To calculate: To test for symmetry with respect to the line
Answer to Problem 15E
The polar equation is symmetric with respect to the line
Explanation of Solution
Given information: Polar equation is
Formula Used:
Test for Symmetry:
To test symmetry with respect to the line
To test symmetry with respect to the polar axis, replace
To test symmetry with respect to the pole, replace
Calculation:
Polar equation is given as follows:
To test Symmetry respect with respect to the line
Replacing
Thus, polar equation is symmetric with respect to the line
To test Symmetry with respect to the polar axis
Replacing
Thus, polar equation is symmetric with respect to the polar axis
To test Symmetry with respect to the pole
Replacing
Thus, polar equation is symmetric with respect to the pole
Conclusion:
Hence, polar equation is symmetric with respect to the line
Chapter 9 Solutions
Precalculus with Limits: A Graphing Approach
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