Chapter 11.3, Problem 32E

To determine

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

Answer to Problem 32E

The curve is a parabola.

Explanation of Solution

Given information:

The polar equation: $r=-\csc \theta \cot \theta$

Calculation:

The given equation is $r=-\csc \theta \cot \theta$ .

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

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

The graph of the curve is shown below:

  

From the above graph, it is seen that the curve is a parabola.