Find the principal value (in radians) of $displaystyleco{s}^{-1}!(-\frac{\sqrt{3}}{2})$.

Step-by-step solution

1. The principal value of $co{s}^{-1}y$ lies in $[0,pi]$.
2. For $y=-\frac{\sqrt{3}}{2}$ the reference angle is $\frac{\pi }{6}$ because $cos\frac{\pi }{6}=\frac{\sqrt{3}}{2}$.
3. Since $y$ is negative, the angle is in the second quadrant: $\pi -\frac{\pi }{6}=\frac{5\pi }{6}$.
4. Thus the principal value is $\frac{5\pi }{6}$.

Concept tested: Principal value of arccos

Published 18 September 2026 · How this solution was prepared and checked