Question

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

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{6}$
• C. $\frac{2\pi }{3}$
• D. $\frac{3\pi }{2}$

Answer 1

The correct option is C $\frac{2\pi }{3}$

The principal solution of ${\cos }^{-1}(-\frac{1}{2})$ will lie in $[0,\pi ]$

${\cos }^{-1}(-\frac{1}{2})={\cos }^{-1}\left[\cos (\pi -\frac{\pi }{3})\right]$

$=\pi -\frac{\pi }{3}$

$=\frac{2\pi }{3}$
Hence, the correct answer from the given alternative is option $C$.