Question

Find the principle value of: ${\cos }^{-1}\left(-\frac{1}{2}\right)$.

Answer 1

${\cos }^{-1}(-\frac{1}{2})=\theta$

Range of $\theta =[0,\pi ]$

So, question is what is value of $\theta$ for which $\cos \theta =-\frac{1}{2}$

$\theta =\frac{2\pi }{3}$