How do you graph $r = 2 + 4 cos θ$ $r=2+4costheta$ on a graphing utility?

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Answer 1 · 2018-08-13T10:53:59

See the limacon details and graph.

$cos θ \in [- 1, 1]$ $cos theta in [ - 1, 1 ]$

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

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

no plotting, for $θ \in [\frac{2}{3} π, \frac{4}{3} π]$ $theta in [ 2/3pi, 4/3pi ]$ , in $θ$ $theta$ - positive,

anticlockwise measurement..

Period of r = period of $cos θ = 2 π$ $cos theta = 2pi$ .

Multiply both sides by r and use

$cos θ = \frac{x}{r} and r = \sqrt{x^{2} + y^{2}}$ $cos theta = x/r and r = sqrt ( x^2 + y^2 )$

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

$x^{2} + y^{2} = 2 \sqrt{x^{2} + y^{2}} + 4 x$ $x^2 + y^2 = 2sqrt ( x^2 + y^2 ) + 4x$ . The dimpled apple-like

graph is immediate.

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

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