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Unformatted text preview: in the xy -plane, instead of graphing in Quadrant II, we graph in Quadrant IV, with all
of the angle rotations starting from the negative x-axis.
θ runs from π
2 to π 3 π
2 π 3π
2 2π θ x −3
r < 0 so we plot here
As θ ranges from π to 32 , the r values are still negative, which means the graph is traced out in
Quadrant I instead of Quadrant III. Since the |r| for these values of θ match the r values for θ in
3 The graph looks exactly like y = 6 cos(x) in the xy -plane, and for good reason. At this stage, we are just graphing
the relationship between r and θ before we interpret them as polar coordinates (r, θ) on the xy -plane. 800 Applications of Trigonometry 0, π , we have that the curve begins to retrace itself at this point. Proceeding further, we ﬁnd
that when 32 ≤ θ ≤ 2π , we retrace the portion of the curve in Quadrant IV that we ﬁrst traced
out as 2 ≤ θ ≤ π . The reader is invited to verify that plotting any range of θ outside the in...
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