Question

The principal value of ${\sin }^{-1}\left(\sin \frac{2\pi }{3}\right)$ is:

• A. $\frac{2\pi }{3}$
• B. $-\frac{2\pi }{3}$
• C. $\frac{\pi }{3}$
• D. $\frac{4\pi }{3}$

Answer 1

Answer: (C)

Let ${\sin }^{-1}\left(\sin \frac{2\pi }{3}\right)=\theta$
$\Rightarrow \sin \theta =\sin \frac{2\pi }{3}$
Note: Principle value of sin x lies between
$\frac{-\pi }{2}$ and $\frac{\pi }{2}$
So, here $\sin \theta =\sin \left(\pi -\frac{\pi }{3}\right)=\sin \frac{\pi }{3}$
Therefore, principle value of
${\sin }^{-1}\left(\sin \frac{2\pi }{3}\right)$ is $\frac{\pi }{3}$