Chapter 4.6, Problem 10E

To determine

To state: the period of the function and match with its graph.

Answer to Problem 10E

Graph of $y=\tan \frac{x}{2}$ is graph (c).

  $y=\tan \frac{x}{2}$ has period of $2\pi$ .

Explanation of Solution

Given information:

Given function is

  $y=\tan \frac{x}{2}$ .

Calculation:

Consider the function.

  $y=\tan \frac{x}{2}$

By solving the equations,

  $\frac{x}{2}=-\frac{\pi }{2}$ and $\frac{x}{2}=\frac{\pi }{2}$

The value obtained is:

  $x=-\pi$ and $x=\pi$

So for function $y=\tan \frac{x}{2}$ there are two consecutive asymptote occurring at $x=-\pi$ and $x=\pi$ . Hence graph of function $y=\tan \frac{x}{2}$ is as follows:

  

The graph shows that the plotted function that is $y=\tan \frac{x}{2}$ has period of $2\pi$ .

Graph of $y=\tan \frac{x}{2}$ is graph (c).