Question

${\cos }^{-1}\left(\cos \frac{7\pi }{6}\right)$ is equal to

• A. $\frac{7\pi }{6}$
• B. $\frac{5\pi }{6}$
• C. $\frac{\pi }{3}$
• D. $\frac{\pi }{6}$

Answer 1

Answer: (B)

$co{s}^{-1}\left(cos\frac{7\pi }{6}\right)=co{s}^{-1}\left(cos\left(2\pi -\frac{5\pi }{6}\right)\right)$
$=co{s}^{-1}\left(cos\frac{5\pi }{6}\right)=\frac{5\pi }{6}$
$\left[\because co{s}^{-1}\left(cos\theta \right)=\theta \text{ if}0\le \theta \le \pi \right]$