# Residue Theorem

1. Oct 5, 2014

### kq6up

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

Find the residue of $\oint { \frac { sinz }{ 2z-\pi } } dz$ where $\left| z \right| =2$

2. Relevant equations

$f\left( z_{ o } \right) =\frac { 1 }{ 2\pi i } \oint { \frac { f\left( w \right) }{ w-z_{ o } } } dw$

3. The attempt at a solution

It seems to me that the answer is $2\pi i$, but the book gives $\pi i$.

Not sure what I did wrong, I am pretty confident in my answer.

Chris

2. Oct 5, 2014

### ShayanJ

For your integral, $f(z_0)=\frac 1 2 \sin \frac \pi 2$ and $z-z_0=z-\frac \pi 2$.

3. Oct 5, 2014

### Fightfish

I got $\pi i$ as well. You probably forgot a factor of half when calculating the residue.

4. Oct 5, 2014

### kq6up

Where does the 1/2 factor come from?

Thanks,
Chris

5. Oct 5, 2014

### kq6up

Never mind, I see that it the bottom needs to have a two factored out to fit the form.

Thanks,
Chris