Angles x and y are located in the first quadrant such that sin x = 4/5 and Cos y = 7/25. Determine an exact value for sin(x + y).

Question

Looking at sin(x+y) = sinxcosy+cosxsiny, we need to first determine the values for cos x and sin y (using right-angle triangles), then we can determine the exact value of sin (x+y).

Answer 1

cosx = 3/5 and siny = 24/25.

sin(x + y) = sinxcosy + sinycosx = 4/5·7/25 + 24/25·3/5 = 28/125 + 72/125 = 100/125 = 4/5