Polar Graphs (Limacons and Cardioids)

Q:  Are the graphs of the polar equation in the form of r=a+bsinө and r= a-bsinө different in any way?

A: Why not try it out on your calculator?  This is a very easy question to answer on your own.  r=a+bsinθ and r=a-bsinθ are basically the same shape.  As you can see from the picture below, one is a reflection of the other over the x-axis/polar axis.  The blue graph is r = 3+4sinθ and the reddish graph is r = 3-4sinθ.

Blue: r=3+4sin(theta), Red: r=3-4sin(theta)

In case you were wondering, the values of a and b in the equation r=a±bsinθ or r=a±bcosθ affect the shape of the graph.  This diagram summarizes how limacons (w/inner loop, dimpled or convex) differ from cardioids.

Limacons and Cardioids


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