_deg": 254.41, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Tearce at (42.07593°, 21.05179°)", + " To: Boumerdas at (36.76639°, 3.47717°)", + "Step 2: Calculate longitude difference", + " Δlon = 3.47717 - 21.05179 = -17.5746°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 254.41°", + "Step 5: Determine cardinal direction", + " 254.4° → W", + "FINAL ANSWER: 254.41° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -6.7559, + "lon": 111.038, + "name": "Pati" + }, + "point_b": { + "lat": 55.86661, + "lon": 48.35931, + "name": "Volzhsk" + }, + "ground_truth": { + "initial_bearing_deg": 329.68, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Pati at (-6.7559°, 111.038°)", + " To: Volzhsk at (55.86661°, 48.35931°)", + "Step 2: Calculate longitude difference", + " Δlon = 48.35931 - 111.038 = -62.6787°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 329.68°", + "Step 5: Determine cardinal direction", + " 329.7° → NW", + "FINAL ANSWER: 329.68° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 6.84684, + "lon": -1.39612, + "name": "Effiduase" + }, + "point_b": { + "lat": 52.80842, + "lon": 17.19961, + "name": "Wągrowiec" + }, + "ground_truth": { + "initial_bearing_deg": 14.94, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Effiduase at (6.84684°, -1.39612°)", + " To: Wągrowiec at (52.80842°, 17.19961°)", + "Step 2: Calculate longitude difference", + " Δlon = 17.19961 - -1.39612 = 18.5957°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 14.94°", + "Step 5: Determine cardinal direction", + " 14.9° → N", + "FINAL ANSWER: 14.94° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -26.8089, + "lon": -55.02147, + "name": "Puerto Rico" + }, + "point_b": { + "lat": -4.85889, + "lon": -43.35611, + "name": "Caxias" + }, + "ground_truth": { + "initial_bearing_deg": 28.93, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Puerto Rico at (-26.8089°, -55.02147°)", + " To: Caxias at (-4.85889°, -43.35611°)", + "Step 2: Calculate longitude difference", + " Δlon = -43.35611 - -55.02147 = 11.6654°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat��) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 28.93°", + "Step 5: Determine cardinal direction", + " 28.9° → NE", + "FINAL ANSWER: 28.93° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 36.84774, + "lon": 10.11083, + "name": "Mnihla" + }, + "point_b": { + "lat": 29.90565, + "lon": 107.63853, + "name": "Huwei" + }, + "ground_truth": { + "initial_bearing_deg": 61.48, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Mnihla at (36.84774°, 10.11083°)", + " To: Huwei at (29.90565°, 107.63853°)", + "Step 2: Calculate longitude difference", + " Δlon = 107.63853 - 10.11083 = 97.5277°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 61.48°", + "Step 5: Determine cardinal direction", + " 61.5° → NE", + "FINAL ANSWER: 61.48° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -3.50306, + "lon": -80.27306, + "name": "Zarumilla" + }, + "point_b": { + "lat": 39.98111, + "lon": 125.24472, + "name": "Kusŏng" + }, + "ground_truth": { + "initial_bearing_deg": 331.15, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Zarumilla at (-3.50306°, -80.27306°)", + " To: Kusŏng at (39.98111°, 125.24472°)", + "Step 2: Calculate longitude difference", + " Δlon = 125.24472 - -80.27306 = 205.5178°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 331.15°", + "Step 5: Determine cardinal direction", + " 331.1° → NW", + "FINAL ANSWER: 331.15° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 41.13121, + "lon": -74.36737, + "name": "West Milford" + }, + "point_b": { + "lat": 36.82657, + "lon": 10.08974, + "name": "Douar Hicher" + }, + "ground_truth": { + "initial_bearing_deg": 63.31, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: West Milford at (41.13121°, -74.36737°)", + " To: Douar Hicher at (36.82657°, 10.08974°)", + "Step 2: Calculate longitude difference", + " Δlon = 10.08974 - -74.36737 = 84.4571°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 63.31°", + "Step 5: Determine cardinal direction", + " 63.3° → NE", + "FINAL ANSWER: 63.31° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 28.23937, + "lon": 75.64035, + "name": "Chidawa" + }, + "point_b": { + "lat": 39.42417, + "lon": 29.98333, + "name": "Kütahya" + }, + "ground_truth": { + "initial_bearing_deg": 298.82, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Chidawa at (28.23937°, 75.64035°)", + " To: Kütahya at (39.42417°, 29.98333°)", + "Step 2: Calculate longitude difference", + " Δlon = 29.98333 - 75.64035 = -45.6570°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 298.82°", + "Step 5: Determine cardinal direction", + " 298.8° → NW", + "FINAL ANSWER: 298.82° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -18.06354, + "lon": 44.02951, + "name": "Maintirano" + }, + "point_b": { + "lat": 35.79154, + "lon": -78.78112, + "name": "Cary" + }, + "ground_truth": { + "initial_bearing_deg": 301.62, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Maintirano at (-18.06354°, 44.02951°)", + " To: Cary at (35.79154°, -78.78112°)", + "Step 2: Calculate longitude difference", + " Δlon = -78.78112 - 44.02951 = -122.8106°", + "Step 3: Apply bearing formula", + " �� = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 301.62°", + "Step 5: Determine cardinal direction", + " 301.6° → NW", + "FINAL ANSWER: 301.62° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -38.0965, + "lon": 145.26707, + "name": "Cranbourne West" + }, + "point_b": { + "lat": -23.56729, + "lon": -46.69232, + "name": "Pinheiros" + }, + "ground_truth": { + "initial_bearing_deg": 167.66, + "cardinal_direction": "S", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Cranbourne West at (-38.0965°, 145.26707°)", + " To: Pinheiros at (-23.56729°, -46.69232°)", + "Step 2: Calculate longitude difference", + " Δlon = -46.69232 - 145.26707 = -191.9594°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 167.66°", + "Step 5: Determine cardinal direction", + " 167.7° → S", + "FINAL ANSWER: 167.66° (S)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 38.93067, + "lon": -77.04081, + "name": "Mount Pleasant" + }, + "point_b": { + "lat": 36.53628, + "lon": 3.8334, + "name": "Draa el Mizan" + }, + "ground_truth": { + "initial_bearing_deg": 64.23, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Mount Pleasant at (38.93067°, -77.04081°)", + " To: Draa el Mizan at (36.53628°, 3.8334°)", + "Step 2: Calculate longitude difference", + " Δlon = 3.8334 - -77.04081 = 80.8742°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 64.23°", + "Step 5: Determine cardinal direction", + " 64.2° → NE", + "FINAL ANSWER: 64.23° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 42.34166, + "lon": 130.41081, + "name": "Unggi" + }, + "point_b": { + "lat": 53.82901, + "lon": -1.53834, + "name": "Chapel Allerton" + }, + "ground_truth": { + "initial_bearing_deg": 333.02, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Unggi at (42.34166°, 130.41081°)", + " To: Chapel Allerton at (53.82901°, -1.53834°)", + "Step 2: Calculate longitude difference", + " Δlon = -1.53834 - 130.41081 = -131.9492°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 333.02°", + "Step 5: Determine cardinal direction", + " 333.0° → NW", + "FINAL ANSWER: 333.02° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 27.6327, + "lon": 85.52201, + "name": "Banepā" + }, + "point_b": { + "lat": 19.11683, + "lon": -70.63595, + "name": "Jarabacoa" + }, + "ground_truth": { + "initial_bearing_deg": 331.07, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Banepā at (27.6327°, 85.52201°)", + " To: Jarabacoa at (19.11683°, -70.63595°)", + "Step 2: Calculate longitude difference", + " Δlon = -70.63595 - 85.52201 = -156.1580°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 331.07°", + "Step 5: Determine cardinal direction", + " 331.1° → NW", + "FINAL ANSWER: 331.07° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 36.74445, + "lon": 49.40082, + "name": "Manjīl" + }, + "point_b": { + "lat": 10.3258, + "lon": -72.31343, + "name": "La Villa del Rosario" + }, + "ground_truth": { + "initial_bearing_deg": 298.43, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Manjīl at (36.74445°, 49.40082°)", + " To: La Villa del Rosario at (10.3258°, -72.31343°)", + "Step 2: Calculate longitude difference", + " Δlon = -72.31343 - 49.40082 = -121.7142°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 298.43°", + "Step 5: Determine cardinal direction", + " 298.4° → NW", + "FINAL ANSWER: 298.43° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -18.14307, + "lon": 177.50691, + "name": "Sigatoka" + }, + "point_b": { + "lat": -36.96807, + "lon": 174.79875, + "name": "Mangere" + }, + "ground_truth": { + "initial_bearing_deg": 186.67, + "cardinal_direction": "S", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Sigatoka at (-18.14307°, 177.50691°)", + " To: Mangere at (-36.96807°, 174.79875°)", + "Step 2: Calculate longitude difference", + " Δlon = 174.79875 - 177.50691 = -2.7082°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 186.67°", + "Step 5: Determine cardinal direction", + " 186.7° → S", + "FINAL ANSWER: 186.67° (S)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 31.07287, + "lon": 31.49503, + "name": "Maḩallat Damanah" + }, + "point_b": { + "lat": 60.26711, + "lon": 24.84713, + "name": "Myyrmäki" + }, + "ground_truth": { + "initial_bearing_deg": 353.31, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Maḩallat Damanah at (31.07287°, 31.49503°)", + " To: Myyrmäki at (60.26711°, 24.84713°)", + "Step 2: Calculate longitude difference", + " Δlon = 24.84713 - 31.49503 = -6.6479°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 353.31°", + "Step 5: Determine cardinal direction", + " 353.3° → N", + "FINAL ANSWER: 353.31° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 50.31297, + "lon": 11.91261, + "name": "Hof" + }, + "point_b": { + "lat": 42.21421, + "lon": -83.14992, + "name": "Wyandotte" + }, + "ground_truth": { + "initial_bearing_deg": 303.01, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Hof at (50.31297°, 11.91261°)", + " To: Wyandotte at (42.21421°, -83.14992°)", + "Step 2: Calculate longitude difference", + " Δlon = -83.14992 - 11.91261 = -95.0625°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 303.01°", + "Step 5: Determine cardinal direction", + " 303.0° → NW", + "FINAL ANSWER: 303.01° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 10.09085, + "lon": -5.19482, + "name": "Kaouara" + }, + "point_b": { + "lat": 55.75, + "lon": -4.03333, + "name": "Meikle Earnock" + }, + "ground_truth": { + "initial_bearing_deg": 0.91, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Kaouara at (10.09085°, -5.19482°)", + " To: Meikle Earnock at (55.75°, -4.03333°)", + "Step 2: Calculate longitude difference", + " Δlon = -4.03333 - -5.19482 = 1.1615°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 0.91°", + "Step 5: Determine cardinal direction", + " 0.9° → N", + "FINAL ANSWER: 0.91° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 25.42595, + "lon": -100.97963, + "name": "Saltillo" + }, + "point_b": { + "lat": 50.93333, + "lon": 6.95, + "name": "Köln" + }, + "ground_truth": { + "initial_bearing_deg": 37.39, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Saltillo at (25.42595°, -100.97963°)", + " To: Köln at (50.93333°, 6.95°)", + "Step 2: Calculate longitude difference", + " Δlon = 6.95 - -100.97963 = 107.9296°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 37.39°", + "Step 5: Determine cardinal direction", + " 37.4° → NE", + "FINAL ANSWER: 37.39° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -17.13806, + "lon": -49.98806, + "name": "Indiara" + }, + "point_b": { + "lat": 38.63706, + "lon": -77.31109, + "name": "Dale City" + }, + "ground_truth": { + "initial_bearing_deg": 335.89, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Indiara at (-17.13806°, -49.98806°)", + " To: Dale City at (38.63706°, -77.31109°)", + "Step 2: Calculate longitude difference", + " Δlon = -77.31109 - -49.98806 = -27.3230°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 335.89°", + "Step 5: Determine cardinal direction", + " 335.9° → NW", + "FINAL ANSWER: 335.89° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 27.23818, + "lon": 111.46214, + "name": "Shaoyang" + }, + "point_b": { + "lat": 37.66442, + "lon": 139.03502, + "name": "Kamo" + }, + "ground_truth": { + "initial_bearing_deg": 58.78, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Shaoyang at (27.23818°, 111.46214°)", + " To: Kamo at (37.66442°, 139.03502°)", + "Step 2: Calculate longitude difference", + " Δlon = 139.03502 - 111.46214 = 27.5729°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 58.78°", + "Step 5: Determine cardinal direction", + " 58.8° → NE", + "FINAL ANSWER: 58.78° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -22.88583, + "lon": -48.445, + "name": "Botucatu" + }, + "point_b": { + "lat": 21.11667, + "lon": 105.86667, + "name": "Cổ Lóa" + }, + "ground_truth": { + "initial_bearing_deg": 89.29, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Botucatu at (-22.88583°, -48.445°)", + " To: Cổ Lóa at (21.11667°, 105.86667°)", + "Step 2: Calculate longitude difference", + " Δlon = 105.86667 - -48.445 = 154.3117°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 89.29°", + "Step 5: Determine cardinal direction", + " 89.3° → E", + "FINAL ANSWER: 89.29° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -3.45571, + "lon": -79.9637, + "name": "Santa Rosa" + }, + "point_b": { + "lat": 22.34835, + "lon": 73.13313, + "name": "Undera" + }, + "ground_truth": { + "initial_bearing_deg": 51.76, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Santa Rosa at (-3.45571°, -79.9637°)", + " To: Undera at (22.34835°, 73.13313°)", + "Step 2: Calculate longitude difference", + " Δlon = 73.13313 - -79.9637 = 153.0968°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 51.76°", + "Step 5: Determine cardinal direction", + " 51.8° → NE", + "FINAL ANSWER: 51.76° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 40.9983, + "lon": 71.67257, + "name": "Namangan" + }, + "point_b": { + "lat": 36.53628, + "lon": 3.8334, + "name": "Draa el Mizan" + }, + "ground_truth": { + "initial_bearing_deg": 288.6, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Namangan at (40.9983°, 71.67257°)", + " To: Draa el Mizan at (36.53628°, 3.8334°)", + "Step 2: Calculate longitude difference", + " Δlon = 3.8334 - 71.67257 = -67.8392°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 288.60°", + "Step 5: Determine cardinal direction", + " 288.6° → W", + "FINAL ANSWER: 288.60° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -33.92399, + "lon": 151.22749, + "name": "Kingsford" + }, + "point_b": { + "lat": 37.3625, + "lon": 38.52667, + "name": "Bozova" + }, + "ground_truth": { + "initial_bearing_deg": 294.38, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Kingsford at (-33.92399°, 151.22749°)", + " To: Bozova at (37.3625°, 38.52667°)", + "Step 2: Calculate longitude difference", + " Δlon = 38.52667 - 151.22749 = -112.7008°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 294.38°", + "Step 5: Determine cardinal direction", + " 294.4° → NW", + "FINAL ANSWER: 294.38° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 39.30927, + "lon": -76.47496, + "name": "Essex" + }, + "point_b": { + "lat": -21.28861, + "lon": -50.34, + "name": "Birigui" + }, + "ground_truth": { + "initial_bearing_deg": 153.15, + "cardinal_direction": "SE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Essex at (39.30927°, -76.47496°)", + " To: Birigui at (-21.28861°, -50.34°)", + "Step 2: Calculate longitude difference", + " Δlon = -50.34 - -76.47496 = 26.1350°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 153.15°", + "Step 5: Determine cardinal direction", + " 153.2° → SE", + "FINAL ANSWER: 153.15° (SE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -33.36889, + "lon": 19.31095, + "name": "Ceres" + }, + "point_b": { + "lat": 51.95951, + "lon": 4.54533, + "name": "Ommoord" + }, + "ground_truth": { + "initial_bearing_deg": 350.95, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Ceres at (-33.36889°, 19.31095°)", + " To: Ommoord at (51.95951°, 4.54533°)", + "Step 2: Calculate longitude difference", + " Δlon = 4.54533 - 19.31095 = -14.7656°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 350.95°", + "Step 5: Determine cardinal direction", + " 350.9° → N", + "FINAL ANSWER: 350.95° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 4.775, + "lon": 103.4162, + "name": "Dungun" + }, + "point_b": { + "lat": 51.22134, + "lon": 4.46595, + "name": "Deurne" + }, + "ground_truth": { + "initial_bearing_deg": 321.76, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Dungun at (4.775°, 103.4162°)", + " To: Deurne at (51.22134°, 4.46595°)", + "Step 2: Calculate longitude difference", + " Δlon = 4.46595 - 103.4162 = -98.9502°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 321.76°", + "Step 5: Determine cardinal direction", + " 321.8° → NW", + "FINAL ANSWER: 321.76° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 13.74155, + "lon": 76.9043, + "name": "Sīra" + }, + "point_b": { + "lat": -2.93323, + "lon": 10.98178, + "name": "Tchibanga" + }, + "ground_truth": { + "initial_bearing_deg": 260.87, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Sīra at (13.74155°, 76.9043°)", + " To: Tchibanga at (-2.93323°, 10.98178°)", + "Step 2: Calculate longitude difference", + " Δlon = 10.98178 - 76.9043 = -65.9225°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 260.87°", + "Step 5: Determine cardinal direction", + " 260.9° → W", + "FINAL ANSWER: 260.87° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 22.2475, + "lon": -97.83665, + "name": "Ciudad Madero" + }, + "point_b": { + "lat": 34.92915, + "lon": 43.48878, + "name": "Bayjī" + }, + "ground_truth": { + "initial_bearing_deg": 33.56, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Ciudad Madero at (22.2475°, -97.83665°)", + " To: Bayjī at (34.92915°, 43.48878°)", + "Step 2: Calculate longitude difference", + " Δlon = 43.48878 - -97.83665 = 141.3254°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 33.56°", + "Step 5: Determine cardinal direction", + " 33.6° → NE", + "FINAL ANSWER: 33.56° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 38.05, + "lon": 23.83333, + "name": "Melíssia" + }, + "point_b": { + "lat": 13.83446, + "lon": 44.11469, + "name": "Dhī as Sufāl" + }, + "ground_truth": { + "initial_bearing_deg": 137.94, + "cardinal_direction": "SE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Melíssia at (38.05°, 23.83333°)", + " To: Dhī as Sufāl at (13.83446°, 44.11469°)", + "Step 2: Calculate longitude difference", + " Δlon = 44.11469 - 23.83333 = 20.2814°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 137.94°", + "Step 5: Determine cardinal direction", + " 137.9° → SE", + "FINAL ANSWER: 137.94° (SE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 50.3505, + "lon": 14.47411, + "name": "Mělník" + }, + "point_b": { + "lat": 25.27139, + "lon": 55.30323, + "name": "Nāyf" + }, + "ground_truth": { + "initial_bearing_deg": 113.28, + "cardinal_direction": "SE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Mělník at (50.3505°, 14.47411°)", + " To: Nāyf at (25.27139°, 55.30323°)", + "Step 2: Calculate longitude difference", + " Δlon = 55.30323 - 14.47411 = 40.8291°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 113.28°", + "Step 5: Determine cardinal direction", + " 113.3° → SE", + "FINAL ANSWER: 113.28° (SE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 13.4, + "lon": -14.21667, + "name": "Farato" + }, + "point_b": { + "lat": 25.13994, + "lon": 85.84096, + "name": "Sheikhpura" + }, + "ground_truth": { + "initial_bearing_deg": 63.22, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Farato at (13.4°, -14.21667°)", + " To: Sheikhpura at (25.13994°, 85.84096°)", + "Step 2: Calculate longitude difference", + " Δlon = 85.84096 - -14.21667 = 100.0576°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 63.22°", + "Step 5: Determine cardinal direction", + " 63.2° → NE", + "FINAL ANSWER: 63.22° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 36.80377, + "lon": 7.73684, + "name": "El Hadjar" + }, + "point_b": { + "lat": -37.66667, + "lon": 145.01667, + "name": "Lalor" + }, + "ground_truth": { + "initial_bearing_deg": 104.7, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: El Hadjar at (36.80377°, 7.73684°)", + " To: Lalor at (-37.66667°, 145.01667°)", + "Step 2: Calculate longitude difference", + " Δlon = 145.01667 - 7.73684 = 137.2798°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 104.70°", + "Step 5: Determine cardinal direction", + " 104.7° → E", + "FINAL ANSWER: 104.70° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 36.92917, + "lon": 6.58556, + "name": "Kerkera" + }, + "point_b": { + "lat": 51.55295, + "lon": 0.55962, + "name": "South Benfleet" + }, + "ground_truth": { + "initial_bearing_deg": 345.62, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Kerkera at (36.92917°, 6.58556°)", + " To: South Benfleet at (51.55295°, 0.55962°)", + "Step 2: Calculate longitude difference", + " Δlon = 0.55962 - 6.58556 = -6.0259°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 345.62°", + "Step 5: Determine cardinal direction", + " 345.6° → N", + "FINAL ANSWER: 345.62° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 41.40916, + "lon": -75.6649, + "name": "Scranton" + }, + "point_b": { + "lat": 25.48742, + "lon": 28.97918, + "name": "Mūţ" + }, + "ground_truth": { + "initial_bearing_deg": 61.53, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Scranton at (41.40916°, -75.6649°)", + " To: Mūţ at (25.48742°, 28.97918°)", + "Step 2: Calculate longitude difference", + " Δlon = 28.97918 - -75.6649 = 104.6441°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 61.53°", + "Step 5: Determine cardinal direction", + " 61.5° → NE", + "FINAL ANSWER: 61.53° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 23.64824, + "lon": -100.64334, + "name": "Matehuala" + }, + "point_b": { + "lat": 35.44934, + "lon": 119.23607, + "name": "Xihu" + }, + "ground_truth": { + "initial_bearing_deg": 326.26, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Matehuala at (23.64824°, -100.64334°)", + " To: Xihu at (35.44934°, 119.23607°)", + "Step 2: Calculate longitude difference", + " Δlon = 119.23607 - -100.64334 = 219.8794°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 326.26°", + "Step 5: Determine cardinal direction", + " 326.3° → NW", + "FINAL ANSWER: 326.26° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 22.4382, + "lon": 88.43205, + "name": "Rajpur Sonarpur" + }, + "point_b": { + "lat": 39.34788, + "lon": -76.76997, + "name": "Milford Mill" + }, + "ground_truth": { + "initial_bearing_deg": 347.23, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Rajpur Sonarpur at (22.4382°, 88.43205°)", + " To: Milford Mill at (39.34788°, -76.76997°)", + "Step 2: Calculate longitude difference", + " Δlon = -76.76997 - 88.43205 = -165.2020°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 347.23°", + "Step 5: Determine cardinal direction", + " 347.2° → N", + "FINAL ANSWER: 347.23° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 40.84816, + "lon": -73.99764, + "name": "Palisades Park" + }, + "point_b": { + "lat": 10.78556, + "lon": -0.85139, + "name": "Bolgatanga" + }, + "ground_truth": { + "initial_bearing_deg": 92.72, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Palisades Park at (40.84816°, -73.99764°)", + " To: Bolgatanga at (10.78556°, -0.85139°)", + "Step 2: Calculate longitude difference", + " Δlon = -0.85139 - -73.99764 = 73.1463°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 92.72°", + "Step 5: Determine cardinal direction", + " 92.7° → E", + "FINAL ANSWER: 92.72° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -33.01529, + "lon": 27.91162, + "name": "East London" + }, + "point_b": { + "lat": 38.32614, + "lon": 26.30574, + "name": "Çeşme" + }, + "ground_truth": { + "initial_bearing_deg": 358.67, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: East London at (-33.01529°, 27.91162°)", + " To: Çeşme at (38.32614°, 26.30574°)", + "Step 2: Calculate longitude difference", + " Δlon = 26.30574 - 27.91162 = -1.6059°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 358.67°", + "Step 5: Determine cardinal direction", + " 358.7° → N", + "FINAL ANSWER: 358.67° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 12.05267, + "lon": 78.48023, + "name": "Harūr" + }, + "point_b": { + "lat": 45.58882, + "lon": 9.19792, + "name": "Nova Milanese" + }, + "ground_truth": { + "initial_bearing_deg": 314.66, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Harūr at (12.05267°, 78.48023°)", + " To: Nova Milanese at (45.58882°, 9.19792°)", + "Step 2: Calculate longitude difference", + " Δlon = 9.19792 - 78.48023 = -69.2823°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 314.66°", + "Step 5: Determine cardinal direction", + " 314.7° → NW", + "FINAL ANSWER: 314.66° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 30.73916, + "lon": 108.59976, + "name": "Changtan" + }, + "point_b": { + "lat": -33.2792, + "lon": 115.71504, + "name": "Australind" + }, + "ground_truth": { + "initial_bearing_deg": 173.4, + "cardinal_direction": "S", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Changtan at (30.73916°, 108.59976°)", + " To: Australind at (-33.2792°, 115.71504°)", + "Step 2: Calculate longitude difference", + " Δlon = 115.71504 - 108.59976 = 7.1153°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 173.40°", + "Step 5: Determine cardinal direction", + " 173.4° → S", + "FINAL ANSWER: 173.40° (S)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 33.39678, + "lon": -84.59576, + "name": "Peachtree City" + }, + "point_b": { + "lat": 34.68406, + "lon": 33.03794, + "name": "Limassol" + }, + "ground_truth": { + "initial_bearing_deg": 46.76, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Peachtree City at (33.39678°, -84.59576°)", + " To: Limassol at (34.68406°, 33.03794°)", + "Step 2: Calculate longitude difference", + " Δlon = 33.03794 - -84.59576 = 117.6337°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 46.76°", + "Step 5: Determine cardinal direction", + " 46.8° → NE", + "FINAL ANSWER: 46.76° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 40.72861, + "lon": 124.78472, + "name": "Kuandian" + }, + "point_b": { + "lat": 39.42417, + "lon": 29.98333, + "name": "Kütahya" + }, + "ground_truth": { + "initial_bearing_deg": 304.22, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Kuandian at (40.72861°, 124.78472°)", + " To: Kütahya at (39.42417°, 29.98333°)", + "Step 2: Calculate longitude difference", + " Δlon = 29.98333 - 124.78472 = -94.8014°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 304.22°", + "Step 5: Determine cardinal direction", + " 304.2° → NW", + "FINAL ANSWER: 304.22° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 12.63056, + "lon": 39.03472, + "name": "Sek’ot’a" + }, + "point_b": { + "lat": 0.18333, + "lon": 30.08333, + "name": "Kasese" + }, + "ground_truth": { + "initial_bearing_deg": 216.16, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Sek’ot’a at (12.63056°, 39.03472°)", + " To: Kasese at (0.18333°, 30.08333°)", + "Step 2: Calculate longitude difference", + " Δlon = 30.08333 - 39.03472 = -8.9514°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 216.16°", + "Step 5: Determine cardinal direction", + " 216.2° → SW", + "FINAL ANSWER: 216.16° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 7.25597, + "lon": -7.23508, + "name": "Kouibly" + }, + "point_b": { + "lat": 43.1689, + "lon": -86.26395, + "name": "Norton Shores" + }, + "ground_truth": { + "initial_bearing_deg": 312.72, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Kouibly at (7.25597°, -7.23508°)", + " To: Norton Shores at (43.1689°, -86.26395°)", + "Step 2: Calculate longitude difference", + " Δlon = -86.26395 - -7.23508 = -79.0289°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 312.72°", + "Step 5: Determine cardinal direction", + " 312.7° → NW", + "FINAL ANSWER: 312.72° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 51.1681, + "lon": 52.99782, + "name": "Aqsay" + }, + "point_b": { + "lat": 9.91861, + "lon": -68.30472, + "name": "Tinaquillo" + }, + "ground_truth": { + "initial_bearing_deg": 301.05, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Aqsay at (51.1681°, 52.99782°)", + " To: Tinaquillo at (9.91861°, -68.30472°)", + "Step 2: Calculate longitude difference", + " Δlon = -68.30472 - 52.99782 = -121.3025°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 301.05°", + "Step 5: Determine cardinal direction", + " 301.1° → NW", + "FINAL ANSWER: 301.05° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 17.20667, + "lon": -100.43306, + "name": "Atoyac de Álvarez" + }, + "point_b": { + "lat": 50.90769, + "lon": 5.41875, + "name": "Diepenbeek" + }, + "ground_truth": { + "initial_bearing_deg": 37.44, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Atoyac de Álvarez at (17.20667°, -100.43306°)", + " To: Diepenbeek at (50.90769°, 5.41875°)", + "Step 2: Calculate longitude difference", + " Δlon = 5.41875 - -100.43306 = 105.8518°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 37.44°", + "Step 5: Determine cardinal direction", + " 37.4° → NE", + "FINAL ANSWER: 37.44° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -22.59861, + "lon": -48.80028, + "name": "Lençóis Paulista" + }, + "point_b": { + "lat": -4.66667, + "lon": 34.86667, + "name": "Ilongero" + }, + "ground_truth": { + "initial_bearing_deg": 91.9, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Lençóis Paulista at (-22.59861°, -48.80028°)", + " To: Ilongero at (-4.66667°, 34.86667°)", + "Step 2: Calculate longitude difference", + " Δlon = 34.86667 - -48.80028 = 83.6669°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 91.90°", + "Step 5: Determine cardinal direction", + " 91.9° → E", + "FINAL ANSWER: 91.90° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 34.99921, + "lon": 136.09674, + "name": "Konan" + }, + "point_b": { + "lat": -27.25204, + "lon": 152.99226, + "name": "Kallangur" + }, + "ground_truth": { + "initial_bearing_deg": 163.33, + "cardinal_direction": "S", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Konan at (34.99921°, 136.09674°)", + " To: Kallangur at (-27.25204°, 152.99226°)", + "Step 2: Calculate longitude difference", + " Δlon = 152.99226 - 136.09674 = 16.8955°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 163.33°", + "Step 5: Determine cardinal direction", + " 163.3° → S", + "FINAL ANSWER: 163.33° (S)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -12.6125, + "lon": -38.29694, + "name": "Dias d'Ávila" + }, + "point_b": { + "lat": -25.77889, + "lon": -49.32611, + "name": "Mandirituba" + }, + "ground_truth": { + "initial_bearing_deg": 216.67, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Dias d'Ávila at (-12.6125°, -38.29694°)", + " To: Mandirituba at (-25.77889°, -49.32611°)", + "Step 2: Calculate longitude difference", + " Δlon = -49.32611 - -38.29694 = -11.0292°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 216.67°", + "Step 5: Determine cardinal direction", + " 216.7° → SW", + "FINAL ANSWER: 216.67° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 1.8681, + "lon": 103.1124, + "name": "Parit Raja" + }, + "point_b": { + "lat": -9.11139, + "lon": -37.12306, + "name": "Águas Belas" + }, + "ground_truth": { + "initial_bearing_deg": 258.06, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Parit Raja at (1.8681°, 103.1124°)", + " To: Águas Belas at (-9.11139°, -37.12306°)", + "Step 2: Calculate longitude difference", + " Δlon = -37.12306 - 103.1124 = -140.2355°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 258.06°", + "Step 5: Determine cardinal direction", + " 258.1° → W", + "FINAL ANSWER: 258.06° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -34.75705, + "lon": 138.60819, + "name": "Paralowie" + }, + "point_b": { + "lat": 48.0021, + "lon": 0.20251, + "name": "Le Mans" + }, + "ground_truth": { + "initial_bearing_deg": 306.22, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Paralowie at (-34.75705°, 138.60819°)", + " To: Le Mans at (48.0021°, 0.20251°)", + "Step 2: Calculate longitude difference", + " Δlon = 0.20251 - 138.60819 = -138.4057°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 306.22°", + "Step 5: Determine cardinal direction", + " 306.2° → NW", + "FINAL ANSWER: 306.22° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 20.51167, + "lon": -103.23689, + "name": "San José del Castillo" + }, + "point_b": { + "lat": -37.74124, + "lon": 144.73631, + "name": "Caroline Springs" + }, + "ground_truth": { + "initial_bearing_deg": 237.37, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: San José del Castillo at (20.51167°, -103.23689°)", + " To: Caroline Springs at (-37.74124°, 144.73631°)", + "Step 2: Calculate longitude difference", + " Δlon = 144.73631 - -103.23689 = 247.9732°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 237.37°", + "Step 5: Determine cardinal direction", + " 237.4° → SW", + "FINAL ANSWER: 237.37° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 42.49747, + "lon": -94.16802, + "name": "Fort Dodge" + }, + "point_b": { + "lat": -24.51667, + "lon": 28.71667, + "name": "Mookgophong" + }, + "ground_truth": { + "initial_bearing_deg": 87.92, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Fort Dodge at (42.49747°, -94.16802°)", + " To: Mookgophong at (-24.51667°, 28.71667°)", + "Step 2: Calculate longitude difference", + " Δlon = 28.71667 - -94.16802 = 122.8847°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 87.92°", + "Step 5: Determine cardinal direction", + " 87.9° → E", + "FINAL ANSWER: 87.92° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 36.45833, + "lon": 7.51389, + "name": "Boumahra Ahmed" + }, + "point_b": { + "lat": 34.1064, + "lon": -117.37032, + "name": "Rialto" + }, + "ground_truth": { + "initial_bearing_deg": 317.16, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Boumahra Ahmed at (36.45833°, 7.51389°)", + " To: Rialto at (34.1064°, -117.37032°)", + "Step 2: Calculate longitude difference", + " Δlon = -117.37032 - 7.51389 = -124.8842°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 317.16°", + "Step 5: Determine cardinal direction", + " 317.2° → NW", + "FINAL ANSWER: 317.16° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 27.06309, + "lon": 31.34425, + "name": "As Sāḩil" + }, + "point_b": { + "lat": -34.15152, + "lon": 19.01509, + "name": "Grabouw" + }, + "ground_truth": { + "initial_bearing_deg": 191.51, + "cardinal_direction": "S", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: As Sāḩil at (27.06309°, 31.34425°)", + " To: Grabouw at (-34.15152°, 19.01509°)", + "Step 2: Calculate longitude difference", + " Δlon = 19.01509 - 31.34425 = -12.3292°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 191.51°", + "Step 5: Determine cardinal direction", + " 191.5° → S", + "FINAL ANSWER: 191.51° (S)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 0.0607, + "lon": 34.28806, + "name": "Siaya" + }, + "point_b": { + "lat": 53.32641, + "lon": 9.86812, + "name": "Buchholz in der Nordheide" + }, + "ground_truth": { + "initial_bearing_deg": 342.88, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Siaya at (0.0607°, 34.28806°)", + " To: Buchholz in der Nordheide at (53.32641°, 9.86812°)", + "Step 2: Calculate longitude difference", + " Δlon = 9.86812 - 34.28806 = -24.4199°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 342.88°", + "Step 5: Determine cardinal direction", + " 342.9° → N", + "FINAL ANSWER: 342.88° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 34.275, + "lon": 133.75, + "name": "Tadotsu" + }, + "point_b": { + "lat": 44.1494, + "lon": 43.47019, + "name": "Georgiyevsk" + }, + "ground_truth": { + "initial_bearing_deg": 308.83, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Tadotsu at (34.275°, 133.75°)", + " To: Georgiyevsk at (44.1494°, 43.47019°)", + "Step 2: Calculate longitude difference", + " Δlon = 43.47019 - 133.75 = -90.2798°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 308.83°", + "Step 5: Determine cardinal direction", + " 308.8° → NW", + "FINAL ANSWER: 308.83° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -6.14755, + "lon": 143.65633, + "name": "Mendi" + }, + "point_b": { + "lat": -19.39111, + "lon": -40.07222, + "name": "Linhares" + }, + "ground_truth": { + "initial_bearing_deg": 171.9, + "cardinal_direction": "S", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Mendi at (-6.14755°, 143.65633°)", + " To: Linhares at (-19.39111°, -40.07222°)", + "Step 2: Calculate longitude difference", + " Δlon = -40.07222 - 143.65633 = -183.7285°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 171.90°", + "Step 5: Determine cardinal direction", + " 171.9° → S", + "FINAL ANSWER: 171.90° (S)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 37.7966, + "lon": -122.40858, + "name": "Chinatown" + }, + "point_b": { + "lat": -7.12056, + "lon": -38.50194, + "name": "São José de Piranhas" + }, + "ground_truth": { + "initial_bearing_deg": 99.35, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Chinatown at (37.7966°, -122.40858°)", + " To: São José de Piranhas at (-7.12056°, -38.50194°)", + "Step 2: Calculate longitude difference", + " Δlon = -38.50194 - -122.40858 = 83.9066°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 99.35°", + "Step 5: Determine cardinal direction", + " 99.3° → E", + "FINAL ANSWER: 99.35° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 5.89405, + "lon": 5.67666, + "name": "Sapele" + }, + "point_b": { + "lat": 2.269, + "lon": 102.1427, + "name": "Sungai Udang" + }, + "ground_truth": { + "initial_bearing_deg": 87.06, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Sapele at (5.89405°, 5.67666°)", + " To: Sungai Udang at (2.269°, 102.1427°)", + "Step 2: Calculate longitude difference", + " Δlon = 102.1427 - 5.67666 = 96.4660°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 87.06°", + "Step 5: Determine cardinal direction", + " 87.1° → E", + "FINAL ANSWER: 87.06° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 42.81084, + "lon": -1.66409, + "name": "Ermitagaña" + }, + "point_b": { + "lat": 28.25849, + "lon": 42.92457, + "name": "Turubah" + }, + "ground_truth": { + "initial_bearing_deg": 97.28, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Ermitagaña at (42.81084°, -1.66409°)", + " To: Turubah at (28.25849°, 42.92457°)", + "Step 2: Calculate longitude difference", + " Δlon = 42.92457 - -1.66409 = 44.5887°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 97.28°", + "Step 5: Determine cardinal direction", + " 97.3° → E", + "FINAL ANSWER: 97.28° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 34.34381, + "lon": 3.22475, + "name": "’Aïn el Bell" + }, + "point_b": { + "lat": -34.61315, + "lon": -58.37723, + "name": "Buenos Aires" + }, + "ground_truth": { + "initial_bearing_deg": 226.38, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: ’Aïn el Bell at (34.34381°, 3.22475°)", + " To: Buenos Aires at (-34.61315°, -58.37723°)", + "Step 2: Calculate longitude difference", + " Δlon = -58.37723 - 3.22475 = -61.6020°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 226.38°", + "Step 5: Determine cardinal direction", + " 226.4° → SW", + "FINAL ANSWER: 226.38° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -28.13442, + "lon": -58.76685, + "name": "San Lorenzo" + }, + "point_b": { + "lat": 51.09242, + "lon": 4.3717, + "name": "Boom" + }, + "ground_truth": { + "initial_bearing_deg": 34.34, + "cardinal_direction": "NE", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: San Lorenzo at (-28.13442°, -58.76685°)", + " To: Boom at (51.09242°, 4.3717°)", + "Step 2: Calculate longitude difference", + " Δlon = 4.3717 - -58.76685 = 63.1385°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 34.34°", + "Step 5: Determine cardinal direction", + " 34.3° → NE", + "FINAL ANSWER: 34.34° (NE)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -18.11094, + "lon": 178.40943, + "name": "Lami" + }, + "point_b": { + "lat": 36.20389, + "lon": 127.08472, + "name": "Nonsan" + }, + "ground_truth": { + "initial_bearing_deg": 318.74, + "cardinal_direction": "NW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Lami at (-18.11094°, 178.40943°)", + " To: Nonsan at (36.20389°, 127.08472°)", + "Step 2: Calculate longitude difference", + " Δlon = 127.08472 - 178.40943 = -51.3247°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 318.74°", + "Step 5: Determine cardinal direction", + " 318.7° → NW", + "FINAL ANSWER: 318.74° (NW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 33.86751, + "lon": -117.99812, + "name": "Buena Park" + }, + "point_b": { + "lat": 59.51404, + "lon": 15.99255, + "name": "Köping" + }, + "ground_truth": { + "initial_bearing_deg": 21.81, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Buena Park at (33.86751°, -117.99812°)", + " To: Köping at (59.51404°, 15.99255°)", + "Step 2: Calculate longitude difference", + " Δlon = 15.99255 - -117.99812 = 133.9907°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 21.81°", + "Step 5: Determine cardinal direction", + " 21.8° → N", + "FINAL ANSWER: 21.81° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 43.73149, + "lon": -79.42023, + "name": "Bedford Park-Nortown" + }, + "point_b": { + "lat": 34.36591, + "lon": 107.35904, + "name": "Guozhen" + }, + "ground_truth": { + "initial_bearing_deg": 354.29, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Bedford Park-Nortown at (43.73149°, -79.42023°)", + " To: Guozhen at (34.36591°, 107.35904°)", + "Step 2: Calculate longitude difference", + " Δlon = 107.35904 - -79.42023 = 186.7793°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 354.29°", + "Step 5: Determine cardinal direction", + " 354.3° → N", + "FINAL ANSWER: 354.29° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 44.95719, + "lon": 34.11079, + "name": "Simferopol" + }, + "point_b": { + "lat": 29.86632, + "lon": 77.89118, + "name": "Roorkee" + }, + "ground_truth": { + "initial_bearing_deg": 98.53, + "cardinal_direction": "E", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Simferopol at (44.95719°, 34.11079°)", + " To: Roorkee at (29.86632°, 77.89118°)", + "Step 2: Calculate longitude difference", + " Δlon = 77.89118 - 34.11079 = 43.7804°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 98.53°", + "Step 5: Determine cardinal direction", + " 98.5° → E", + "FINAL ANSWER: 98.53° (E)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -22.97111, + "lon": 30.67361, + "name": "Malamulele" + }, + "point_b": { + "lat": 53.14083, + "lon": -6.06306, + "name": "Greystones" + }, + "ground_truth": { + "initial_bearing_deg": 338.78, + "cardinal_direction": "N", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Malamulele at (-22.97111°, 30.67361°)", + " To: Greystones at (53.14083°, -6.06306°)", + "Step 2: Calculate longitude difference", + " Δlon = -6.06306 - 30.67361 = -36.7367°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 338.78°", + "Step 5: Determine cardinal direction", + " 338.8° → N", + "FINAL ANSWER: 338.78° (N)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": -21.40611, + "lon": -48.50472, + "name": "Taquaritinga" + }, + "point_b": { + "lat": -5.55694, + "lon": -80.82222, + "name": "Sechura" + }, + "ground_truth": { + "initial_bearing_deg": 292.17, + "cardinal_direction": "W", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Taquaritinga at (-21.40611°, -48.50472°)", + " To: Sechura at (-5.55694°, -80.82222°)", + "Step 2: Calculate longitude difference", + " Δlon = -80.82222 - -48.50472 = -32.3175°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 292.17°", + "Step 5: Determine cardinal direction", + " 292.2° → W", + "FINAL ANSWER: 292.17° (W)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 52.01682, + "lon": 11.7307, + "name": "Schönebeck" + }, + "point_b": { + "lat": -22.39028, + "lon": -44.96667, + "name": "Passa Quatro" + }, + "ground_truth": { + "initial_bearing_deg": 230.61, + "cardinal_direction": "SW", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Schönebeck at (52.01682°, 11.7307°)", + " To: Passa Quatro at (-22.39028°, -44.96667°)", + "Step 2: Calculate longitude difference", + " Δlon = -44.96667 - 11.7307 = -56.6974°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 230.61°", + "Step 5: Determine cardinal direction", + " 230.6° → SW", + "FINAL ANSWER: 230.61° (SW)" + ] + }, + { + "task": "bearing_computation", + "point_a": { + "lat": 42.90395, + "lon": -78.69225, + "name": "Depew" + }, + "point_b": { + "lat": 23.02389, + "lon": -82.408, + "name": "Fontanar" + }, + "ground_truth": { + "initial_bearing_deg": 189.99, + "cardinal_direction": "S", + "tolerance_deg": 5.0 + }, + "reasoning_steps": [ + "Step 1: Identify the coordinates", + " From: Depew at (42.90395°, -78.69225°)", + " To: Fontanar at (23.02389°, -82.408°)", + "Step 2: Calculate longitude difference", + " Δlon = -82.408 - -78.69225 = -3.7157°", + "Step 3: Apply bearing formula", + " θ = atan2(sin(Δlon) × cos(lat₂), cos(lat₁) × sin(lat₂) - sin(lat₁) × cos(lat₂) × cos(Δlon))", + "Step 4: Convert to degrees and normalize to 0-360°", + " Initial bearing = 189.99°", + "Step 5: Determine cardinal direction", + " 190.0° → S", + "FINAL ANSWER: 189.99° (S)" + ] + } +] \ No newline at end of file