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

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Answer 1 · 2018-07-11T12:42:25

SWee graph and explanation

In Cartesian frame, #r = 3 + 2 sin theta# becomes

#x^2+y^2 = 3 sqrt(x^2+y^2) + 2 y#.

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

For clockwise rotation of this limacon, about the pole r = 0, through

#90^o#, use r = 3 + 2 sin (theta + pi/2)= 3 + 2 cos theta#, instead.

The Cartesian form for this limacon is

#x^2+y^2 = 3 sqrt(x^2+y^2) + 2 x#. See graph.
graph{x^2+y^2-3 sqrt(x^2+y^2)-2x = 0}.