SOLUTION: Using your knowledge of trigonometric identities, find the exact value of sin(x+y) knowing that x and y are between 0 and π/2, that sin(x)=4/5 and that sec(y)=13/5. Your

Algebra ->  Trigonometry-basics -> SOLUTION: Using your knowledge of trigonometric identities, find the exact value of sin(x+y) knowing that x and y are between 0 and π/2, that sin(x)=4/5 and that sec(y)=13/5. Your      Log On


   

Question 904452: Using your knowledge of trigonometric identities, find the exact value of sin(x+y) knowing that x and y are between 0 and π/2, that sin(x)=4/5 and that sec(y)=13/5. Your answer must be a rational number, written in the form of an irreducible fraction p/q (such as 2/3, 4/5, −1/4, etc.), with q>0. Give the integers p and q.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
1%2Fcos%28y%29+=+13%2F5, cos(y) = 5/13 and sin(y) = 12/13 12+=+sqrt%28169-25%29
sin(x) = 4/5, cos(x) = 3/5 3+=+sqrt%2825-16%29
sin(x+y) = sin(x)c0s(y)+ cos(x)sin(y) = %284%2F5%29%285%2F13%29+%2B+%283%2F5%29%2812%2F13%29+=+56%2F65