Mark the tick against the correct answer in the following:
Question:

Mark the tick against the correct answer in the following:

The principal value of $\cos ^{-1}\left(\frac{-1}{2}\right)$ is

A. $\frac{-\pi}{3}$

B. $\frac{2 \pi}{3}$

C. $\frac{4 \pi}{3}$

D. $\frac{\pi}{3}$

Solution:

To Find: The Principle value of $\cos ^{-1}\left(\frac{-1}{2}\right)$

Let the principle value be given by $\mathrm{x}$

Now, let $x=\cos ^{-1}\left(\frac{-1}{2}\right)$

$\Rightarrow \cos x=\frac{-1}{2}$

$\Rightarrow \cos x=-\cos \left(\frac{\pi}{3}\right)\left(\because \cos \left(\frac{\pi}{3}\right)=\frac{1}{2}\right)$

$\Rightarrow \cos x=\cos \left(\pi-\frac{\pi}{3}\right)(\because-\cos (\theta)=\cos (\pi-\theta))$

$\Rightarrow x=\frac{2 \pi}{3}$