1. Find the Fourier sine and cosine series of f(x) in each case. a. f(x) = = π − x on [0, π], [Hint : recall that we have calculated the Fourier sine and cosine series of g(x) = x on the same interval and have found the following ]. π (−1)n+1 X 1 (2k-1)² cos ((2k-1)x), x~2 sin(nx) 2 π n n=1 1 1 ~ 4 1 π 2k 1 sin ((2k-1)x) b. (*) f(x) = ². Further, sketch the periodic even and odd extensions of f corresponding to the Fourier sine and cosine series. c. (**) See if you can see any relationship between the various Fourier series of functions 1, x, and x².