Question

Find the value of ${\sin }^{-1}\left(\sin \frac{3\pi }{5}\right)$

Answer 1

The argument $\frac{3\pi }{5}\notin [\frac{-\pi }{2},\frac{\pi }{2}]$

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