Chapter 6.5, Problem 70E

Solution

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

The graph of $r_1$ and $r_2$ represent the same graph but $r_2$ is rotated by $\frac{\pi }{12}$ radians in clockwise direction.

The graph of $r_1$ and $r_3$ represent the same graph but $r_2$ is rotated by $\frac{\pi }{4}$ radians in clockwise direction.

Given information:

The given equation are $r_1=3\sin 3\theta$ , $r_2=3\sin 3\left(\theta +\frac{\pi }{12}\right)$ , and $r_3=3\sin 3\left(\theta +\frac{\pi }{4}\right)$ .

Explanation:

Plot the graph for $r_1=3\sin 3\theta$ .

  

Figure (1)

Plot the graph for $r_2=3\sin 3\left(\theta +\frac{\pi }{12}\right)$ .

  

Figure (2)

Plot the graph for $r_3=3\sin 3\left(\theta +\frac{\pi }{4}\right)$ .

  

Figure (3)

The graph of $r_1$ and $r_2$ represent the same graph but $r_2$ is rotated by $\frac{\pi }{12}$ radians in clockwise direction.

The graph of $r_1$ and $r_3$ represent the same graph but $r_2$ is rotated by $\frac{\pi }{4}$ radians in clockwise direction.