
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.
Chapter 9 Solutions
Precalculus
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