The following graphs are related.
On the right is a rectangular plot of
, with the dependent variable,
r, plotted vertically, and the independent variable, θ,
plotted to the right.
It shows θ
varying from 0 to 2 π, and three complete oscillations of the function.
On the left, the polar plot is developed one
point at a time, with the colors matching those on the right.
θ varies from 0 to 2 π here also.
You can restart the graph on the left by double-clicking the Start button.
Notice the order in which the petals are drawn.
θ increases steadily and
r is positive for the green points in
the first half of the first petal.
Then
r is negative for the cyan (light blue) points of the
next petal.
So, as the polar plot progresses, it starts with half of a
positive green petal, then does the negative cyan (light blue) petal, the positive orange
petal, the negative red petal (overlapping part of the green one), the positive purple petal (overlapping the cyan petal), the negative blue petal (overlapping the orange one), and finally completes the positive green
petal (partially overlapping the red one). Notice how this order matches the
order of the colors of the graph on the right.