#### Answer

$\displaystyle \{\frac{\pi}{6}, \ \ \frac{11\pi}{6}\}$

#### Work Step by Step

For a point on the unit circle, the coordinates are
($\cos x,\sin x)$, $x\in[0,2\pi)$
To solve the problem, find the points for which
the x-coordinate is $\displaystyle \frac{\sqrt{3}}{2}$, ($\cos x$=$\displaystyle \frac{\sqrt{3}}{2}$)
Using the given unit circle, we find such points
in quadrant I, for $x=\displaystyle \frac{\pi}{6}$
in quadrant IV, for $x=\displaystyle \frac{11\pi}{6}$
Solution set: $\displaystyle \{\frac{\pi}{6}, \ \ \frac{11\pi}{6}\}$