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

Step-by-step solution

1. Recall the range of ${\cos }^{-1}x$ is $[0,\pi ]$.
2. Set $\theta ={\cos }^{-1}\left(-\frac{1}{2}\right)$ so that $\cos \theta =-\frac{1}{2}$.
3. The angle in $[0,\pi ]$ with cosine $-\frac{1}{2}$ is $\theta =\frac{2\pi }{3}$.
4. Hence the principal value is $\frac{2\pi }{3}$.

Concept tested: Principal value of inverse cosine

Published 16 September 2026 · How this solution was prepared and checked