Question

Find the principle value of ${\sin }^{-1}\sin \frac{2\pi }{3}$.

Answer 1

We know $-\frac{\pi }{2}\le {\sin }^{-1}x\le \frac{\pi }{2}$.

Now,

${\sin }^{-1}\sin \frac{2\pi }{3}$

$={\sin }^{-1}\sin (\pi -\frac{\pi }{3})$

$={\sin }^{-1}\sin \frac{\pi }{3}$

$=\frac{\pi }{3}$.