what is the exact value of tan⁻¹(0)? a π/6 b π/3 c 0 d π/4

Explanation:

Step1: Recall inverse - tangent definition

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

Step2: Find the angle

We know that $\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}$. We want to find $\theta$ such that $\tan(\theta) = 0$. This occurs when $\sin(\theta)=0$ and $\cos(\theta)\neq0$ in the domain $-\frac{\pi}{2}<\theta<\frac{\pi}{2}$. The angle $\theta = 0$ satisfies $\tan(0)=\frac{\sin(0)}{\cos(0)}=\frac{0}{1}=0$.

Answer:

C. 0