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The principal value of the given equation   y=sin^{-1}\left ( \frac{\sqrt{3}}{2} \right )   is

Option: 1

\frac{\pi}{4}


Option: 2

\frac{\pi}{3}


Option: 3

\frac{\pi}{2}


Option: 4

\frac{\pi}{6}


Answers (1)

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Given that,

y=sin^{-1}\left ( \frac{\sqrt{3}}{2} \right )

 sin\ y=\left ( \frac{\sqrt{3}}{2} \right )

We know that the range of the principal value branch of  sin^{-1}x  is   \left ( -\frac{\pi}{2},\frac{\pi}{2} \right ).

Thus,

  sin\left ( \frac{\pi}{3} \right )=\frac{\sqrt{3}}{2}

Therefore, the principal value of   sin^{-1}\left ( \frac{\sqrt{3}}{2} \right )=\frac{\pi}{3}.

 

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mansi

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