Perhaps this is what you are looking for.
minSin[x_] := Sin[x] /; Sin[x] < Cos[x]
minCos[x_] := Cos[x]Sin[x]
minCos[x_] /; Sin[x] > Cos[x]
maxSin[x_] := Sin[x]Cos[x]
maxSin[x_] /; Sin[x] > Cos[x]
maxCos[x_] := Cos[x]Sin[x]
maxCos[x_] /; Sin[x] < Cos[x] := Cos[x]
Plot[{minSin[x], maxSin[x], minCos[x], maxCos[x]}, {x, 0, 2 \[Pi]π},
PlotStyle ->
{{Blue, Thickness[0.02]}, {Blue, Thickness[0.01]},
{Red, Thickness[0.02]}, {Red, Thickness[0.01]}}]