POSSIBLE SOLUTION

The solutions may be developed from the geometry of this triangle. The two relationships that get you to the solution are:
x = r cos(q) + L cos(f)
r sin(q) = L sin(f)

Input := 

data = { r -> .08, L -> .245, w -> 1000 (2 Pi / 60)} //N;
T = N[60/1000];

It is very easy to implement these if you are using a computer algebra system such as Mathematica.

Input := 

x[t_] := r Cos[w t] - L Cos[ fi[t] ] /. data

Input := 

fi[t_] := Pi - ArcSin[ r / L Sin[w t] ] /. data

Plots of Desired Functions

Connecting Rod Angle

Piston Position

Explicit values of the Desired Functions.