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6.5 Graphs of Polar Equations
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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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On your TI-83+, change your MODE to POLAR
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)
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B.) Ex. 1- Try a few of these. Make a table!!!
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II. Analyzing Polar Equations
A.) Characteristics of a Polar: (Much the same as the characteristics of a rectangular equation.)
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B.) Symmetry Tests - TEST REPLACE WITH x-axis y-axis Origin
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NO! YES! NO! C.) Ex. 2- Determine the symmetry for x-axis: y-axis:
Origin: NO! YES! NO!
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D.) Ex. 3 - Analyze
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E.) Ex. 4 – Use the graph from example 1 to analyze
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F.) Ex. 5 – Use your graphing calculator to analyze the following polar equations:
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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.
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B.) For all rose curves .
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MORE EXCITEMENT TO COME TOMORROW!!!!!
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IV. Limaçon Curves A.) Any polar equation in the form of is called
a LIMAÇON (“leemasahn” or “snail”) CURVE.
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B.) Ex. 6- Analyze
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C.) In general-
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V. Lemniscate Curves A.) Any polar equation in the form of or is called a LEMNISCATE CURVE.
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B.) Ex. 7- Analyze
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C.) In general-
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VI. The Spiral of Archimedes
A.) The polar equation is called THE SPIRAL OF ARCHIMEDES.
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B.) Ex. 8- Analyze
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