Question
The following is a problem in Fourier Analysis:
Suppose that m and n are positive integers. Compute (cos(mx)) (cos(nx)) dx. Be careful, there will be two different results: one when m = n and one when m n. Now suppose there's some mystery function of the form f(x) = A cos(x) + B cos(2x) + C cos(3x) (where A, B, and C are some unknown constants), and suppose we know f(x) cos(x) dx = 5, f(x) cos(2x) dx = 6, and f(x) cos(3x) dx = 7. Use this information and your answer from part (a) to find the constants A and B and C. In solving part (a), the trigonometric identity 2 cos(alpha) cos(beta) = cos(alpha - beta) + cos(alpha + beta) will be useful.
Explanation / Answer
(a)
