How do you solve $\sin(x) = x$ with algebra?

Asked Nov 29 '16 at 12:09

Active Nov 29 '16 at 12:27

Viewed 111 times

I'm making a quick program in excel to calculate the height of a ball over time and I need to know when it will hit a vibrating plate. I cannot find a way in which to make the formula say x = [something]

$$A\sin(2\pi fx)+A = (((ax)^2)/2a)+h$$

If you have spare time solving this one would be of great help too:

$$V(x-t)-a(x-t)^2 = A\sin(2\pi fx)+A$$

If you only have enough time for one or only feel like doing one, that's also okay.

Thanks for anyone's help in advance.

edit: Someone asked what the variables meant so I'm here to specify A = Amplitude (in my case 0.0075m) x = the variable (time) f = frequency (in my case 10 hertz, however in the program I'm making I would like to be able to change the frequency) h = height at which the ball is dropped (in my case 0.2m) V = speed of the ball after it's thrown upwards by an outside force

edited Nov 29 '16 at 12:27

asked Nov 29 '16 at 12:09

Nick Brantjes

7

Both are impossible to solve exactly. The best you can do is use an approximate method, like Newton's method, for example. – Nov 29 '16 at 12:11
@tilper Has it been proved that it cannot be solved exactly or has a method just not been found as of yet? – David Nov 29 '16 at 12:18
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@David, tilper said what he meant, and meant what he said. – Gerry Myerson Nov 29 '16 at 12:19
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Can you please specify ,exactly what $A,x,f,h,V$ are? – Qwerty Nov 29 '16 at 12:19
@Gerry Myerson how does one go about proving that? – David Nov 29 '16 at 12:23
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@David, you may find http://math.stackexchange.com/questions/257873/why-isnt-the-inverse-of-the-function-x-mapsto-x-sinx-expressible-in-terms helpful. – Gerry Myerson Nov 29 '16 at 12:30
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@GerryMyerson a tilper is faithful 100%. – Nov 29 '16 at 12:32
@Gerry Myerson thank you. – David Nov 29 '16 at 12:33
It is not possible to solve a combination of algebraic and transcendental functions using algebra – Simply Beautiful Art Nov 29 '16 at 13:16
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The title has little to do with the question. Solution to $\sin x=x$ is $x=0$. – A.Γ. Nov 29 '16 at 13:17

How do you solve $\sin(x) = x$ with algebra?

0 Answers0