How can I solve for $x$ in this equation?

Question

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?

Answer 1

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: $x=0.275$.