Chapter 5, Problem 43RE

To determine

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

Answer to Problem 43RE

The period here is $\text{π}$ .

Explanation of Solution

Given:

  $\text{y=2Cot}\left(\text{x-}\frac{\text{π}}{\text{2}}\right)$ .

Concept used:

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

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

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

or

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

Calculation:

The period of the Cotangent 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

  $\text{y=2Cot}\left(\text{x-}\frac{\text{π}}{\text{2}}\right)$

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

  $\text{B=1}$ .

Replace B by the $\text{1}$ in the formula of period.

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

Hence the period here is $\text{π}$ .

The graph of the given equation $\text{y=2Cot}\left(\text{x-}\frac{\text{π}}{\text{2}}\right)$ is below:

  

In the graph the period of the given equation $\text{y=2Cot}\left(\text{x-}\frac{\text{π}}{\text{2}}\right)$ can be verified. Here Period is shown in the graph as $\text{3}\text{.14=π}$ .