I need to find the point of intersection between a line segment and a sine wave.
Line: $y=-2x+1$
Wave: $y=\sin x$
I put both equations together.
$-2x+1=\sin x$
I attempt to isolate $x$.
$\sin x+2x=1$
Now I have no idea what to do next.
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Daniel
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draw a careful picture. Unless the intersection is at an obvious point such as $(0,0),$ which does not happen here, the likelihood is that $x$ is unpleasant and can not be solved for in symbols, only numerically approximated. – Will Jagy Jan 13 '15 at 00:26
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There is likely no closed-form solution, but you can show with some elementary calculus that exactly one solution exists, and you can use numerical methods to show that its expansion begins $x = 0.33541\ldots$. – Travis Willse Jan 13 '15 at 00:27
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Search “Kepler equation” on the site for exact solutions – Тyma Gaidash Aug 08 '23 at 00:28