Question

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

• A. $5\pi /6+n\pi$
• B. $5\pi /6-n\pi$
• C. $\pi /6+2n\pi$
• D. $\pi /6$

Answer 1

Answer: (D)

$\pi /6$

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