Fourier series and integration

I've got partway through this question and i feel like im so close to finishing it but just having a few problems along the way:

The question is:

Express the 2pi periodic function F(t)=Cos(t)sin(4t) as a finite fourier series...

So far i have managed to change the f(t) into a function of sin
f(t)=1/2 (sin(5t)+sin(3t))

from here on i believe the next step is:
Bn= (1/pi) (Integral between 0 and pi of sin(5t)sin(nt)+sin(3t)sin(nt))dt

im unsure as to whether the next step is to use the product of 2 sines trig identity, but then i end up with a big integral in terms of cos with constants n and t and it all gets very confusing from here.

could anyone provide any help?

Reply 1

DFranklin

18

Original post by SassyPete

I've got partway through this question and i feel like im so close to finishing it but just having a few problems along the way:

The question is:

Express the 2pi periodic function F(t)=Cos(t)sin(4t) as a finite fourier series...

So far i have managed to change the f(t) into a function of sin
f(t)=1/2 (sin(5t)+sin(3t))

This *is* a finite Fourier series. You don't need to do anything else.