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## Homework Statement

Hi guys, I don't quite understand how to solve closed integrals "around a given circle." I was given [tex] \oint\frac{dz}{sinz} [/tex] around [tex]|z-6|=4 [/tex] and said that the integral is equal to zero because the singularity [tex] n\pi i [/tex] is not within the circle. Is this correct? Also I need to solve [tex]\oint \frac{sinz}{sinh^{2}z}dz [/tex] around [tex]|z|=3[/tex]. In this case do I just need to solve for the residues of the singularities which are inside of this circle? Or am I going about this completely wrong? Any help would be greatly appreciated.

## Homework Equations

All are given above.

## The Attempt at a Solution

I have attempted to solve the second integral by expanding sinhz and looking for the residues of this function within the given circle. I'm not sure if I've done that right or not. Thanks in advance for any help or a point in the right direction; if anyone knows where I could find some similar examples that would also be awesome.