Here we go: fractal wave analysis, an example from the stock market.
http://blog.afraidtotrade.com/quick-elliott-wave-update-on-the-sp-500/
See how much more elegant an understanding can be developed?
Not saying it’s any more valid than trying to clumsily fit trig curves to non-trig data. Just that it shows how futile trigonometric approaches are to trends like one sees in the stock market, or the climate.