cos^-1frac{-1}{2}=

The value of an inverse trig expression is an angle. ${\displaystyle {\cos }^{-1}\frac{-1}{2}}$ is then asking you what angle on the unit circle has a value of ${\displaystyle \frac{-1}{2}}$ for cosine.
Inverse cosine is restricted to the angles in the first and second quadrant. That is, inverse cosine can only equal an angle ${\displaystyle oslash}$ such that ${\displaystyle 0\le \theta \le \pi }$  or  ${\displaystyle 0^{\circ }\le \theta \le {180}^{\circ }.}$
Since cosine is the x-coordinate of the point on the unit circle, you need to look for what point in the first or second quadrant on the unit circle has an x-coordinate of ${\displaystyle \frac{-1}{2}}$. That point is
${\displaystyle \frac{-1}{2},\sqrt{\frac{3}{2}}}$ in the second quadrant at an angle of ${\displaystyle oslash=2\frac{\pi }{3}}$ if your answer must be in radians and ${\displaystyle {\cos }^{-1}\frac{-1}{2}={120}^{\circ }}$ if your answer must be in degrees.