# How do you graph #r=2 cos 2theta#?

##### 1 Answer

Jul 15, 2018

Here, the non-negative

The period of

In one period

Using,

the Cartesian form of

The 2-loop Socratic graph is immediate.

graph{(x^2+y^2)^1.5-2(x^2-y^2)=0[-6 6 -3 3]}

Invalid ( r < 0 ) loops are shown below.

graph{(x^2+y^2)^1.5+2(x^2-y^2)=0[-6 6. -3 3]}

Valid and invalid combined graph:

graph{(x^2+y^2)^3-4(x^2-y^2)^2=0[-6 6. -3 3]}