Graphs of Polar Coordinates

1
Graphs of Polar Coordinates

• Sections 6.4

2
Objectives

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

3
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)

4
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.

5
Test for symmetry and then graph the polar
equation
6
Circles in Polar Coordinates
a
a
7
Test for symmetry and then graph the polar
equation
8
Limaçons in Polar Coordinates
9
Test for symmetry and then graph the polar
equation
10
Lemniscates in Polar Coordinates
a ? 0
a
a
11
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