1. Finding quadrant for a half angle.

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!

2. Originally Posted by JennyFlowers
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!

$\displaystyle \displaystyle\ {\pi}< x<\frac{3{\pi}}{2}$

$\displaystyle \displaystyle\ \frac{{\pi}}{2}< \frac{x}{2}<\frac{3{\pi}}{4}$

The half-angle is in quadrant 2.

3. Exactly what I needed, thank you!