Find the principal values of the following:

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

Answers (1)

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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