Find the principal value of each of the following :
Question:

Find the principal value of each of the following :

$\sin ^{-1}\left(\frac{-1}{2}\right)$

Solution:

$\sin ^{-1}\left(\frac{-1}{2}\right)=-\sin ^{-1}\left(\frac{1}{2}\right)$ [Formula: $\sin ^{-1}(-x)=\sin ^{-1}(x)$ ]

$=-\frac{\pi}{6}$