#### Answer

$\displaystyle \{\frac{\pi}{3}, \ \ \frac{5\pi}{3}\}$

#### Work Step by Step

For a point on the unit circle, the coordinates are
($\cos x,\sin x)$, $x\in[0,2\pi)$
The problem is solved when we find the points for which
the x-coordinate is $\displaystyle \frac{1}{2}$, ($\cos x$=$\displaystyle \frac{1}{2}$)
Using the given unit circle, we find such points
in quadrant I, for $x=\displaystyle \frac{\pi}{3}$
in quadrant IV, for $x=\displaystyle \frac{5\pi}{3}$
Solution set: $\displaystyle \{\frac{\pi}{3}, \ \ \frac{5\pi}{3}\}$