Choose the one alternative that best completes the statement or answers the question.
Find the exact value of the expression.
-$\cos \left[ \tan ^ { - 1 } \left( \frac { \sqrt { 3 } } { 3 } \right) \right]$
A) $\frac { \pi } { 3 }$
B) $\frac { 1 } { 2 }$
C) $\frac { \sqrt { 3 } } { 3 }$
D) $\frac { \sqrt { 3 } } { 2 }$

Question

Quizplus · Accepted Answer

To find the exact value of $\cos \left[ \tan ^ { - 1 } \left( \frac { \sqrt { 3 } } { 3 } \right) \right]$, recognize that $\tan ^ { - 1 } \left( \frac { \sqrt { 3 } } { 3 } \right)$ corresponds to an angle whose tangent is $\frac{\sqrt{3}}{3}$, which is $\frac{\pi}{6}$ or 30 degrees. The cosine of 30 degrees or $\frac{\pi}{6}$ is $\frac{\sqrt{3}}{2}$.

Choose the One Alternative That Best Completes the Statement or Answers