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I am attempting to generate a plot for which the color changes for selected values of x as determined by a function. Below, is my best, unsuccessful attempt. The specific problem with this is that it worked only once for x = 3Pi/4 but not for x = Pi/4. I am stumped, please help!

Plot[ {Cos[x], Sin[x]}, {x, 0, Pi}, ColorFunction -> Function[ x, If[Abs[Cos[x]] > Abs[Sin[x]], Red, Blue] ] ]

enter image description here

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    $\begingroup$ Plot[{Cos[x], Sin[x]}, {x, 0, Pi}, ColorFunction -> Function[x, If[Abs[Cos[x]] > Abs[Sin[x]], Red, Blue]], ColorFunctionScaling -> False] $\endgroup$ Commented Sep 27, 2020 at 7:44
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    $\begingroup$ Plot[{Sin[x], Cos[x]}, {x, 0, Pi}, MeshFunctions -> Function[{x, y}, Abs[Cos[x]] - Abs[Sin[x]]], MeshShading -> {Blue, Red}, Mesh -> {{0}}] is another way. $\endgroup$ Commented Sep 27, 2020 at 8:19

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You need to set ColorFunctionScaling to False, otherwise the x coordinate will be rescaled to lie between 0 and 1 before it is passed to the color function.

Plot[ {Cos[x], Sin[x]}, {x, 0, Pi}, ColorFunction -> Function[ {x, y}, If[ Abs[Cos[x]] > Abs[Sin[x]], Red, Blue ] ], ColorFunctionScaling -> False ]

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