Line from origin (at angle₀)

= constant = ₀

Circle around origin

r = a

Circle around origin of radius a.

r = 2acos:

We can reexpress this in rectangular coordinates

by multiplying by r, getting:

This is a circle with center at (a, 0), and radius a:

Four leaves clover

r = asin2

This curve can be plotted as indicated.

We can express it in rectangular coordinates again but it is not very illuminating:

multiply by r² and get

 r = a |sin2|

Notice that the curve  is the same but that the path is different.

Cardioid

r = a(1+cos):

This equation can be rewritten as:

Spiral

r = a

Limaçon

r = a(1+2cos)