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Suppose I'm given a function

f(x) = sin(Ax + B) + sin(Cx + D)

is there a simple (or, perhaps, not-so-simple) way to compute the range of this function? My goal is ultimately to construct a function g(x, S, T) that maps f to the range [S, T].

My strategy is to first compute the range of f, then scale it to the range [0,1], then scale that to the range [S, T].

Ideally I would like to be able to do this for an arbitrary number of waves, although to keep things simple I'm willing to be satisfied with 2 if it's the easiest route.

Numerical methods welcome, although an explicit solution would be preferable.

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    I know a simple way to do it only if $A = \pm C$.2011-07-19
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    Heh, unfortunately I can't make that assumption, as that would just simplify to a single wave with appropriate phase shift.2011-07-19
  • 0
    The question was also asked on /r/math on Reddit. Here's [that discussion](http://www.reddit.com/r/math/comments/itm2d/range_of_sum_of_sine_waves/).2011-07-19

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