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

1 Answer
Aug 13, 2018

See the limacon details and graph.

Explanation:

cos theta in [ - 1, 1 ]cosθ[1,1]

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

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

no plotting, for theta in [ 2/3pi, 4/3pi ]θ[23π,43π], in thetaθ- positive,

anticlockwise measurement..

Period of r = period of cos theta = 2picosθ=2π.

Multiply both sides by r and use

cos theta = x/r and r = sqrt ( x^2 + y^2 )cosθ=xrandr=x2+y2

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

x^2 + y^2 = 2sqrt ( x^2 + y^2 ) + 4xx2+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 ]}