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I have this equation, but I don't know how can I isolate the $x$ laying inside the cosine function.

$$x=\cos\left(\frac{4\pi x+2T\phi}{2Tr}\right)\cdot r$$

What are the best steps to pass around this issue?

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  • $\begingroup$ You can't solve for $x$ algebraically, but you can solve for it numerically for general $T,\phi,r$. $\endgroup$
    – Simply Beautiful Art
    Mar 13, 2017 at 14:48
  • $\begingroup$ Could you explain further? Why isn´t possible for x? I already know the values for $T, \phi , r$. Will these help me to find the real value of x? $\endgroup$
    – Chaos
    Mar 13, 2017 at 14:51
  • $\begingroup$ Remember that $x=\cos(x)$ does not show any analytical solution. $\endgroup$
    – Claude Leibovici
    Mar 13, 2017 at 17:07
  • $\begingroup$ That´s right. Thanks. $\endgroup$
    – Chaos
    Mar 14, 2017 at 19:46

1 Answer 1

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While I believe that an analytical solution is difficult to find manually, you can get the solutions using a graphing software with those values.

For example, in Desmos (https://www.desmos.com/calculator), inputting the 2 functions (the left hand side and the right hand side of the equation respectively) along with $T=\phi=r=2$, I get the solution: $x=0.275$.

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  • $\begingroup$ That software is awesome. $\endgroup$
    – Chaos
    Mar 13, 2017 at 15:48

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