very simple Fourier series question

**Dr Zoidburg** · March 10th 2010, 05:23 PM

simple for anyone but myself obviously or else I wouldn't be posting it here!

I know the simple rule $cos(n\pi) = (-1)^n$
but is there a similarly simple way of writing
$cos (n \frac{\pi}{2})$
and
$sin (n \frac{\pi}{2})$
?

**Black** · March 10th 2010, 06:42 PM

$\cos\left(\frac{n\pi}{2}\right)=\frac{i^n}{2}(1+(-1)^n)$

$\sin\left(\frac{n\pi}{2}\right)=\frac{i^{n-1}}{2}(1-(-1)^n)$

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