Answer
$\dfrac{2\pi}{3}$
Work Step by Step
We are given the expression: $\cos^{-1} \left(-\dfrac{1}{2}\right)$
$y=\cos^{-1} x$ is the value of $y$ so that $\cos y=x$, where $0\leq y\leq\pi$.
So $y=\cos^{-1} \left(-\dfrac{1}{2}\right)$ is the value of $y$ so that $\cos y=-\dfrac{1}{2}$, where $0\leq y\leq\pi$
From the unit circle we have:
$x=\cos \left(\dfrac{2\pi}{3}\right)$
Therefore the value of $y$ for which $x=-\dfrac{1}{2}$ in the interval $\left[0,\pi\right]$ is $\dfrac{2\pi}{3}$, so we got:
$\cos^{-1} \left(-\dfrac{1}{2}\right)=\dfrac{2\pi}{3}$
