Plot and animate a parametric circle with a cycloid [duplicate]

Question

I have my cycloid already plotted-

x[t_] := t - Sin[t];
y[t_] := 1 - Cos[t];
ParametricPlot[{x[t], y[t]}, {t, 0, 6Pi}]

But now I need to plot it over the interval 0 <= t <= (13Pi)/3 along with a circle of radius 1 centered at ((13Pi)/3,1).

Then after that, I need to animate the plot over the interval 0 <= t <= u together with a circle of radius 1 at (u,1) for 0 <= u <= 6Pi.

My attempts to do so have been fruitless.

Thanks

Answer 1

There are many ways to do this, e.g. (using the definitions of x[t],y[t]):

pp[u_] := 
 ParametricPlot[{{x[t], y[t]}, {u + Sin[t], 1 + Cos[t]}}, {t, 0, 
   6 Pi}, Epilog -> {Point[{x[u],y[u]}]}]
Manipulate[pp[u], {u, 0, 6 Pi}]