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I am trying to create an animation of sine and cosine on the unit circle. Here is what I have thus far:

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}]}],
     {s, 0, 1}]

I would like to add a dynamic label that keeps track of the expanding angle and a dynamic label for each side of the triangle that keeps track of the sine and cosine functions.

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3
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Just another approach. Not ideal but may be motivating:

f[t_] := With[{c = Cos[t], s = Sin[t]}, 
  Graphics[{Circle[], {Green, Line[{{0, 0}, {c, 0}}]}, {Red, 
     Line[{{c, 0}, {c, s}}]}, {Black, 
     Line[{{0, 0}, {c, s}}]}, {Text[
      Style[NumberForm[180 t/Pi, 3], White], 0.1 {Cos[t/2], Sin[t/2]},
       Background -> Orange]}, {Text[
      Framed[Style[NumberForm[s, 3], Red], Background -> White, 
       FrameStyle -> Red], {c, s/2}]}, {Text[
      Framed[Style[NumberForm[c, 3], Green], Background -> White, 
       FrameStyle -> Green], {c/2, 0}]},
    {Orange, Circle[{0, 0}, 0.2, {0, t}]}}, 
   PlotRange -> Table[{-1.5, 1.5}, {2}]]]
Animate[f[s], {s, 0, 2 Pi}]

enter image description here

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2
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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}]
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