Computing Fourier Coefficients with Integrals

To compute the Fourier coefficients of a periodic function f of period 1, we multiply f by the functions sin 27rkx and cos 2nkx (sines and cosines of integer frequencies k). Since the functions sin 27rkx and cos 27rkx oscillate between +1 and -1, this multiplication produces a function whose graph oscillates between the grabhs of + f and - f .