How do you graph #r=8cos2theta# on a graphing utility?

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Answer 1 · 2016-12-10T16:14:14

Use the Cartesian form.

The period for the graph is #(2pi)/2=pi#.

In one half period #theta in [-pi/4, pi/4], r>=0; r<0#. for the other half

#theta in (pi/4, pi/2]#. In the double period #theta in [0, 2pi], two

loops are created.

The cartesian form of the given equation is

#(x^2+y^2)sqrt(x^2+y^2)=9(x^2-y^2)# that befits the graphic utility

that is readily available here.

graph{(x^2+y^2)^1.5-8(x^2-y^2)=0 [-10, 10, -5, 5]}