Do you want particles to move along a sin/cos wave? The only way I can think of doing that would be to animate the Emission Angle so that it follows a wave pattern.
There is a program called Compath that generates sin/cos position data for emitters
https://www.tpp.le-site-web.com/
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Elvis Deane!
The particleIllusion FAQ
particleIllusion Resources and tutorial CD
Astounding Adventures