I am stuck with this function for couple of days. I wonder how to find the inverse of it.
$y = x + A \sin(2 \pi(B-x))$
with A and B are constants. If you have solution, can you give me some hints?
Thanks !
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I guess you are looking for a solution in terms of elementary functions (like sin, cos, arcsin, exp, ...), however, there is none in your case. Usually you would use numerical methods (like Newton's method or bisectioning, just to name the most basic ones) in order to solve for $x$ given some $y$. Be aware however, that depending on $A$ the solution may not be unique (so there's no inverse in the strict sense anyway). – Elmar Zander Aug 14 '17 at 11:35
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@Elmar: thanks for your advice. but could you please name or give me some documents/examples? – Bui Tuan Khai Aug 14 '17 at 11:39
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See here https://en.wikipedia.org/wiki/Newton%27s_method for example. The function $f$ in your case would be $f(x)=x+A\sin(2\pi(B-x))-y$ such that solving $f(x)=0$ gives your desired $x$. – Elmar Zander Aug 14 '17 at 11:45
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1It's more or less Kepler's equation. – Hans Lundmark Aug 14 '17 at 13:39
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... Too hard to do it by hand. could you guys please suggest me some tool for differential calculation? – Bui Tuan Khai Aug 16 '17 at 06:12