# Equation for a butterfly-shaped sine wave?

• September 5th 2009, 08:52 AM
rainer
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
• September 5th 2009, 09:14 AM
galactus
Here is an equation of a butterfly curve in polar.

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

This produces: