Question

In Problems 13–24, find the exact value of each expression.

tan^-1 0

Short answer

The exact value of tan^-1 0 is 0.

Step-by-step solution

Step 1. Given Information:  

Given expression:tan^-1 0

We want to find the exact value of given expression.

Step 2. Solution:  

The given expression can be rewritten as:

${\tan }^{-1}0=y;-\frac{\mathrm{\pi }}{2}<y<\frac{\mathrm{\pi }}{2}$

Hence we get tan (y) = 0

Since we have tan^-1 function initially, the bounds on the tan function are going to be in the interval $\left(-\frac{\mathrm{\pi }}{2},\frac{\mathrm{\pi }}{2}\right)$ which represents the range of tan^-1 function.

Using the unit circle, we know that in order to get 0 , y must be equal to 0.

Hence, we get tan^-1 0 = 0.