Question

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

• 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 $\frac{\pi }{3}$