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6.5 Graphs of Polar Equations

6.5 Graphs of Polar Equations. I. General Form. A.) Graphs of Polar Functions- An infinite collection of rectangular coordinates ( x , y ) can be represented by an equation in terms of x and/or y. Collections of polar coordinates can be represented in a similar fashion, where.

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6.5 Graphs of Polar Equations

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  1. 6.5 Graphs of Polar Equations

  2. I. General Form A.) Graphs of Polar Functions- An infinite collection of rectangular coordinates (x, y) can be represented by an equation in terms of x and/or y. Collections of polar coordinates can be represented in a similar fashion, where

  3. On your TI-83+, change your MODE to POLAR. Set your window to [0,2π];[-5,5]; [-5,5] and graph This direction Start (0,0)

  4. Make a table!!! B.) Ex. 1- Try a few of these.

  5. II. Analyzing Polar Equations A.) Characteristics of a Polar: (Much the same as the characteristics of a rectangular equation.)

  6. B.) Symmetry Tests - TESTREPLACEWITH x-axis y-axis Origin

  7. C.) Ex. 2- Determine the symmetry for x-axis: y-axis: Origin: NO! YES! NO!

  8. D.) Ex. 3 - Analyze

  9. E.) Ex. 4 – Use the graph from example 1 to analyze

  10. F.) Ex. 5 – Use your graphing calculator to analyze the following polar equations:

  11. III. Rose Curves A.) Def. – A ROSE CURVE is any polar equation in the form of where n is an integer greater than 1. If n is odd, there are n petals. If n is even, there are 2n petals.

  12. B.) For all rose curves .

  13. MORE EXCITEMENT TO COME TOMORROW!!!!!

  14. IV. Limaçon Curves A.) Any polar equation in the form of is called a LIMAÇON (“leemasahn” or “snail”) CURVE.

  15. B.) Ex. 6- Analyze

  16. C.) In general-

  17. V. Lemniscate Curves A.) Any polar equation in the form of or is called a LEMNISCATE CURVE.

  18. B.) Ex. 7- Analyze

  19. C.) In general-

  20. VI. The Spiral of Archimedes A.) The polar equation is called THE SPIRAL OF ARCHIMEDES.

  21. B.) Ex. 8- Analyze

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