find the exact value of tan^(-1)(-√3/3). tan^(-1)(-√3/3)=□ (type your answer in radians.)

Explanation:

Step1: Recall the range of inverse - tangent function

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

Step2: Find the angle whose tangent is (-\frac{\sqrt{3}}{3})

We know that (\tan\left(-\frac{\pi}{6}\right)=-\frac{\sqrt{3}}{3}) and (-\frac{\pi}{6}\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right)).

Answer:

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