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Recently I was looking at modelling tides with the form of $a*\cos(bx)+c*\cos(dx)$. Can I combine these two terms into a single function? I realise that $\cos(bx)+\cos(dx)$ becomes $2\cos\bigl(\frac{(b+d)}{2}\bigr)*\cos\bigl(\frac{(b-d)}{2}\bigr)$, and that I can take $a$ out as a common factor; how do I combine $a*\cos(bx)+c*\cos(dx)$ into one cosine function?

Lalit Tolani
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Angus Rogers
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    If $b,d$ are rationally independent your function is not periodic so can't be written as a single cosine. – coffeemath Jun 27 '21 at 13:47
  • You have varied both frequency and amplitude, which complicates things. Is there any possibility you can fix one of them? – Soham Jun 27 '21 at 13:50
  • Currently I have $b$ and $d$ as rationally dependant values (I think) - the function is periodic @coffeemath. – Angus Rogers Jun 27 '21 at 14:04
  • Because I'm only modelling tides I can make all the variables constant for a specific situation @Soham. I was just interested to know if there was a process to combine the functions. – Angus Rogers Jun 27 '21 at 14:07
  • @AngusRogers https://math.stackexchange.com/questions/397984/identity-for-a-weighted-sum-of-sines-sines-with-different-amplitudes – Soham Jun 27 '21 at 14:36

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