complex trig

**durham2** · November 5th 2009, 10:21 AM

show the interal from 0 to 2pi cos(3theta)/(5-4cos(theta))dtheta=pi/12

I need major help?

**shawsend** · November 5th 2009, 10:58 AM

Let $z=e^{it}$ . Then can you show:

$\int_0^{2\pi}\frac{\cos(3t)}{5-4\cos(t)}dt=\mathop\oint\limits_{|z|=1} \frac{z^6+1}{2z^3}\left( \frac{2z}{10z-4z^2-4}\right)\left(-\frac{i dz}{z}\right)$

Then just use the Residue Theorem.

**DeMath** · November 10th 2009, 10:06 AM

Originally Posted by durham2

show the interal from 0 to 2pi cos(3theta)/(5-4cos(theta))dtheta=pi/12

I need major help?

Also, for example, see this post Contour integration

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