Section 6.4 Graphs of Polar Equations

Section 6.4Graphs of Polar EquationsMA.PC.6.3 2000 Graph equations in the polar coordinate plane.

Graphing a Polar Equation by Point PlottingA polar equation is an equation whose

variables are and . The graph of a polar equation is the set of all points whose polar coordinates satisfy the equation. We use polar grids to graph polar equations.

Let's let each unit be 1/2.

This type of graph is called a ROSE WITH 4 PETALS.

Classical CurvesCircleRoseLemniscateLimaconCardioid

cos3r

Equations of circles would look like one of the following:

CIRCLES

2cos2r

Equations of rose curves would look like one of the following:

Where even has petals and odd has petals.

ROSE

Unit is 1/4

2sin42 r

Equations of lemniscates would like one of the following:

These graphs will pass through the pole and are propeller shaped.

LEMNISCATE

Equations of limaçons would like one of the following:

If there is an inner loop.If there is an indentation.

LIMAÇON

Unit is 1/2

cos21r

Equations of cardiods would like one of the following:

All graphs of cardiods pass through the pole.

CARDIOD

Unit is 1/4

sin1r

ExampleGraph the equation

ExampleGraph the equation

ExampleGraph the equation

ExampleGraph the equation

HomeworkWorksheet