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

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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]}