# Thread: Equation for a butterfly-shaped sine wave?

1. ## Equation for a butterfly-shaped sine wave?

I have here a mysterious sine wave that when plotted in polar coordinates produces a cool butterfly shape.

I would like to know the equation for this sine wave.

Known: the wave period and the maxima and minima of the wave amplitudes. Is it possible to derive the equation from this info?

(See thumbnails or MS Word attachment)

Thanks,
Rainer

2. Here is an equation of a butterfly curve in polar.

$r=e^{cos({\theta})}-2cos(4{\theta})+sin^{3}(\frac{\theta}{4})$

This produces: