$\"\"$

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Two different tests for symmetry with respect to the polar axis:

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Test 1:

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Symmetry with respect to the Polar Axis:

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In a polar equation, replace $\"\"$ by $\"\"$ .

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If an equivalent equation results, the graph is symmetric with respect to the polar axis.

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Test 2:

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In a polar equation, replace $\"\"$ by $\"\"$ and $\"\"$ by $\"\"$ .

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If an equivalent equation results, the graph is symmetric with respect to the polar axis.

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$\"\"$

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Consider the curve equation $\"\"$ .

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Replace $\"\"$ by $\"\"$ .

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$\"\"$

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$\"\"$ .

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The equation $\"\"$ is symmetric about polar axis.

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$\"\"$

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Replace $\"\"$ by $\"\"$ and $\"\"$ by $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Test 2, fails for equation $\"\"$ .

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Replace $\"\"$ by $\"\"$ is prefer to use, because in this test change in $\"\"$ only.

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$\"\"$

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Replace $\"\"$ by $\"\"$ is prefer to use, because in this test change in $\"\"$ only.