The principal value of $ sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)$, is
Answer & explanation
Correct answer: option 2
$ sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)$ is an angle $\theta ∈ \left[-\frac{\pi}{2},\frac{\pi}{2}\right]$ such that $ sin \theta = - \frac{\sqrt{3}}{2}$. Clearly, such an angle is $-\frac{\pi}{3}$.