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

Explanation

1. 01

   Find the angle $\theta$ in the branch $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ with $\sin \theta = - \frac{\sqrt{2}}{2}$.

2. 02

   That angle is $- \frac{\pi}{4}$.