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Find the principal values of the following:

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

Answers (1)

D Divya Prakash Singh

Let us assume that $\sin^{-1}\left(-\frac{1}{2} \right )=z$ ;

Then taking inverse both sides we get;

$\sin z = (\frac{-1}{2}) = -\sin(\frac{\pi}{6})= \sin(\frac{-\pi}{6})$ .

As we know that the range of principal values of $\sin^{-1}$ is from $(\frac{-\pi}{2}, \frac{\pi}{2})$ .

Hence only one possible value is $\frac{-\pi}{6}$ .

Therefore, the principal value of $\sin^{-1}\left(-\frac{1}{2} \right )$ is $\frac{-\pi}{6}$ .

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