$\"\"$

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The polar equation is $\"\"$ .

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The equation $\"\"$ has cosine function is symmetrical about polar axis.

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Graph the polar equation in cartesian plane: $\"\"$ on $\"\"$ .

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$\"\"$

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Observe the graph:

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The equation $\"\"$ is maximum at $\"\"$ and minimum at $\"\"$ .

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The equation $\"\"$ has cosine function is symmetrical about polar axis.

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$ .

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The $\"\"$ remains unchanged, it is symmetrical about polar axis.

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As $\"\"$ increases from $\"\"$ to $\"\"$ , $\"\"$ decreases from $\"\"$ to $\"\"$ .

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As $\"\"$ increases from $\"\"$ to $\"\"$ , $\"\"$ decreases from $\"\"$ to $\"\"$ .

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As $\"\"$ increases from $\"\"$ to $\"\"$ , $\"\"$ increases from $\"\"$ to $\"\"$ .

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As $\"\"$ increases from $\"\"$ to $\"\"$ , $\"\"$ increases from $\"\"$ to $\"\"$ .

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As $\"\"$ increases from $\"\"$ to $\"\"$ , $\"\"$ increases from $\"\"$ to $\"\"$ .

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As $\"\"$ increases from $\"\"$ to $\"\"$ , $\"\"$ increases from $\"\"$ to $\"\"$ .

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This means that the distance from increases from $\"\"$ to $\"\"$ , but instead of being in the first quadrant this portion of the polar curve lies on the opposite side of the pole in the third quadrant.

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The remainder of the curve is drawn in a similar fashion, with the arrows and numbers indicating the order in which the portions are traced out. The resulting curve has 12 loops and it called a 12-leaves rose.

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Graph the polar eqation:

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$\"\"$

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$\"\"$

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Graph of the polar equation in cartesian plane: $\"\"$ .

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$\"\"$