# What are limacons and cardioids?

Dec 28, 2014

Limacons are polar functions of the type:
$r = a \pm b \cos \left(\theta\right)$
$r = a \pm b \sin \left(\theta\right)$
With $| \frac{a}{b} | < 1$ or $1 < | \frac{a}{b} | < 2$ or $| \frac{a}{b} | \ge 2$

Consider, for example: $r = 2 + 3 \cos \left(\theta\right)$
Graphically:

Cardioids are polar functions of the type:
$r = a \pm b \cos \left(\theta\right)$
$r = a \pm b \sin \left(\theta\right)$
But with $| \frac{a}{b} | = 1$

Consider, for example: $r = 2 + 2 \cos \left(\theta\right)$
Graphically:

in both cases:
$0 \le \theta \le 2 \pi$

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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: