# Finding quadrant for a half angle.

#### 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!

#### Archie Meade

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!
In the third quadrant

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

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

The half-angle is in quadrant 2.

JennyFlowers

#### JennyFlowers

Exactly what I needed, thank you!

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