PPT Review 9.1-9.2

Polar Coordinates and Graphing r = directed distance = directed angle Polar Axis O Counterclockwise from polar axis to .

Plotting Points in the Polar Coordinate System The point lies two units from the pole on the terminal side of the angle . The point lies three units from the pole on the terminal side of the angle . The point coincides with the point .

Multiple Representations of Points

Example of Multiple Representations from -360°≤ x ≤360° 1.) (100 , 50°) 2.) (1.2 , 70°) (100 , -310°) (-100 , 230°) (-100 , -130°) (1.2 , -290°) (-1.2 , 250°) (-1.2 , -110°)

Try plotting the following points in polar coordinates and find three additional polar representations of the point: Make sure to go over “sliding” through the pole to opposite ray when negative r is used.

Summary of Special Polar Graphs Limacons: Limacon with inner loop Cardiod (heart-shaped) Dimpled Limacon Convex Limacon

Rose Curves:

Circles and Lemniscates Note that a is the length of the diameter of the circles and length of the loop of a lemnicscate.

MATCH THE POLAR GRAPH WITH IT’S EQUATION 1. 2. 3. 4. 5. 6. 2 4 3 5 6 1

MATCH THE POLAR GRAPH WITH IT’S EQUATION 1. 2. 3. 4. 2 4 3 1

Graphing a Polar Equation circle Note that some points are “retraced” as you mark them.

Using Symmetry to Sketch Limacon DImpled Remind students of even/odd properties: cos(-u)=cos u sin(-u)=-sin u

You can see that the graph is symmetric with respect to the line Spiral of Archimedes

Graph This: Rose Curve with 2b petals = 4 petals

Graph each of these: Convex Limacon Cardioid Limacon

This type of graph is called a cardioid. Scale of this graph is 0.25

This type of graph is called a limacon without an inner loop. Let's let each unit be 1. Let's plot the symmetric points

This type of graph is called a limacon with an inner loop. Let's let each unit be 1/2. Let's plot the symmetric points

This type of graph is called a rose with 4 petals. Let's let each unit be 1/2. Let's plot the symmetric points

This type of graph is called a lemniscate Let's let each unit be 1/4.