Question

The principal value of ${\sin }^{-1}\left(\sin \frac{3\pi }{4}\right)$ is :

• A. $\frac{5\pi }{4}$
• B. $\frac{3\pi }{4}$
• C. $\frac{\pi }{4}$
• D. $-\frac{\pi }{4}$

Answer 1

Answer: (C)

$\frac{\pi }{4}$

${\sin }^{-1}\left(\sin \frac{3\pi }{4}\right)={\sin }^{-1}\left(\frac{1}{\sqrt{2}}\right)$ $={\sin }^{-1}\left(\sin \frac{\pi }{4}\right)=\frac{\pi }{4}$.