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

Answers (1)

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 sin^{-1} is [-\frac{\pi}{2}, \frac{\pi}{2}]

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

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