SOLUTION: Find the exact value if 0 < x < pi/2 and 0 < y < pi/2 ; sin(x+y) if sin(x) = 3/5 and sin(y)= 12/37

Question 1033611: Find the exact value if 0 < x < pi/2 and 0 < y < pi/2 ; sin(x+y) if sin(x) = 3/5 and sin(y)= 12/37
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
sin(x+y) = sin x cos y + sin y cos x
All we need are the cosines...
cos x = sqrt(1 - sin^2 x) = sqrt(1 - (3/5)^2) = 4/5
cos y = sqrt(1 - sin^2 y) = sqrt(1 - (12/37)^2) = 35/37
so that, when we plug in we get
sin(x+y) = 3/5 * 35/37 + 12/37 * 4/5 = 105/185 + 48/185 = 153/185
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