This is not built-in, but is straight-forward to add using the RegionPlot function.
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Filling with Lines
Step one : create the two curves to be plotted together. ps=Plot[Sin,{x,0,2Pi},AspectRatio->Automatic,PlotStyle->Black]
pc=Plot[Cos,{x,0,2Pi},AspectRatio->Automatic,PlotStyle->Black]
Step two: use RegionPlot to create horizontal and vertical lines that fill the area between the curves and the x axis.
The Mesh->n option gives the number of mesh lines, horizontal or vertical.
PlotStyle->None turns off coloring the region that RegionPlot derives.
MeshStyle controls orientation (horizontal vs. vertical). rps=RegionPlot[ 0<=x<=2Pi && Abs<=Abs[Sin] && If[Sin>0,y>0,y<0], {x,0,2 Pi},{y,-1,1},
Mesh->12,MeshStyle->{None,Gray},BoundaryStyle->None,PlotStyle->None,AspectRatio->Automatic]
rpc=RegionPlot[ 0<=x<=2Pi&&Abs<=Abs[Cos]&&If[Cos>0,y>0,y<0], {x,0,2 Pi},{y,-1,1},
Mesh->24,MeshStyle->{Gray,None},BoundaryStyle->None,PlotStyle->None,AspectRatio->Automatic]
Step three: Combine them. The overlap areas have cross-hatching.
Show[{ps,rps,pc,rpc}]
Filling with Dots
Points lined up vertically,
rpc=RegionPlot[0<=x<=2Pi&&Abs<=Abs[Cos]&&If[Cos>0,y>0,y<0], {x,0,2 Pi},{y,-1,1},
Mesh->24, MeshStyle->{Directive[Gray,Dashing[{0.0,0.02}]],None},
BoundaryStyle->None,PlotStyle->None, AspectRatio->Automatic]
Horizontal rows of points. (Maybe looks better.) rpc=RegionPlot[0<=x<=2Pi&&Abs<=Abs[Cos]&&If[Cos>0,y>0,y<0], {x,0,2 Pi},{y,-1,1},
Mesh->24, MeshStyle->{None,Directive[Gray,Dashing[{0.0,0.02}]]},
BoundaryStyle->None,PlotStyle->None, AspectRatio->Automatic]
Combine with previous sine and cosine curves.
Show[{ps,rps,pc,rpc}]
