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9.2 Graphing Polar Equations

9.2 Graphing Polar Equations. Polar Form. When you are graphing equations in polar form, you graph them on a polar coordinate system. Polar Functions. Plotting Polar Equations. A curve generated by the equations below is called a rose. The Rose. The Lemniscate.

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9.2 Graphing Polar Equations

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  1. 9.2 Graphing Polar Equations

  2. Polar Form • When you are graphing equations in polar form, you graph them on a polar coordinate system.

  3. Polar Functions

  4. Plotting Polar Equations

  5. A curve generated by the equations below is called a rose. The Rose

  6. The Lemniscate • In 1694 Jakob Bernoulli published his work Acta Eruditorum in which he called the curve generated by the equations below a lemniscus which is latin for “pendant ribbon”.

  7. The Lemniscate

  8. The Limaçon • AKA the Limaçon of Pascal. • Was first investigated by Dürer in 1525. • Later rediscovered by Étienne Pascal (father of Blaise Pascal). • Formally named by Roberval in 1650. • Limaçon comes from the latin limax which means “snail”.

  9. The Limaçon

  10. The Cardioid • The Cardioid is a type of Limaçon (the degenerate case where a=b). • First used by de Castillon in 1741. • Is named for its resemblance to a heart.

  11. The Cardioid

  12. The Spiral of Archimedes • This curve was first studied by Conon and then later by Archimedes in 225 BC.

  13. Homework!!!! Pg. 480 # 6-17 [5], 27

  14. References • http://mathworld.wolfram.com

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