Question

The principal value of ${\sin }^{-1}\left(\cos \frac{5\pi }{4}\right)$ is

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

Answer 1

The correct option is C $\frac{-\pi }{4}$

${\sin }^{-1}\left(\cos \frac{5\pi }{4}\right)$
$={\sin }^{-1}\left(\cos (\frac{3\pi }{2}-\frac{\pi }{4})\right)$
$={\sin }^{-1}(-\sin \frac{\pi }{4})$
$={\sin }^{-1}\left(\sin \frac{-\pi }{4}\right)$
$=-\frac{\pi }{4}$