Fourier series

**Deadstar** · April 14th 2009, 03:42 PM

Quick Q.

When dealing Fourier series Q's, $\cos(n \pi)$ is written as $(-1)^n$ . What can $\cos (\frac{n \pi}{2})$ be written as? I might as well write out the equation i'm trying to simplify...

$-\frac{2T}{n \pi}( 2 \cos \frac{n \pi}{2} - 1 - \cos{n \pi} )$ = ?

**Calculus26** · April 14th 2009, 04:21 PM

its either -1,0, or 1

if n is odd it is 0

If n is even its either -1 or 1

So there is no simple form

**Deadstar** · April 14th 2009, 04:33 PM

Cheers, think I've got it figured out anyway...

It equals $\frac{8T}{n \pi}$ whenever n is in the form 4m + 2 and 0 otherwise.

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