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The value of ...

Question

The value of ${sin}^{- 1} (sin \frac{2 π}{3})$ is

A

\frac{π}{4}

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B

\frac{π}{2}

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C

\frac{π}{3}

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D

\frac{2 π}{3}

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Solution

The correct option is C $\frac{π}{3}$
${sin}^{- 1} (sin (\frac{2 π}{3})) = {sin}^{- 1} (sin (π - \frac{π}{3})) = {sin}^{- 1} (sin \frac{π}{3}) = \frac{π}{3} [∵ {sin}^{- 1} (sin x) = x, x \in [- \frac{π}{2}, \frac{π}{2}]]$

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