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

Question

5582 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-23T04:34:19

See the graph of this dimpled limacon and details.

This limacon #r = 3 + 2 cos theta in [ 1, 5 ]#.

The pole r = 0 is outside.

As r is f ( cos theta ) = f ( cos (- theta ))#, the graph is symmetrical

about the initial line #theta = 0#.

Use #r = sqrt ( x^2 + y^2 ) >= 0#

and #r (cos theta. sin theta ) = ( x, y )#, for the Cartesian form

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

The Socratic graph of this dimpled limacon is immediate.
graph{ ( x^2 + y^2 ) - 3 sqrt ( x^2 + y^2 ) - 2 x =0}