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# 0804 ch 8 day 4

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• ### 0804 ch 8 day 4

1. 1. 8.2 Graphs of Polar Equations2 Timothy 3:16 "All Scripture is breathed out by Godand proﬁtable for teaching, for reproof, for correction,and for training in righteousness."
2. 2. We graph on the r-θ plane.(Review the design of the polar graph paper)
3. 3. We graph on the r-θ plane.(Review the design of the polar graph paper)Just as we did when learning how to graph usinga Cartesian Coordinate plane in Algebra, we willstart off by graphing a polar equation “by hand”.
4. 4. We graph on the r-θ plane.(Review the design of the polar graph paper)Just as we did when learning how to graph usinga Cartesian Coordinate plane in Algebra, we willstart off by graphing a polar equation “by hand”.We will set up a table of values for this equation: r = 3sin θ “pick a θ , ﬁnd r “
5. 5. r = 3sin θθ r
6. 6. r = 3sin θθ r0°
7. 7. r = 3sin θθ r0° 0
8. 8. r = 3sin θ θ r0° 030°
9. 9. r = 3sin θθ r0° 030° 1.5
10. 10. r = 3sin θ θ r0° 030° 1.545°
11. 11. r = 3sin θ θ r0° 030° 1.545° 2.12
12. 12. r = 3sin θ θ r0° 030° 1.545° 2.1260°
13. 13. r = 3sin θ θ r0° 030° 1.545° 2.1260° 2.6
14. 14. r = 3sin θ θ r0° 030° 1.545° 2.1260° 2.690°
15. 15. r = 3sin θ θ r0° 030° 1.545° 2.1260° 2.690° 3
16. 16. r = 3sin θ θ r θ r0° 030° 1.545° 2.1260° 2.690° 3
17. 17. r = 3sin θ θ r θ r0° 0 120°30° 1.545° 2.1260° 2.690° 3
18. 18. r = 3sin θ θ r θ r0° 0 120° 2.630° 1.545° 2.1260° 2.690° 3
19. 19. r = 3sin θ θ r θ r0° 0 120° 2.630° 1.5 135°45° 2.1260° 2.690° 3
20. 20. r = 3sin θ θ r θ r0° 0 120° 2.630° 1.5 135° 2.1245° 2.1260° 2.690° 3
21. 21. r = 3sin θ θ r θ r0° 0 120° 2.630° 1.5 135° 2.1245° 2.12 150°60° 2.690° 3
22. 22. r = 3sin θ θ r θ r0° 0 120° 2.630° 1.5 135° 2.1245° 2.12 150° 1.560° 2.690° 3
23. 23. r = 3sin θ θ r θ r0° 0 120° 2.630° 1.5 135° 2.1245° 2.12 150° 1.560° 2.6 180°90° 3
24. 24. r = 3sin θ θ r θ r0° 0 120° 2.630° 1.5 135° 2.1245° 2.12 150° 1.560° 2.6 180° 090° 3
25. 25. r = 3sin θ θ r θ r0° 0 120° 2.630° 1.5 135° 2.1245° 2.12 150° 1.560° 2.6 180° 090° 3 210°
26. 26. r = 3sin θ θ r θ r0° 0 120° 2.630° 1.5 135° 2.1245° 2.12 150° 1.560° 2.6 180° 090° 3 210° −1.5
27. 27. r = 3sin θ θ r θ r0° 0 120° 2.630° 1.5 135° 2.1245° 2.12 150° 1.560° 2.6 180° 090° 3 210° −1.5 225°
28. 28. r = 3sin θ θ r θ r0° 0 120° 2.630° 1.5 135° 2.1245° 2.12 150° 1.560° 2.6 180° 090° 3 210° −1.5 225° −2.12
29. 29. Now, sketch these points on your graph paper.When done, compare your graph with the personnext to you.
30. 30. r = 3sin θ θ r θ r0° 0 120° 2.630° 1.5 135° 2.1245° 2.12 150° 1.560° 2.6 180° 090° 3 210° −1.5 225° −2.12
31. 31. Let’s graph it on your calculator ... mode: Polar format: Polar GCGraph in Radian mode ... and trace thenGraph in Degree mode ... and trace
32. 32. Let’s graph it on your calculator ... mode: Polar format: Polar GCGraph in Radian mode ... and trace thenGraph in Degree mode ... and traceYou need to be able to graph polar equations usingyour calculator and the trace feature.Let’s do some examples ...
33. 33. 1. r = 5 zoom standard zoom square
34. 34. 1. r = 5 zoom standard zoom square cos ( 3θ )2. r = [ −1, 1], [ −1, 1] graph 2
35. 35. 1. r = 5 zoom standard zoom square cos ( 3θ )2. r = [ −1, 1], [ −1, 1] graph 23. r = 8 cos ( 2θ ) [ −8, 8 ], [ −8, 8 ] so zoom standard zoom square works ...
36. 36. 4. pg. 592 figure 12 3 ⎛ 5θ ⎞ θ max : 720° r = sin θ + sin ⎜ ⎟ ⎝ 2 ⎠ [ −2, 2 ], [ −2, 2 ]
37. 37. 4. pg. 592 figure 12 3 ⎛ 5θ ⎞ θ max : 720° r = sin θ + sin ⎜ ⎟ ⎝ 2 ⎠ [ −2, 2 ], [ −2, 2 ]5. pg. 593 figure 13 ⎛ 2θ ⎞ θ max : 1080° r = cos ⎜ ⎟ ⎝ 3 ⎠ [ −1, 1], [ −1, 1] graph zoom square
38. 38. Tomorrow we will look at some speciﬁc “families”of polar equations.Do you know how to get your calculator back to“normal”? No HW!!!The price of greatness is responsibility. Winston Churchill