Like this?

        Animate[ParametricPlot[{{Cos[2 Pi t], Sin[2 Pi t]}, {t Cos[2 Pi s], 
        t Sin[2 Pi s]}, {t Cos[2 Pi s], 0}, {Cos[2 Pi s], 
        t Sin[2 Pi s]}, {.1 Cos[2 Pi s t], .1 Sin[2 Pi s t]}}, {t, 0, 1}, 
      PlotStyle -> {{Thick, Blue}, {Thick, Black}, {Thick, Green}, {Thick,
          Red}, {Thick, Orange}}, PlotRange -> {{-1.3, 1.3}, {-1.3, 1.3}},
      Epilog -> {PointSize[Large], Point[{Cos[2 Pi s], 0}],
        Text[2 \[Pi] s, {0.1 Cos[2 Pi (s/2)], 0.1 Sin[2 Pi (s/2)]}],
        Text[Norm[{ Cos[2 Pi s], 0}], {0.5 Cos[2 Pi s], 0}],
        Text[Sqrt[
         1 - (Norm[{ Cos[2 Pi s], 0}])^2], {Cos[2 Pi s], 0.5 Sin[2 Pi s]}],
        Text[1, {0.5 Cos[2 Pi (s - .01)], 0.5 Sin[2 Pi (s - .01)]}]}], {s,
       0, 1}]