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Is it possible to develop a process for using a trigonometric function to successfully model any parabolic function?

I have tried doing this question however there are functions such as this one where I cannot find a fit to it. Graph Equation: y=a sin0.703(x-c)+10

Blue
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Phillip K
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    Define "develop a process." Please give examples from elsewhere. – David G. Stork Apr 16 '20 at 17:25
  • "a trigonometric function to successfully model any parabolic function": what ? –  Apr 16 '20 at 17:27
  • In what field $\ 0$ and $\ 1$ belong to? – Manjoy Das Apr 16 '20 at 18:20
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    Please do not try to completely change a question to something completely different after you have received an answer to your initial question. I have rolled back your nonsensical edit. – K.Power Apr 16 '20 at 18:31
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    Please do not vandalize your question, especially after it has received an answer. (Questions are free to post, you don't have to recycle!) I have rolled the question back. – Blue Apr 17 '20 at 09:45

1 Answers1

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If you mean $f(x) = ax^2 + bx + c$, then yes, on any bounded interval. You can start with $g(x) = x^2$, develop a Fourier series (regarding it as an even periodic function on a symmetric interval about the origin), then use translation/scaling of $x$ and $y$ to move it to the desired function. The approximation will only be valid on a fixed interval.

MPW
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  • Say example, I have the trigonometric function of y= -16 sin 0.3925 (x-1). What is the process of me getting the parabola of a half of a period? – Phillip K Apr 16 '20 at 17:35
  • No, it works the other way around. You said you wanted to model a parabola by trig functions, not model a trig function by a parabola. So you specify the parabola, and I will generate a trig function to approximate it. – MPW Apr 16 '20 at 17:49
  • A new question, how can I do if I want to do it the other way around, so having a trig function first then state a parabola? – Phillip K Apr 16 '20 at 17:53
  • @PhillipK you can evaluate the Taylor series of your trig function $f(x)$ (just until second derivative) at your chosen $x = a$ as long as $f'(a) = 0$ (meaning that $x = a$ is an extrema of the wave). – Poypoyan Apr 16 '20 at 18:04
  • @poypoyan Thank you – Phillip K Apr 16 '20 at 18:09