Having familiarized myself with the parametric formula of a circular involute (i.e. x = a(cos t + t sin t), y = a(sin t - t cos t)), I was wondering if it is possible to derive an equation which will solve y for any given value of x.
I currently visualise the parametric formula as two adjoining right-angle triangles, the second being derived from the x/y values of the first. However, due to the implicit relationship exhibited between these two structures, I fear that this problem far exceeds the elementary trigonometry I currently understand.
As I'm reasonably sure that this problem cannot be solved using Trigonometry alone, any help or advice as to how I should approach a solution would be very much appreciated.