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c#mathtrigonometrycalculus

Get Points of Intersection with Sine Wave

I have a particle at a fixed position X and fixed amplitude AMP that travels on a sin wave.

I'd like to be able to dynamically change the period of the target sine wave WITHOUT moving the particle. (When I change the period, its X position doesn't line up to the same Y position of the graph with a different period, so it jumps all over the place.

I have a solution for this - Find where the graph with the new period intersects with the graph of the old period and create an X-offset, lining these two figures up.

For any given y on a sin wave, there will be 2 corresponding X values per period. I'm trying to get these two values. I'll then compare the derivatives to choose which one I want.

However, I don't know how to get both of these values. Any ideas?

Here's an image of what I'm after: Sin Wave Logic

Solution

  • If you have a sine-wave defined by

    y = sin(a*(x+c))+d

    then you can reverse it by

    x = (arcsin(y-d)-c)/a

    for a given a.

    This yields the solution in the range of [-pi;pi]

    The other solution you are looking for is then 2*pi-x