Find the exact value of the expression. Do not use a calculator.
-$$\tan ^ { - 1 } \left[ \tan \left( - \frac { \pi } { 8 } \right) \right]$$
A) $- 8 \pi$
B) $\frac { \pi } { 8 }$
C) $8 \pi$
D) $- \frac { \pi } { 8 }$

Question

Quizplus · Accepted Answer

The inverse tangent function, $\tan^{-1}$, undoes the effect of the tangent function, $\tan$, within its principal range of $-\frac{\pi}{2}$ to $\frac{\pi}{2}$. Since $-\frac{\pi}{8}$ is within this range, $\tan^{-1}(\tan(-\frac{\pi}{8})) = -\frac{\pi}{8}$.

Find the Exact Value of the Expression tan⁡−1[tan⁡(−π8)]\tan ^ { - 1 } \left[ \tan \left( - \frac { \pi } { 8 } \right) \right]tan−1[tan(−8π​)]

Find the Exact Value of the Expression $\tan ^ { - 1 } \left[ \tan \left( - \frac { \pi } { 8 } \right) \right]$