Question

The value of $co{s}^{-1}\left(cos\frac{3\pi }{2}\right)$ 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)

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