The graphs of some specific polar equations are explored using java applet. You can also plot your own points generated using the polar equation under investigation.A tutorial on Graphing Polar Equations is in this website. Free polar graph paper is available.
Interactive Tutorial Using Java Applet
A- you can graph an equation or single points.
B- r is the radial coordinate and t is the angular coordinate.
1- Click on button "click here to start" and maximize the window obtained.
2- Choose one of the polar equations r = a + b*cos(t) or r = a*sin(nt) and plot its graph. Then use the "point by point" plot to fully understand how is the
graph generated by checking the position of a point against r ant t.
Use the scrollbars to change the parameters.
3- choose the equation r = a + b*cos(t) and set a and b such that:
a) a / b = 1 (cardioid)
b) a / b < 1 (limacon with loop)
c) 1 < a/b < 2 (limacon)
d) a / b > 2 (limacon)
4- choose the equation r = a*sin(nt) ( n is an integer not equal to zero)
set a to certain value and set n to 1,2,3,.... you obtain flower shaped
More references on polar coordinates.