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## PPT Review 9.1-9.2

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**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 .**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:**Summary of Special Polar Graphs**Limacons: Convex Limacon Limacon with inner loop Cardiod (heart-shaped) Dimpled Limacon**Circles and Lemniscates**Circles Lemniscates**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**Using Symmetry to Sketch**Limacon DImpled**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.