# Residue of sin(1/z)/cos(z)

1. Apr 15, 2016

### saybrook1

1. The problem statement, all variables and given/known data
Hello guys, I need to find the orders of each pole as well as the residue of the function sin(1/z)/cos(z).

2. Relevant equations
I imagine that this is a simple pole so I will either find the Laurent series and get the coefficient of $$(z-z_0)^{-1}$$ or use the simpler limiting case.

3. The attempt at a solution
So far, I think that there is clearly a pole at $$n\pi-\frac{\pi}{2}$$ due to the z in the cosine term, although I'm not sure whether it's considered a pole when the value of z causes the term sin(1/z) to go to zero. Any help here and further direction on calculating the residue from there would be awesome. Thank you very much.

2. Apr 15, 2016

### Theengr7

What is the name of this chapter ?

3. Apr 15, 2016

### saybrook1

Calculus of Residues? No particular book.

4. Apr 15, 2016

### Theengr7

Alright. I have not heard about it before.