Chapter 6.5, Problem 72E

Solution

To graph: The given three equations and describe their relation with each other.

The graph of $r_2$ is obtained when graph of $r_1$ is rotated by $\frac{\pi }{4}$ radians in clockwise direction.

The graph of $r_3$ is obtained when graph of $r_1$ is rotated by $\frac{\pi }{3}$ radians in clockwise direction.

Given information:

The given equation are $r_1=2-2\cos \theta$ , $r_2=r_1\left(\theta +\frac{\pi }{4}\right)$ , and $r_3=r_1\left(\theta +\frac{\pi }{3}\right)$ .

Calculation:

Plot the graph for $r_1=2-2\cos \theta$ .

  

Figure (1)

Plot the graph for $r_2=r_1\left(\theta +\frac{\pi }{4}\right)$ .

  

Figure (2)

Plot the graph for $r_3=r_1\left(\theta +\frac{\pi }{3}\right)$ .

  

Figure (3)

The graph of $r_2$ is obtained when graph of $r_1$ is rotated by $\frac{\pi }{4}$ radians in clockwise direction.

The graph of $r_3$ is obtained when graph of $r_1$ is rotated by $\frac{\pi }{3}$ radians in clockwise direction.