To write down two different tests for symmetry with respect to the polar axis and find the examples.
Explanation of Solution
Tests for symmetry:
Symmetry along the polar axis (x- axis)
In a polar equation, replacebyIf an equitant equation results, the graph has a symmetry along the polar axis.
Symmetry along the line (y- axis)
In a polar equation, replacebyIf an equivalent equation results, the graph has a symmetry along the line.
Symmetry along the pole(origin)
In a polar equation, replacebyorbyIf an equivalent equation results, the graph is symmetric with respect to the pole.
Observe the tests for symmetry, an equation may fail these tests and still have a graph that has a symmetry along the pole origin, the line or the pole.
For example:
The graph of turns out to be symmetric with respect to the polar axis, the lineand the pole, but only the test for symmetry with respect to the pole (replacebyworks.
Chapter 9 Solutions
Precalculus
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