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)

$\frac{\pi}{6}$

Answer 2

\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.