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The equation y(x)=sin(kx) where x needs to be the subject

Note:y function of x not y times x

What I did is x=1/ksin^-1(y(x)) However, x is still on the right-hand side. How should I approach this further? Any suggestions?

Nino Mae 21
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  • If $y(x)$ means $y$ is a function of $x$ then you are done. However if $y(x)$ means multiplication then I have no idea. – player3236 Oct 24 '20 at 18:11

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Assuming that the equation to be solved is $$x \times y=\sin(k x)$$ there is no analytical solutions and numerical methods are required. We can make more or less accurate approximations .

To simplify the problem, let $kx=t$ and $a=\frac t k$ making the equation $$\sin(t)=a t\qquad \text{with} \qquad 0 < a < 1$$

If I may suggest, have a look at this question of mine where the problem has been quite extensively discussed.

Claude Leibovici
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