# Find the principal values of the following : $\sin^{-1}\left ( \frac{-1}{2} \right )$

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

$\implies \sin x = \frac{-1}{2}= -\sin(\frac{\pi}{6}) = \sin(-\frac{\pi}{6})$
We know, principle value range of $\dpi{100} sin^{-1}$ is $\dpi{100} [-\frac{\pi}{2}, \frac{\pi}{2}]$

$\dpi{100} \therefore$ Principle value of $\dpi{100} \sin^{-1}\left ( \frac{-1}{2} \right )$ is $\dpi{100} -\frac{\pi}{6},$

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