Find the exact value of the expression. Do not use a calculator.
-$$\cos ^ { - 1 } \left[ \cos \left( \frac { \pi } { 10 } \right) \right]$$
A) $\frac { \pi } { 10 }$
B) $10 \pi$
C) $- 10 \pi$
D) $- \frac { \pi } { 10 }$

Question

Quizplus · Accepted Answer

The cosine inverse of cosine of an angle returns the original angle, provided the angle is within the domain of the cosine inverse function, which is $[0, \pi]$ for real numbers. Since $\frac{\pi}{10}$ is within this domain, $\cos^{-1}[\cos(\frac{\pi}{10})] = \frac{\pi}{10}$.

Find the Exact Value of the Expression cos⁡−1[cos⁡(π10)]\cos ^ { - 1 } \left[ \cos \left( \frac { \pi } { 10 } \right) \right]cos−1[cos(10π​)]

Find the Exact Value of the Expression $\cos ^ { - 1 } \left[ \cos \left( \frac { \pi } { 10 } \right) \right]$