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.