Question

Find the principal value $co{s}^{-1}\left(\frac{1}{2}\right)$

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

Answer 1

Answer: (B)

Let ${\cos }^{-1}\left(\frac{1}{2}\right)=\theta$
$\Rightarrow \cos \theta =\frac{1}{2}$
$=\cos \frac{\pi }{3}$
$\Rightarrow \theta =\frac{\pi }{3}\in \left[0,\pi \right]$
$\therefore$ Principal value of ${\cos }^{-1}\left(\frac{1}{2}\right)$ is $\frac{\pi }{3}$