What is the equation of a limacon?

1 Answer
Apr 27, 2016

r^2=a^2 cos 2thetar2=a2cos2θ.
The graph is the fallen eight, looking like the symbol oo...

Explanation:

For the double loop of r^2=a^2 cos 2theta, cos 2theta >=0r2=a2cos2θ,cos2θ0.

So, the range for theta in [0, 2pi]θ[0,2π] excludes (pi/4, (3pi)/4)(π4,3π4) and

((5pi)/4, (7pi)/4)(5π4,7π4), Here, cos 2theta < 0cos2θ<0...