A periodic function f(t) of period 2 is defined within the domain 0 t by Sketch a graph of f(t) for 2 (a)

A periodic function f(t) of period 2π is defined within the domain 0 ≤ t ≤ by

Sketch a graph of f(t) for –2π

(a) f(t) is an even function;
(b) f(t) is an odd function.

Find the Fourier series expansion that represents the even function for all values of t, and use it to show that

f(t) = (0 t n) -t (tn) t