# Problem with the fourier series

1. Jun 12, 2012

### robertjford80

1. The problem statement, all variables and given/known data

this comes from a problem with the fourier series

3. The attempt at a solution

I don't get the above step.

2. Jun 12, 2012

### clamtrox

What is cos(0)? How about cos(π)? cos(2π)? What's the period of cosine?

3. Jun 12, 2012

### robertjford80

here's another photo. I think the period is pi, but I would think cos npi would simplify to 1 not -1

4. Jun 12, 2012

### HallsofIvy

I have no idea why you would think that! Surely you know that $cos(\pi)= -1$?

5. Jun 12, 2012

### Infinitum

The period of cos is not ∏. Think at what intervals does cos give you the same numbers it was giving for the previous interval?

In other words,

$$cos(T+x) = cos(x)$$

For which smallest non-zero, positive value of T??

Also, cos(n∏) has both the possibilities of being cos(∏) at n=1 and cos(2∏) at n=2. What are the values of each?