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What is the equation of a limacon?

1 Answer

A. S. Adikesavan

Apr 27, 2016

$r^{2} = a^{2} cos 2 θ$ $r^2=a^2 cos 2theta$ .
The graph is the fallen eight, looking like the symbol $\infty$ $oo$ ...

Explanation:

For the double loop of $r^{2} = a^{2} cos 2 θ, cos 2 θ \geq 0$ $r^2=a^2 cos 2theta, cos 2theta >=0$ .

So, the range for $θ \in [0, 2 π]$ $theta in [0, 2pi]$ excludes $(\frac{π}{4}, \frac{3 π}{4})$ $(pi/4, (3pi)/4)$ and

$(\frac{5 π}{4}, \frac{7 π}{4})$ $((5pi)/4, (7pi)/4)$ , Here, $cos 2 θ < 0$ $cos 2theta < 0$ ...

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