find the exact value of tan^(-1)(0). tan^(-1)(0)= (type your answer in radians.)

Explanation:

Step1: Recall inverse - tangent definition

The inverse - tangent function, $y = \tan^{-1}(x)$, is defined as the angle $\theta$ such that $\tan(\theta)=x$ and $-\frac{\pi}{2}<\theta<\frac{\pi}{2}$.

Step2: Find the angle

We need to find $\theta$ such that $\tan(\theta) = 0$ and $-\frac{\pi}{2}<\theta<\frac{\pi}{2}$. We know that $\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}$, and $\tan(\theta) = 0$ when $\sin(\theta)=0$. In the interval $(-\frac{\pi}{2},\frac{\pi}{2})$, the value of $\theta$ for which $\sin(\theta)=0$ is $\theta = 0$.

Answer:

$0$