Question

What are limacons and cardioids?

Answer 1

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:

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:

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: