Question

The value of ${\sin }^{-1}\left(\sin 5\frac{\pi }{3}\right)=$

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

Answer 1

The correct option is A $-\frac{\pi }{3}$

Given,

${\sin }^{-1}\left(\sin 5\frac{\pi }{3}\right)$

Let $\theta ={\sin }^{-1}\left(\sin 5\frac{\pi }{3}\right)$

$\sin \theta =\left(\sin 5\frac{\pi }{3}\right)=\sin (2\pi -\frac{\pi }{3})$

$\Rightarrow \sin \theta =-\sin \frac{\pi }{3}$

$\therefore \theta =-\frac{\pi }{3}$