Chapter 1.6, Problem 48E

To determine

To describe: The period of $\tan x$ is $\pi$ .

Answer to Problem 48E

The period of $\tan x$ is $\pi$ verify.

Explanation of Solution

Given information:The given function is $\tan x$ .

Simplify the function.

  $\tan x=\frac{\sin x}{\cos x}$

Let the point on a unit circle with angle $\theta$ is $\left(a,b\right)$ . Also, the point on a unit circle with angle $\left(\theta +\pi \right)$ is $\left(-a,-b\right)$ . It can be observed that the angle $\left(\theta +\pi \right)$ is at the exactly half around the circle.

  $\tan \left(\theta \right)=\tan \left(\theta +\pi \right)=\frac{b}{a}$

Therefore, the period of $\tan x$ is $\pi$ .