Question

Write the value of \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]

Answer 1

\[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right) = \sin^{- 1} \left[ \sin\left( \pi - \frac{2\pi}{5} \right) \right]\]
\[ = \sin^{- 1} \left( \sin\frac{2\pi}{5} \right)\]
\[ = \frac{2\pi}{5}\]