- #1

jameson2

- 53

- 0

[tex]\int_0^{2\pi} \frac{d\theta}{24-6sin\theta}

[/tex]

using calculus of residues.

I've tried this so far:

Let [tex]z=e^{i\theta}[/tex] so

[tex]d\theta=\frac{dz}{iz}[/tex].

Also, using the exponential definition of sine,

[tex]sin\theta=\frac{z^2-1}{2iz}[/tex]

This gives messy expressions for the singularities of the function, and therefore the residue I got is messy and not useful(it gives the wrong answer). The same kind of calculation is done in my book with cosine instead of sine, and it works out nicely, so I think I must be missing something in this question.

Anything in specific I should try?