Answer
$\dfrac{2\sqrt3}{2}$
Work Step by Step
Note that $\sin^{-1}{\left(-\dfrac{1}{2}\right)}=-\dfrac{\pi}{6}$, because $\sin{\left(-\dfrac{\pi}{6}\right)}=-\dfrac{1}{2}$ and $-\dfrac{\pi}{6}$ is in the range of $\sin^{-1}{x}$, which is $\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right].$
Thus
$\sec{\left(\sin^{-1}{\left(-\dfrac{1}{2}\right)}\right)}=\sec{\left(-\dfrac{\pi}{6}\right)}=\dfrac{2\sqrt3}{2}$