find the exact value of tan^(-1)(-sqrt(3)/3). write your answer in radians in terms of pi…

find the exact value of tan^(-1)(-sqrt(3)/3). write your answer in radians in terms of pi. tan^(-1)(-sqrt(3)/3) =

find the exact value of tan^(-1)(-sqrt(3)/3). write your answer in radians in terms of pi. tan^(-1)(-sqrt(3)/3) =

Answer

Explanation:

Step1: Recall inverse - tangent range

The range of (y = \tan^{-1}(x)) is ((-\frac{\pi}{2},\frac{\pi}{2})).

Step2: Find the angle

We know that (\tan(\frac{\pi}{6})=\frac{\sqrt{3}}{3}), and since (\tan^{-1}) is an odd - function, (\tan^{-1}(-x)=-\tan^{-1}(x)). So (\tan^{-1}(-\frac{\sqrt{3}}{3})=-\frac{\pi}{6}).

Answer:

(-\frac{\pi}{6})