TITLE: How to evaluate trigonometric functions by pen and paper?
QUESTION [18 upvotes]: How did people determined the values of trigonometric functions before calculators, like e.g. $\sin 37^\circ$ up to five decimal places? Was that possible to find before series were invented?

REPLY [3 votes]: You could also compute it from the series.  Not that this is better than the accepted answer, but just for completeness.
http://en.wikipedia.org/wiki/Taylor_series#List_of_Maclaurin_series_of_some_common_functions