You probably need ParametricPlot
:
functs = 50 {Cos[(x - 3)/4.4], Cos[(x - 7)/4.4]};
Plot[functs, {x, 0, 10}, GridLines -> {{3, 7}, None}]
Show[ParametricPlot[Evaluate@functs, {x, 0, 10}],
ParametricPlot[Evaluate@functs, {x, 3, 7},
PlotStyle -> {Blue, Thickness[.01]}]]