Chapter 5, Problem 42RE

To determine

Tofind:the period of the equation and sketch its graph.

Answer to Problem 42RE

The period here is $1$ .

Explanation of Solution

Given:

  $\text{y=tanπx}$ .

Concept used:

Period is measured as distance it takes for the entire graph to repeat.

Since the period of the Tangent function is $\text{π}$ .

  $\text{period=}\frac{\text{π}}{\text{B}}$ .

or

  $\text{B=}\frac{\text{π}}{\text{period}}$ .

Calculation:

The period of the Tangent function is $\text{π}$ .

The period of the function can be calculated using $\text{period=}\frac{\text{π}}{\text{B}}$ .

Comparing the equation with general equation

  $\text{y=tanπx}$

  $\text{y=ASin}\left(\text{B}\left(\text{x+C}\right)\right)\text{+D}$

  $\text{B=π}$ .

Replace B by the $\text{π}$ in the formula of period.

  $\text{period=}\frac{\text{π}}{\text{π}}=1$ .

Hence the period here is $1$ .

The graph of the given equation $\text{y=tanπx}$ is below:

  

In the graph the period of the given equation $\text{y=tanπx}$ can be verified that range will be approximately to $\text{1}\text{.}$