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

Explanation:

Step1: Recall the range of inverse - tangent

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:

$-\frac{\pi}{6}$