Residue Theorem: Finding Residue at ##|z|=2##

[kq6up]

Homework Statement

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

Homework Equations

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

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

 

[ShayanJ]

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

 

[Fightfish]

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

 

[kq6up]

Where does the 1/2 factor come from?

Thanks,
Chris

 

[kq6up]

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

Thanks,
Chris