Unformatted text preview: e graph of θ = 5π
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
r>0 4 r=0
x −4 4 x π
θ = − 32 −4 r<0
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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