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I'm helping my students with parametrization. I tried to change the color on the second rotation of the unit circle with this code:

Manipulate[
 ParametricPlot[{Cos[2 t], Sin[2 t]}, {t, 0, tau}, PlotRange -> 1.2, 
  PlotStyle -> {If[t <= π, "Blue", "Red"]}],
 {{tau, 0.1}, 0, 2 π}]

But it remains blue after the first rotation. Can someone make a suggestion how to change the color?

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    $\begingroup$ "Blue" and "Red" should probably be replaced with just Blue and Red; colors are keywords in Mathematica mostly; see also GrayLevel, Hue, and RGBColor. Also, the parameter t is not defined generally outside of the first argument to the function; you should look at the ColorFunction option. $\endgroup$ – user16054 Jan 31 '17 at 19:28
  • $\begingroup$ @user16054 Yep, my mistake. Thanks for pointing it out. $\endgroup$ – David Jan 31 '17 at 19:42
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You should be using ColorFunction, as PlotStyle does not do variable-dependent coloring:

Manipulate[ParametricPlot[{Cos[2 t], Sin[2 t]}, {t, -$MachineEpsilon, τ}, 
                          ColorFunction -> Function[{x, y, t}, If[t <= π, Blue, Red]], 
                          ColorFunctionScaling -> False, PlotRange -> 1.2],
           {{τ, 0.1}, 0, 2 π}]

Manipulate of colored circle

where I have also taken the liberty of offsetting the starting point in ParametricPlot[] to prevent errors when τ becomes 0, and using the colors as symbols instead of strings.

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  • $\begingroup$ This provided some excellent help. May I ask one more question? How can I change the thickness on the second rotation? $\endgroup$ – David Jan 31 '17 at 19:56
  • $\begingroup$ Now that... is an excellent question. Let me think about it. $\endgroup$ – J. M. is away Jan 31 '17 at 20:08

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