Do what topsquark said: where on . This means, . Now we expand into a Fourier series on . This function is odd so we will just have sine terms. Meaning where . Once you find that you will have Fourier for this means .
Do what topsquark said: where on . This means, . Now we expand into a Fourier series on . This function is odd so we will just have sine terms. Meaning where *. Once you find that you will have Fourier for this means .
The function g(x) = -x is an odd function. Therefore the F series expansion for it has to be odd as well. So we can have no cosine terms in the expansion since cosine is an even function.