# Sum of sinosoids that can be a Fourier Series expansion

1. Aug 26, 2016

### Chris Y

1. The problem statement, all variables and given/known data
I was given a problem with a list of sums of sinusoidal signals, such as
Example that I made up: x(t)=cos(t)+5sin(5*t). The problem asks if a given expression could be a Fourier expansion.
2. Relevant equations

3. The attempt at a solution
My guess is that it has something to do with 5 being an integer multiple of 1.

2. Aug 26, 2016

### LCKurtz

Can you write your sum as$$\cos t + 5\sin(5t) = a_0 + \sum_{n=1}^\infty \left ( a_n\cos(\frac {n\pi t} p) + b_n\sin(\frac {n\pi t} p)\right )$$
by choosing certain values for the $a_n,~b_n,~p$? Hint: lots of them can be $0$.