Sullivan Algebra and Trigonometry: Section 10.2

1
Sullivan Algebra and Trigonometry Section 10.2

• Objectives of this Section
• Graph and Identify Polar Equations by Converting
  to Rectangular Coordinates
• Test Polar Equations for Symmetry
• Graph Polar Equations by Plotting Points

2
An equation whose variables are polar coordinates
is called a polar equation. The graph of a polar
equation consists of all points whose polar
coordinates satisfy the equation.
3
Identify and graph the equation r 2
Circle with center at the pole and radius 2.
4
(No Transcript)
5
(No Transcript)
6
Let a be a nonzero real number, the graph of the
equation
is a horizontal line a units above the pole if a
gt 0 and units below the pole if a lt 0.
7
Let a be a nonzero real number, the graph of the
equation
is a vertical line a units to the right of the
pole if a gt 0 and units to the left of the
pole if a lt 0.
8
(No Transcript)
9
(No Transcript)
10
Let a be a positive real number. Then,
Circle radius a center at (0, a) in rectangular
coordinates.
Circle radius a center at (0, -a) in
rectangular coordinates.
11
Let a be a positive real number. Then,
Circle radius a center at (a, 0) in rectangular
coordinates.
Circle radius a center at (-a, 0) in
rectangular coordinates.
12
Symmetry with Respect to the Polar Axis (x-axis)
13
Symmetry with Respect to the Line
(y-axis)
14
Symmetry with Respect to the Pole (Origin)
15
Tests for Symmetry
Symmetry with Respect to the Polar Axis (x-axis)
16
Tests for Symmetry
Symmetry with Respect to the Line
(y-axis)
17
Tests for Symmetry
Symmetry with Respect to the Pole (Origin)