# Thread: Trigo question. Help needed. Need to pass up on tomorrow.

1. ## Trigo question. Help needed. Need to pass up on tomorrow.

Given that $\displaystyle \cos x = -\frac{2}{3}$ and $\displaystyle \sin y = -\frac{1}{\sqrt 6}$, that $\displaystyle 0^\circ\le x \le360^\circ$ and that $\displaystyle x$ and $\displaystyle y$ are in the same quadrant, find, without calculator, the values of $\displaystyle \cos\frac{x}{2}$.

Man. This question is killing me. I only get to know $\displaystyle x$ and $\displaystyle y$ are in quadrant 3.

2. Hi
Originally Posted by simonsong
Given that $\displaystyle \cos x = -\frac{2}{3}$ and $\displaystyle \sin y = -\frac{1}{\sqrt 6}$, that $\displaystyle 0^\circ\le x \le360^\circ$ and that $\displaystyle x$ and $\displaystyle y$ are in the same quadrant, find, without calculator, the values of $\displaystyle \cos\frac{x}{2}$.

Man. This question is killing me. I only get to know $\displaystyle x$ and $\displaystyle y$ are in quadrant 3.
$\displaystyle \cos x=\cos \left(\frac{x}{2}+\frac{x}{2}\right)=2\cos^2\frac{ x}{2}-1$ hence $\displaystyle \cos \frac{x}{2}=\ldots$

This should give you two values for $\displaystyle \cos \frac{x}{2}$. As you also know in which quadrant is $\displaystyle \frac{x}{2}$, you can choose the right solution among the two you've found.

3. Omg. Never thought of that. Haha. Really thanks pal.