Graphs of Functions in Polar and Rectangular Coordinates
The function f is geometrically interpreted
as a curve in the plane in two ways:
first as its graph y=f(x) in rectangular (Cartesian) coordinates
as the locus of points (x,f(x)),
and second as its graph r=f(θ) in polar coordinates
as the locus of (rectangular) points (rcos(θ),rsin(θ)).
A bubble traces out corresponding points on these two graphs
between θmin and θmax,
shading in the area “under” the polar graph,
green for positive area and red for negative area.