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  • Fill in the blanks The value of sin inverse into bracket sin 3 pi divided 5 is ...

Fill in the blanks The value of sin^{-1}\left ( sin \frac{3\pi}{5} \right ) is_______.

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The value of \sin^{-1}\left ( \sin\frac{3\pi}{5} \right ) is \frac{2\pi}{5}

Principal value of \sin^{-1} is \left [ -\frac{\pi}{2} ,\frac{\pi}{2}\right ]

now, \sin^{-1}\left ( \sin\frac{3\pi}{5} \right ) should be in the given range

\frac{3\pi}{5} is outside the range \left [ -\frac{\pi}{2} ,\frac{\pi}{2}\right ]

As, sin (π – x) = sin x

So, \sin^{-1}\left ( \sin\frac{3\pi}{5} \right )=\sin^{-1}\left ( \sin \left ( \pi-\frac{3\pi}{5} \right ) \right )

=\sin^{-1}\left ( \sin\frac{2\pi}{5} \right )

=\sin^{-1}\left ( \sin\frac{2\pi}{5} \right )=\frac{2\pi}{5}

 

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