How do you graph $r=3-2costheta$ ?

Question

6707 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-08-01T12:04:10

See the graph of this dimpled limacon.

$0 <= r = 3 - 2 cos theta in [ 1, 5 ]$

Period = period of $cos theta = 2pi$ .

Using $r = sqrt ( x^2 +t^2 ) and cos theta = x/r$ ,

the Cartesian form is obtained as

$x^2 + y^2 - 3 sqrt ( x^2 + y^2 )= 2x = 0$

The graph of this dimpled limacon is immediate.

graph{ x^2 + y^2 -3sqrt ( x^2 + y^2 )+ 2x = 0[-20 20 -10 10]}

How do you graph r=3-2costhetar=3-2costheta?