Chapter 11.3, Problem 15E

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 15E

The curve is a Limacon.

Explanation of Solution

Given information:

The equation in polar coordinate system: $r=1-2\sin \theta$

Calculation:

The given equation is $r=1-2\sin \theta$ .

From the above equation, it is seen that $\left|r\right|=\left|1-2\sin \theta \right|\le 3$ .

So, consider the point $\left[-3,3\right]$ for y -range and $\left[-4.5,4.5\right]$ 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 Limacon.