Question

How do you graph `r=2+2costheta`?

Answer 1

Take a sample point and draw.

Explanation:

get a sample point of `0, pi/6, pi/3, pi/2, pi`(or more)
draw a curve connecting each line.
Since there are only function of `costheta` related to angle `theta`,
the graph is symmetry to polar axis.
graph{((x^2)+(y^2))^2=4(x^3+y^2+x*(y^2)) [-10, 10, -5, 5]}
These type of graph is called Limaçon.
general form is `r=a+b cos theta`
The shape depends on the relationship between a and b.
In this case a=b