Question

The value of $cos^{-1}\left(cos \frac{3\pi}{2}\right)$ is equal to

• A. $\frac{\pi}{2}$
• B. $\frac{3\pi}{2}$
• C. $\frac{5\pi}{2}$
• D. $\frac{7\pi}{2}$

Answer 1

Answer: (A)

$cos^{-1}\left(cos \frac{3\pi}{2}\right)$
$=cos^{-1}\left(cos \left(\pi + \frac{\pi}{2}\right)\right)$
$= cos^{-1}\left(-cos \frac{\pi}{2}\right) = \pi -cos^{-1}\left(cos \frac{\pi}{2}\right)$
$\Rightarrow \pi - \frac{\pi }{2} = \frac{\pi }{2}$