How do you graph r=2+4cosθ on a graphing utility?

1 Answer
Aug 13, 2018

See the limacon details and graph.

Explanation:

cosθ[1,1]

0<= r = 2 + 4 cos theta in [ 2 - 4, 2 + 4 ]#

=[0,6], sans negative, and so,

no plotting, for θ[23π,43π], in θ- positive,

anticlockwise measurement..

Period of r = period of cosθ=2π.

Multiply both sides by r and use

cosθ=xrandr=x2+y2

Now, the Cartesian form for Socratic graphic utility is obtained.

x2+y2=2x2+y2+4x. The dimpled apple-like

graph is immediate.

graph{ x^2 + y^2 - 2sqrt ( x^2 + y^2 ) - 4x=0 [ - 6 10 -4 4 ]}