Suppose that sin x = 1/5 and cos y = 2/3, and x and y are each angles in Quadrant 1. Determine sin(x+y).

Answer 1

make triangles for each case , then use Pythagoras

if sinx = 1/5, then cosx = √24/5

if cosy = 2/3 , the siny = √5/3

sin(x+y) = sinxcosy + cosxsiny
= (1/5)(2/3) + (√24/5)(√5/3)
= (2 + √120)/15