Question

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

• A. $\frac{\pi }{6}$
• B. $\frac{5\pi }{6}$
• C. $\frac{7\pi }{6}$
• D. None of these

Answer 1

Answer: (A)

${\sin }^{-1}\left\{\sin \frac{5\pi }{6}\right\}$
$={\sin }^{-1}\left\{\sin \left(\pi -\frac{\pi }{6}\right)\right\}$
$\left[\because \sin \left(\pi -\theta \right)=\sin \theta \right]$
$={\sin }^{-1}\left\{\sin \frac{\pi }{6}\right\}$
[$\because$ Principal values] $\in \left[0,\pi /2\right]$
$=\frac{\pi }{6}$
which is the required principal value.