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I have two functions of time: function_graphs The linear black line is the current output and the tangent red line is the desired output.

I'm trying to create a map (function) between the two functions where the linear black line is the input and the red tangent is the output with no time variables involved.

I have tried just subtracting the functions, but its still a function of time.

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I'm going to name your two functions $f$ for the sinusoid and $g$ for the function in black. What I get from your question is that you are looking for a function that takes every value of $g(t)$ to $f(t)$. The function that satisfies this is $k(x) = f(g^{-1}(x))$. The way you can think about this is simple: $g^{-1}(x)$ takes you from your "black line" to the value in time that leads to that point on the line. Then $f(g^{-1}(x))$ gives the value on the sinusoid that belongs to that value of time.

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  • $\begingroup$ So x is the value and not the time? $\endgroup$ Commented May 29, 2022 at 21:28

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