Finding quadrant for a half angle.

Jan 2010
66
1
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!
 
Dec 2009
3,120
1,342
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.
 
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