PPT Review 9.1-9.2 - PowerPoint PPT Presentation

ppt review 9 1 9 2 n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
PPT Review 9.1-9.2 PowerPoint Presentation
Download Presentation
PPT Review 9.1-9.2

play fullscreen
1 / 22
PPT Review 9.1-9.2
116 Views
Download Presentation
kyra-franco
Download Presentation

PPT Review 9.1-9.2

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

  1. PPT Review 9.1-9.2

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

  3. 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 .

  4. Multiple Representations of Points

  5. 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°)

  6. Try plotting the following points in polar coordinates and find three additional polar representations of the point:

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

  8. Rose Curves:

  9. Circles and Lemniscates Circles Lemniscates

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

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

  12. Graphing a Polar Equation circle

  13. Using Symmetry to Sketch Limacon DImpled

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

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

  16. Graph each of these: Convex Limacon Cardioid Limacon

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

  18. 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

  19. 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

  20. 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

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