Quote: "I have been able to plot the graph..."
With the following expression?
f(x) = Sin[2Pi*t](1+(1/5)Sin(6Pi*t)+ (1/10)Sin(8Pi*t))
I cannot believe you did!!
several issues when working with Mathematica
1. Square brackets for function arguments
Sin(6 Pi*t) is the multiplication os Sin with (6 Pi*t) not the Sine of it
2. The (dummy) argument of the function is with an underscore
that is, f[x_]:= rathe tan f(x) (which is again multiplication)
3. The name of the dummy argument should appear in the right hand side of the expression. Your "expression" has "x" on the left hand side and t in the right hand side.
So, how did you REALLY got your plot
I will help you with the rest of your question, since it is more advanced, but to do it you still need to correct the first part
you should write
f[t_]:=... with all the corrections mentioned above
and decide what are the tmin and tmax that work for you
p=Cases[g, Line[x_] :> x, Infinity]