Chapter 11.3, Problem 13E

To determine

To determine: The appropriate window to produce the polar curve. Also, sketch the complete curve and identify the type of the curve by name.

Answer to Problem 13E

The curve is a Rose.

Explanation of Solution

Given information:

The equation in polar coordinate system: $r=2\cos 3\theta$

Calculation:

The given equation is $r=2\cos 3\theta$ .

From the above equation, it is seen that

  $\left|r\right|=\left|2\cos 3\theta \right|\le 2$ .

So, consider the point $\left[-2,2\right]$ for y -range and $\left[-3,3\right]$ for the x -range.

The graph of the given equation is shown below:

  

From the above graph it is seen that the curve is a Rose.