Question

Find the value of ${\displaystyle {\sin }^{-1}\left(\sin \left(\frac{2\pi }{3}\right)\right)}$

Answer 1

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

= ${\displaystyle {\sin }^{-1}\left(\sin (\pi -\frac{\pi }{3})\right)}$

= ${\displaystyle {\sin }^{-1}\left(\sin \frac{\pi }{3}\right)}$

= ${\displaystyle \frac{\pi }{3}}$