$\text{Recall that } \cos \left( \frac{\pi}{6}\right) = \frac{1}{2},$
$\text{ so the reference angle will be } 30^\circ.$

In which quadrants is cosine negative? Sketch a unit circle with right triangles with $30^\circ$ angles at the origin in the second and third quadrants. What are the circular angles?

$x = 120^\circ$ and $240^\circ$

Now convert the angles into radians.

$120\left(\frac{\pi}{180}\right)\ \ \ \ \ \ \ \ 240\left(\frac{\pi}{180}\right)$

$x = \frac{2{\pi}}{3}, \frac{4{\pi}}{3}$

See part (a).

If $\text{sin}\left(x\right) = 0, x = 0$.

$x = 0$

Remember the side ratios of $45^\circ$ right triangles.