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.