Chapter 9.2, Problem 88AYU

To determine

To write down two different tests for symmetry with respect to the polar axis and find the examples.

Explanation of Solution

Consider the polar equation

  

Now, using pole test according to the symmetry replace with

So,

  

These two are not equivalent.

Hence the test fails.

Now, try to replace with

  

Hence, the new test works.

Consider the polar equation

  

Now, using pole test according to the symmetry replace with

So,

  

These two are equivalent.

Hence the test works.

Now, try to replace with

  

Since the two are not equivalent.

Hence, the new test fails.