Question

The value of ${\sin }^{-1}\left(\sin \frac{5\pi }{6}\right)$ is

• A. $\frac{7\pi }{6}$
• B. $\frac{\pi }{6}$
• C. $\frac{5\pi }{6}$
• D. $-\frac{\pi }{6}$

Answer 1

The correct option is B $\frac{\pi }{6}$

${\sin }^{-1}\left(\sin \frac{5\pi }{6}\right)={\sin }^{-1}\left(\sin (\pi -\frac{\pi }{6})\right)={\sin }^{-1}\left(\sin \left(\frac{\pi }{6}\right)\right)=\frac{\pi }{6}(\because {\sin }^{-1}\left(\sin x\right)=x,x\in [-\frac{\pi }{2},\frac{\pi }{2}])$