How to ask Mathematica to show the negative parts of $\sin x$ as some lines on the $x$ axis?

Question

I want to ask Mathematica to show the domain of negative parts of the function $\sin x$ as red lines on the $x$ axis, like this picture

Is it possible to do it automatically? If not, I will be grateful if please tell me how I can do it manually.

Plot[Sin[x], {x, 0, 20}]

Answer 1

1. Use Plot with two functions ({Sin[x], If[Sin[x] <= 0, 0]}) in the first argument:

Plot[{Sin[x], If[Sin[x] <= 0, 0]}, {x, 0, 20}, 
 PlotStyle -> {Automatic, Directive[Red, Opacity[1], Thick]},
 Method -> {"AxesInFront" -> False}]

2. Use NumberLinePlot + Plot

Show[Plot[Sin[x], {x, 0, 20}], 
 NumberLinePlot[Sin[x] < 0, {x, 0, 20}, 
   PlotStyle -> Directive[Thick, Red], Spacings -> 0,
   Method -> {"AxesInFront" -> False}]]

Answer 2

Also Mesh, MeshShading and MeshFunctions

a = Plot[0, {x, 0, 20}, Mesh -> {{0}}, MeshFunctions -> (Sin[#] &), 
   MeshShading -> {Directive[Thickness[.01], Red], None}, 
   MeshStyle -> Directive[PointSize[Large], Green]];
b = Plot[Sin[x], {x, 0, 20}];
Show[b, a]