The angle $\sec ^ { - 1 } \left( \sec \frac { 2 \pi } { 3 } \right)$ is

A) $\frac { 2 \pi } { 3 }$
B) $\frac { 4 \pi } { 3 }$
C) $- \frac { \pi } { 3 }$
D) $- \frac { 2 \pi } { 3 }$
E) $- \frac { 4 \pi } { 3 }$

Question

The angle $\sec ^ { - 1 } \left( \sec \frac { 2 \pi } { 3 } \right)$ is

A) $\frac { 2 \pi } { 3 }$
B) $\frac { 4 \pi } { 3 }$
C) $- \frac { \pi } { 3 }$
D) $- \frac { 2 \pi } { 3 }$
E) $- \frac { 4 \pi } { 3 }$

Quizplus · Accepted Answer

The expression simplifies directly because $\sec^{-1}(\sec(\theta)) = \theta$ for $\theta$ in the domain of the $\sec^{-1}$ function, which is $[0, \pi]$ excluding $\frac{\pi}{2}$. Since $\frac{2\pi}{3}$ is within this domain, the answer is $\frac{2\pi}{3}$.

The Angle sec⁡−1(sec⁡2π3)\sec ^ { - 1 } \left( \sec \frac { 2 \pi } { 3 } \right)sec−1(sec32π​)

The Angle $\sec ^ { - 1 } \left( \sec \frac { 2 \pi } { 3 } \right)$