Consider the function f : [−π, π] → R given by f(θ) = θ(π − |θ|), periodic of period 2π.
(a) Show that the function is odd.
(b) Verify that the Fourier series of f is:
(c) What is the series of sines and the series of cosines of f? Justify your answer.
8
sin[(2n+1)θ] .. (2n +1)³ n=0
f