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 two 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 clicking the
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 blue petal, the positive orange
petal, the negative purple petal, and finally completes the positive green
petal. Notice how this matches the
algebraic sign of the graph on the right.