complex trig

durham2 · #1 $Old$ November 5th, 2009, 12:21 PM

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

I need major help?

shawsend · #2 $Old$ November 5th, 2009, 12:58 PM

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 · #3 $Old$ November 10th, 2009, 12:06 PM

Quote:

Originally Posted by durham2 $View Post$

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