Question

Consider the following function defined on the interval [0,pi]:

f(t)=8 t(pi-t).

The Fourier cosine series of f(t) is
where a_0= ,
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 Fourier sine series of f(t) is

where 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 s

Answer 1

I got a0 to be 8pi^2 - (16pi^2)/3

and a_k = -32/k^2

I can't seem to get b_k :(