I'm given the following problem:

If cos(x) = $\displaystyle \frac{-5}{13}$ and sin(x) < 0 find $\displaystyle cos(\frac{x}{2})$

Since both cos(x) and sin(x) are negative, I know that x lies in quadrant III. But I'm not sure how I can determine what quadrant $\displaystyle (\frac{x}{2})$ lies in. I know how to solve this problem using the half angle identity, except I'll need to know what sign to put in front of my answer.

Thanks!