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Graphs of Polar Coordinates

- Sections 6.4

Objectives

- Use point plotting to graph polar equations.
- Use symmetry to graph polar equations.

Symmetry Tests

- symmetry with respect to the polar axis replace

? with ? (check for equivalent equation) - symmetry with respect to the line replace ?

with ? and r with r (check for equivalent

equation) - symmetry with respect to the pole replace r

with r (check for equivalent equation)

Symmetry Tests

- If a polar equation passes a symmetry test, then

its graph exhibits that symmetry - If a polar equation does not pass a symmetry

test, then its graph may or may not exhibit that

symmetry.

Test for symmetry and then graph the polar

equation

Circles in Polar Coordinates

a

a

Test for symmetry and then graph the polar

equation

Limaçons in Polar Coordinates

Test for symmetry and then graph the polar

equation

Lemniscates in Polar Coordinates

a ? 0

a

a

Rose Curves in Polar Coordinates

If n is even, the rose has 2n petals. If n is

odd, the rose has n petals.

a is the distance from the tip of the petal to

the pole

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