Chapter 9.7, Problem 68E

To determine

True or false:

The graph shown by polar equation $r=\frac{5}{1-\sin \left[\theta -\left(\pi /4\right)\right]}$ is obtained by rotating the graph of the function $r=\frac{5}{1+\sin \theta }$ about pole.

Answer to Problem 68E

True. The graph shown by polar equation $r=\frac{5}{1-\sin \left[\theta -\left(\pi /4\right)\right]}$ is obtained by rotating the graph of the function $r=\frac{5}{1+\sin \theta }$ about pole.

Explanation of Solution

Given information:

Polar equations: $\begin{array}{l}r=\frac{5}{1-\sin \left[\theta -\left(\pi /4\right)\right]}\\ r=\frac{5}{1+\sin \theta }\end{array}$

The given two polar equations are as:

  $r=\frac{5}{1+\sin \theta }$.........(1)

  $r=\frac{5}{1-\sin \left[\theta -\left(\pi /4\right)\right]}$.........(2)

The graphs of both equations are as follows:

  

From graph get that:

Graph of the polar equation (2) can be obtained by rotating the polar equation (1) about the pole.

Hence the statement is true.