1. 10.2 Polar Equations and Graphs

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.

4. Identify and graph the equation: r = 2

10. Graphing a polar Equation Using a Graphing Utility
Solve the equation for r in terms of
Select a viewing window in POLar mode. In addition to setting Xmax, Xmin, Xscl, and so forth the polar mode requires setting max and min and step values for Use radian mode and a square window.
Enter the expression from Step1.
Graph.

11. Theorem
Let a be a nonzero real number, the graph of the equation
is a horizontal line a units above the pole if a > 0 and |a| units below the pole if a < 0.

12. Theorem
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 > 0 and |a| units to the left of the pole if a < 0.

15. Theorem
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.

16. Theorem
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.

20. Theorem Tests for Symmetry
Symmetry with Respect to the Polar Axis (x-axis):

21. Theorem Tests for Symmetry

22. Theorem Tests for Symmetry
Symmetry with Respect to the Pole (Origin):

24. Cardioids (a heart-shaped curves)
are given by an equation of the form
where a > 0. The graph of cardioid passes through the pole.

26. Limacons without the inner loop
are given by equations of the form
where a > 0, b > 0, and a > b. The graph of limacon without an inner loop does not pass through the pole.

27. Limacons with an inner loop
are given by equations of the form
where a > 0, b > 0, and a < b. The graph of limacon with an inner loop will pass through the pole twice.

28. Rose curves
are given by equations of the form
and have graphs that are rose shaped. If n is even and not equal to zero, the rose has 2n petals; if n is odd not equal to +1, the rose has n petals.

29. Lemniscates
are given by equations of the form
and have graphs that are propeller shaped.