Section 9-2
Graphs of Polar Equations
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You can create a table of values for r and θ. Then you can use the table to plot points in the polar plane. Ordered pair ( r, θ)
Example: Graph r = sin θ
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Some of the interesting curves we can graph are called classical
curves. Below is a chart of the classical curves. Patterns in textile
often portray classical curves.
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A limacon is a curve with the equation r = a
+ b sin(θ) or r = a + b cos(θ), where a, b≠ 0.
Below is the limacon r = 2 + 3 cos(θ).
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A rose curve is a curve with the equation r = a sin(n θ) or
r = a cos(n θ), where n is an integer. Each loop in a rose curve is
called a petal. The number of petals in a given curve is n if n is odd,
and 2n if n is even. The length of each petal is a. Below is the rose
curve r = 3 sin(2θ).
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Two common kinds of spirals are called spirals of Archimedes and
logarithmic spirals. A spiral of Archimedes is of the form r = aθ + b,
and a logarithmic spiral is of the form r = ab θ. They are pictured
below.
Spiral of Archimedes
Logarithmic spiral
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Graph r = 1- 2cos θ
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Table of values
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θ
0
30
45
60
90
120
135
150
180
210
225
240
270
300
315
330
360
1‐2cosθ
1- (2cos 0)
1-(2cos 30)
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r
-1
- .73205
- .41421
0
1
2
2.41421
2.73205
3
2.73205
2.41421
2
1
0
- .41421
- .73205
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Section 9-2
`Pp. 565-567
`#11-17 all, 23,38,41
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