trigonometry
posted by kath .
why does supplementary angles always have the same sin?

trigonometry 
Steve
use the difference formula:
sin(πx) = sinπ cosx  cosπ sinx
sinπ=0 and cosπ = 1, so you wind up with
0  (1)(sinx) = sinx
Also, if you draw the angles in standard position, recall that
sinθ = y/r
cosθ = x/r
since y is positive in QI and QII, the two angles have the same sine value.
This also shows why cos(πx) = cosx  x is negative in QII.
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