TITLE: How to find the coordinates of the vertices of a pentagon centered at the origin
QUESTION [6 upvotes]: I am attempting to follow this tutorial here: http://www.mathopenref.com/polygonradius.html
My goal is to find the coordinates of vertices of a pentagon, given some radius. For example, if I know that the center is at $(0,0)$, and my radius is $8.1$, what formula can I use to get the coordinates of points A, E, B, D, C, if I know the center point between D, C (i.e $(0,5)$

REPLY [4 votes]: Assuming starting with   b on $y$ axis,
$$(x,y)=  ( 8.1 \cos ( t + k \, 2 \pi/5)  , 8.1 \sin( t + k\, 2 \pi/5)) $$
where $t$ is polar coordinate angle at (0,0)  and $k$ is varied between 0 to 5 to arrive at all vertex coordinates of the regular pentagon.