Find the principal value of each of the following : sin^-1(sin.2π/3)

Question

Find the principal value of each of the following :

\(\sin^{-1}\left(\sin\frac{2\pi}{3}\right)\)

Answer 1

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

[ Formula: sin(π – x) = sin x )

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

[ Formula: sin ^-1( sin x) = x ]

\(=\frac{\pi}{3}\)