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)

$\frac{\pi}{3}$

Answer 2

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 $\frac{\pi }{3}$