Find the exact value of the expression, if possible. Do not use a calculator.
-$\cos ^ { - 1 } \left( \cos \frac { 7 \pi } { 6 } \right)$
A) $\frac { 5 \pi } { 6 }$
B) $\frac { 4 \pi } { 3 }$
C) $\frac { \pi } { 6 }$
D) $\frac { \pi } { 3 }$

Question

Quizplus · Accepted Answer

The principal value of $\cos^{-1}(x)$ lies in the interval $[0, \pi]$. Since $\cos\left(\frac{7\pi}{6}\right) = \cos\left(\frac{5\pi}{6}\right)$, and $\frac{5\pi}{6}$ is within the principal value range, the exact value is $\frac{5\pi}{6}$.

Find the Exact Value of the Expression, If Possible cos⁡−1(cos⁡7π6)\cos ^ { - 1 } \left( \cos \frac { 7 \pi } { 6 } \right)cos−1(cos67π​)

Find the Exact Value of the Expression, If Possible $\cos ^ { - 1 } \left( \cos \frac { 7 \pi } { 6 } \right)$