SOLUTION: If 4cos^2(x) + 3sin(2x) is equivalent to A + Rcos(2x-y), find the values of A,R and y.

Algebra ->  Trigonometry-basics -> SOLUTION: If 4cos^2(x) + 3sin(2x) is equivalent to A + Rcos(2x-y), find the values of A,R and y.      Log On


   

Question 1027793: If 4cos^2(x) + 3sin(2x) is equivalent to A + Rcos(2x-y), find the values of A,R and y.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
4cos%5E2%28x%29+%2B+3sin%282x%29+=+4%28%281%2Bcos2x%29%2F2%29%2B3sin2x+
=
= 2%2Bsqrt%2813%29%28cosy%2Acos2x+%2B+siny%2Asin2x%29+
=+2%2Bsqrt%2813%29%28cos%282x-y%29%29, where
cosy+=+2%2Fsqrt%2813%29, siny+=+3%2Fsqrt%2813%29, and y+=+tan%5E-1%283%2F2%29.
Therefore,
A = 2, R+=+sqrt%2813%29, and y+=+tan%5E-1%283%2F2%29.