Show[
 ParametricPlot[{x, t Sin[x]}, {x, -2 Pi, 2 Pi}, {t, 0, 1},
  MeshFunctions -> {Sin[#1] &}, Mesh -> {Range[-2, 2]/3},
  MeshShading -> {{Opacity[0.4], Blue}, {Opacity[0.4], Orange}}],
 Plot[Sin[x], {x, -2 Pi, 2 Pi},
  MeshFunctions -> {Sin[#1] &}, Mesh -> {Range[-2, 2]/3},
  MeshShading -> {Blue, Orange}],
 Plot[Sign[Sin[x]] Ceiling[Abs[Sin[x]], 1/3], {x, -2 Pi, 2 Pi},
  PlotStyle -> Red],
 AspectRatio -> 1/GoldenRatio, Frame -> False
 ]