College Trigonometry, 2011a

11.5 Graphs of Polar Equations 939
y
y
4
θ0
x
−4 4
x
−4
In r = −3 √ 2, θ is free The graph of r = −3 √ 2
3. In the equation θ = 5π 4 , r is free, so we plot all of the points with polar representation ( r, 5π )
4 .
What we find is that we are tracing out the line which contains the terminal side of θ = 5π 4
when plotted in standard position.
y
y
4
r0
−4
In θ = 5π 4 , r is free The graph of θ = 5π 4
4. As in the previous example, the variable r is free in the equation θ = − 3π 2 . Plotting ( r, − 3π 2
for various values of r showsusthatwearetracingoutthey-axis.
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