0.5ππ1.5π2.5π0.20.40.60.81tf(t)Open image in a new page

Graph of `f(t)`, where `f(t + π) = f(t)`.

As the question states, the function is periodic with period `pi`.

So, we conclude that the Fourier series will have even harmonics, and will be of the form:

`(a_0)/2+(a_2\ cos 2t + b_2\ sin 2t)` ` +\ (a_4\ cos 4t + b_4\ sin 4t)` ` +\ (a_6\ cos 6t+ b_6\ sin 6t)+...`