Chapter 11.3, Problem 19E

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 19E

The curve is a Circle.

Explanation of Solution

Given information:

The equation in polar coordinate system: $r=4\sin \theta$

Calculation:

The given equation is $r=4\sin \theta$ .

From the above equation, it is seen that $\left|r\right|=\left|4\sin \theta \right|\le 4$ .

So, consider the point $\left[-4,4\right]$ for y -range and $\left[-6,6\right]$ 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 Circle.