Question

Consider thefollowing function defined on the interval [0,pi]

.

The Fouriercosine series of f(t) is

a_k= when k=4n for some n,

a_k= when k=4n+1 for some n,

a_k= when k=4n+2 for some n,

a_k= when k=4n+3 for some n.

The Fouriersine series of f(t) is

b_k= when k=4n for some n,
b_k= when k=4n+1 for some n,

b_k= when k=4n+2 for some n,

b_k= when k=4n+3 for some n.