Find the exact value of the expression.
-$$\tan ^ { - 1 } \frac { \sqrt { 3 } } { 3 }$$
A) $\frac { \pi } { 6 }$
B) $\frac { \pi } { 4 }$
C) $\frac { \pi } { 3 }$
D) $\frac { 7 \pi } { 6 }$

Question

Quizplus · Accepted Answer

The expression $\tan^{-1}\frac{\sqrt{3}}{3}$ asks for the angle whose tangent is $\frac{\sqrt{3}}{3}$. This is equivalent to $\tan^{-1}\left(\frac{1}{\sqrt{3}}\right)$, which is the angle whose tangent is the reciprocal of $\sqrt{3}$, known to be $\frac{\pi}{6}$ or 30 degrees in standard position.

Find the Exact Value of the Expression tan⁡−133\tan ^ { - 1 } \frac { \sqrt { 3 } } { 3 }tan−133​​

Find the Exact Value of the Expression $\tan ^ { - 1 } \frac { \sqrt { 3 } } { 3 }$