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16 requires a healthy mix of denition arithmetic and

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Unformatted text preview: e graph of θ = 5π 4 π π 4. As in the previous example, the variable r is free in the equation θ = − 32 . Plotting r, − 32 for various values of r shows us that we are tracing out the y -axis. 798 Applications of Trigonometry y y r>0 4 r=0 x −4 4 x π θ = − 32 −4 r<0 π In θ = − 32 , r is free π The graph of θ = − 32 Hopefully, our experience in Example 11.5.1 makes the following result clear. Theorem 11.8. Graphs of Constant r and θ: Suppose a and α are constants, a = 0. • The graph of the polar equation r = a on the Cartesian plane is a circle centered at the origin of radius |a|. • The graph of the polar equation θ = α on the Cartesian plane is the line containing the terminal side of α when plotted in standard position. Suppose we wish to graph r = 6 cos(θ). A reasonable way to start is to treat θ as the independent variable, r as the dependent variable, evaluate r = f (θ) at some ‘friendly’ values of θ and plot the resulting points.2 We generate the table...
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