plotting - Combining many plots with Show produces wrong x-axis position and wrong filling

The code is as follows,

g1 = Plot[Sin[x], {x, -2*Pi, 2*Pi}, 
   RegionFunction -> Function[x, ArcSin[2/3] < Sin[x] < ArcSin[1]], 

   PlotStyle -> Red, Filling -> Axis];
g2 = Plot[Sin[x], {x, -2*Pi, 2*Pi}, 
   RegionFunction -> Function[x, ArcSin[1/3] < Sin[x] < ArcSin[2/3]], 
   PlotStyle -> Green, Filling -> Axis];
g3 = Plot[Sin[x], {x, -2*Pi, 2*Pi}, 
   RegionFunction -> Function[x, ArcSin[0] < Sin[x] < ArcSin[1/3]], 
   PlotStyle -> Blue, Filling -> Axis];
g4 = Plot[Sin[x], {x, -2*Pi, 2*Pi}, 
   RegionFunction -> Function[x, ArcSin[-1/3] < Sin[x] < ArcSin[0]], 
   PlotStyle -> Gray, Filling -> Axis];

g5 = Plot[Sin[x], {x, -2*Pi, 2*Pi}, 
   RegionFunction -> 
    Function[x, ArcSin[-2/3] < Sin[x] < ArcSin[-1/3]], 
   PlotStyle -> Orange, Filling -> Axis];
g6 = Plot[Sin[x], {x, -2*Pi, 2*Pi}, 
   RegionFunction -> Function[x, ArcSin[-1] < Sin[x] < ArcSin[-2/3]], 
   PlotStyle -> Brown, Filling -> Axis];
Show[{g1, g2, g3, g4, g5, g6}, PlotRange -> {{-2*Pi, 2*Pi}, {-1, 1}}]

What I get is this. The x axis is not at the right position, and some filling is not to the axis. What is wrong with my code?

Answer

Show combines multiple Graphics objects together, but it only works after everything has already been processed. So, it has to make some judgements on how to combine the resulting options together, and for most it uses the options present in the first Graphics object. Looking at your original graphic, I suspect it is the first plot that causes the issues,

In[17]:= Options[g1, {PlotRange, AxesOrigin}]

Out[17]= {PlotRange -> {{-2 \[Pi], 2 \[Pi]}, {0.536887, 0.999999}}, 
 AxesOrigin -> {0, 0.52}}

As you can see, Plot is setting the PlotRange fairly high, but the issue is the AxesOrigin which is causing the fill to not go to the same point as the other graphs. To correct that, add AxesOrigin -> {0, 0} to all your plots, but it is not needed in Show. Then you get this,

Now time for overkill. As there are a number of options that are the same across the plots, it often pays to set them for all the plots, but if you use SetOptions you need to remember to restore them afterwards. So, I would use a custom environment:

ClearAll[BlockOptions];
SetAttributes[BlockOptions, HoldAll];
BlockOptions[f : {_Symbol, ___?OptionQ | {___?OptionQ}}, body_] := 
 BlockOptions[{f}, body]
BlockOptions[f : {{_Symbol, ___?OptionQ | {___?OptionQ}} ...}, 
  body_] :=
 With[{fcns = f[[All, 1]]},
  Internal`InheritedBlock[fcns,
   SetOptions @@@ f;

   body
   ]
  ]

where BlockOptions temporarily changes the options for you. (See this answer for the details of Internal`InheritedBlock). Then, your code becomes

Show@
 BlockOptions[
  {Plot, Filling -> Axis, PlotRange -> {-1, 1}},
  {
   Plot[Sin[x], {x, -2*Pi, 2*Pi}, 

    RegionFunction -> Function[x, ArcSin[2/3] < Sin[x] < ArcSin[1]], 
    PlotStyle -> Red], 
   Plot[Sin[x], {x, -2*Pi, 2*Pi}, 
    RegionFunction -> Function[x, ArcSin[1/3] < Sin[x] < ArcSin[2/3]],
     PlotStyle -> Green], 
   Plot[Sin[x], {x, -2*Pi, 2*Pi}, 
    RegionFunction -> Function[x, ArcSin[0] < Sin[x] < ArcSin[1/3]], 
    PlotStyle -> Blue], 
   Plot[Sin[x], {x, -2*Pi, 2*Pi}, 
    RegionFunction -> Function[x, ArcSin[-1/3] < Sin[x] < ArcSin[0]], 

    PlotStyle -> Gray], 
   Plot[Sin[x], {x, -2*Pi, 2*Pi}, 
    RegionFunction -> 
     Function[x, ArcSin[-2/3] < Sin[x] < ArcSin[-1/3]], 
    PlotStyle -> Orange], 
   Plot[Sin[x], {x, -2*Pi, 2*Pi}, 
    RegionFunction -> Function[x, ArcSin[-1] < Sin[x] < ArcSin[-2/3]],
     PlotStyle -> Brown]
   }
  ]

giving the same result. I used PlotRange here, instead of AxesOrigin, as it gives the same result, and I could move it out of Show.