The angle $\cos ^ { - 1 } \left( \cos \frac { 5 \pi } { 3 } \right)$ is

A) $- \frac { 2 \pi } { 3 }$
B) $- \frac { 5 \pi } { 3 }$
C) $\frac { 2 \pi } { 3 }$
D) $\frac { \pi } { 3 }$
E) $\frac { 8 \pi } { 3 }$

Question

The angle $\cos ^ { - 1 } \left( \cos \frac { 5 \pi } { 3 } \right)$ is

A) $- \frac { 2 \pi } { 3 }$
B) $- \frac { 5 \pi } { 3 }$
C) $\frac { 2 \pi } { 3 }$
D) $\frac { \pi } { 3 }$
E) $\frac { 8 \pi } { 3 }$

Quizplus · Accepted Answer

The range of the principal value of the inverse cosine function, $\cos^{-1}(x)$, is $0$ to $\pi$. Since $\cos\left(\frac{5\pi}{3}\right) = \cos\left(\frac{\pi}{3}\right)$, and $\frac{\pi}{3}$ is within the principal range of $\cos^{-1}$, the angle $\cos^{-1}\left(\cos\left(\frac{5\pi}{3}\right)\right) = \frac{\pi}{3}$.

The Angle cos⁡−1(cos⁡5π3)\cos ^ { - 1 } \left( \cos \frac { 5 \pi } { 3 } \right)cos−1(cos35π​)

The Angle $\cos ^ { - 1 } \left( \cos \frac { 5 \pi } { 3 } \right)$