What are limacons and cardioids?

1 Answer
Gió
Dec 28, 2014

Limacons are polar functions of the type:
r=a+-bcos(theta)
r=a+-bsin(theta)
With |a/b|<1 or 1<|a/b|<2 or |a/b|>=2

Consider, for example: r=2+3cos(theta)
Graphically:
enter image source here

Cardioids are polar functions of the type:
r=a+-bcos(theta)
r=a+-bsin(theta)
But with |a/b|=1

Consider, for example: r=2+2cos(theta)
Graphically:
enter image source here

in both cases:
0<=theta<=2pi

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I used Excel to plot the graphs and in both cases to obtain the values in the x and y columns you must remember the relationship between polar (first two columns) and rectangular (second two columns) coordinates:

enter image source here

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