What is the value of $\sin^{-1}\left(-\frac{1}{2}\right) + \cos^{-1}\left(-\frac{1}{2}\right)$?

Explanation

1. 01

   Take each principal value on its own branch.

2. 02

   $-\frac{\pi}{6} + \frac{2\pi}{3} = \frac{\pi}{2}$.