Compute cosx y Given that sinx 35 with x in quadrant I siny

Compute cos(x y) Given that sin(x) = 3/5 with x in quadrant I, sin(y) = 7/25 with y in quadrant II.

Solution

sin(x) = 3/5 = 0.6 ========> x = 36.9 degree

Then cosx = 0.8

sin(y) = 7/25 = 0.28============> y = 163.7 degree

Then cosy = -0.96

cos(X + Y) = cosX cosY - sinX sinY = -0.8*0.96 - 0.6*0.28 = -0.936