# Orthogonality of sine and cosine question

1. Jun 10, 2014

### Tikkelsen

Hello,

I'm trying to solve Fourier Series, but I have a question.
I know that cos(nx) is even and sin(nx) is odd. But what does this mean when I take the integral or sum of cos(nx) or sin(nx)? Do they have a value or do they just keep their form?

2. Jun 10, 2014

### Simon Bridge

$$\int_a^a \sin kx \; dx = 0\\ \int_a^a \cos kx \; dx = 2\int_0^a \cos kx\; dx$$
... with the fourier series you are more interested in the integral of f(x) multiplied by a sine or a cosine though.

3. Jun 11, 2014

### Tikkelsen

I found the answer to my own question.
I wasn't concerned about cos(nx), but by cos(npi) which is equal to (-1)^n and for sin(npi) it's equal to 0. I now understand that this is only for a particular result of the Fourier Series where the integral includes pi. Thank you for your answer though Simon.

4. Jun 12, 2014

### Simon Bridge

No worries, and well done.
Thanks for sharing too.
:)