# Method of residues

1. May 15, 2012

### gtfitzpatrick

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

$\int^{0}_{2\pi}$ $\frac{d\theta}{13+5sin\theta}$

2. Relevant equations

3. The attempt at a solution

so i changed it using $sin \theta = \frac{1}{2i} (z - \frac{1}{z})$

and i get$\oint \frac{2}{5z^2+26zi-5}$ which i factored down to $(z = \frac{-26±\sqrt{776}}{10})$

but no matter how i proceed from here i cant get the answer, any ideas anyone?

2. May 15, 2012

### vela

Staff Emeritus
How did you get real roots to a polynomial with complex coefficients?