1. Graphing Polar Equations To graph polar equations we need to use a modified coordinate system that better suits the values we will be calculating.

2. Graphing Polar Equations Lets begin with a normal x, y axis

3. Graphing Polar Equations Lets begin with a normal x, y axis Next, create concentric circles all of which are increasing in radius by 1… 2 4

4. Graphing Polar Equations 2 4

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15. 2 4 1.5

16. Graphing Polar Equations 2 4 1.5 1.866

17. Graphing Polar Equations 2 4 1.5 1.866 2

18. Graphing Polar Equations 2 4 1.5 1.866 2

19. Graphing Polar Equations 2 4 1.5 1.866 2 1.5

20. Graphing Polar Equations 2 4 1.5 1.866 2 1.5 1

21. Graphing Polar Equations 2 4 1.5 1.866 2 1.5 1 0.5

22. Graphing Polar Equations 2 4 1.5 1.866 2 1.5 1 0.5 0.13 0 Didn’t graph

23. Graphing Polar Equations 2 4 1.5 1.866 2 1.5 1 0.5 0.13 0 0.5 Didn’t graph

24. Graphing Polar Equations 2 4 1.5 1.866 2 1.5 1 0.5 0.13 0 0.5 1 Didn’t graph

25. Graphing Polar Equations Some polar equations when graphed have symmetry about the x axis, y axis, or origin.

26. Graphing Polar Equations Some polar equations when graphed have symmetry about the x axis, y axis, or origin. Use this chart to help determine if a polar graph will have symmetry…

27. Graphing Polar Equations Some polar equations when graphed have symmetry about the x axis, y axis, or origin. Use this chart to help determine if a polar graph will have symmetry…

28. Graphing Polar Equations Some polar equations when graphed have symmetry about the x axis, y axis, or origin. Use this chart to help determine if a polar graph will have symmetry…

29. Graphing Polar Equations Some polar equations when graphed have symmetry about the x axis, y axis, or origin. Use this chart to help determine if a polar graph will have symmetry…

30. Graphing Polar Equations 2 4

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39. 2 4 To finish the graph using symmetry, we simply reflect the graph about the x – axis

40. Graphing Polar Equations As you can see, graphs of polar equations create some very unique shapes. Here is a guide to help you create these graphs…

41. Graphing Polar Equations