9.2 Graphing Polar Equations

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Presentation transcript:

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

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

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”.

The Lemniscate

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”.

The Limaçon

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.

The Cardioid

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

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

References http://mathworld.wolfram.com