Question

Write the principal value of $\sin ^{-1}\left(-\frac{1}{2}\right)$.

Answer 1

SOLUTION : Since $\sin ^{-1}(-x)=-\sin ^{-1} x \quad \therefore$ The principal value of $\sin ^{-1}\left(-\frac{1}{2}\right)=-\sin ^{-1}\left(\frac{1}{2}\right)=-\frac{\pi}{6}$. (The principal value of $\sin ^{-1} x$ must lie in $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ ).