Can you re-arrange the following equation for t?

Equation: (2*A)/(r^2) = t - sin(t)

I need to re-arrange this equation for t using matlab. I don't have the symbolic math toolbox, and if I did I would use syms. I understand it won't be a definite solution, but I need to see what matlab will give me.

Would syms work in this case if I had it? Also, is there another way to re-arrange this equation in matlab? (I have the signal processing toolbox).

Answer 1

[Walter Roberson]

This is essentially (t - sin(t) = C), and there is no analytic solution for it.

You can approximate it with a series solution. If you use order 3 or order 4 you can solve the result analytically to get an exact approximation. For order 3 the positive root is

(C*sin(C)+sqrt(2*sin(C)^2+cos(C)^2-2*cos(C)+1)+cos(C)-1)/sin(C)

where C = (2*A)/r^2

[John D'Errico]

Oh, was that t - sin(t)? I read it as 1-sin(t).