Argthtjtr

I have this image:

That is made with this code:

     documentclass{article}

     usepackage{tikz}

usepackage{amssymb,amsthm,amsmath}

usetikzlibrary{shapes,positioning,intersections,quotes}



begin{document}



begin{center}

         begin{tikzpicture}

         draw [rotate=270] (0,0)  arc (180:0:1);

         draw [rotate=270] (-2,0)  arc (180:0:1);

         draw (0,0) circle (2cm);

         draw[dashed] (0,2.5) -- (0,-2.5);

         draw[dashed](-2.5,0) -- (2.5,0);

         draw (0,0) -- (-1.1547,1.9);

         draw (0,0) -- (-1.01,2);

         draw [rotate=120](0,0) -- (-1.1547,1.9);

         draw [rotate=120](0,0) -- (-1.01,2);

        filldraw[black] (1.2,0) circle (0pt)

 node[anchor=west] {$S_0$};

        filldraw[black] (-1.2,0) circle (0pt)

  node[anchor=west] {$S_3$};

        filldraw[black] (0,1.2) circle (0pt)

  node[anchor=west] {$S_1$};

        filldraw[black] (0,-1.2) circle (0pt)

  node[anchor=west] {$S_2$};



        filldraw[black] (-1,2.1) circle (0pt)

  node[anchor=west] {tiny{$R_1$}};

         end{tikzpicture}

end{center}









end{document}

And I want to know if there is a way to color in gray the zone that is between the 2 lines (in both zones). Any ideas? Thanks.

Sure. (But why do you not use polar coordinates?)

documentclass{article}

usepackage{tikz}

begin{document}

section*{Two methods that do not require libraries}

subsection*{Method 1: clip}

begin{center}

  begin{tikzpicture}

         draw [rotate=270] (0,0)  arc (180:0:1);

         draw [rotate=270] (-2,0)  arc (180:0:1);

         draw (0,0) circle (2cm);

         draw[dashed] (0,2.5) -- (0,-2.5);

         draw[dashed](-2.5,0) -- (2.5,0);

         draw (0,0) -- (-1.1547,1.9);

         draw (0,0) -- (-1.01,2);

         draw [rotate=120](0,0) -- (-1.1547,1.9);

         draw [rotate=120](0,0) -- (-1.01,2);

         path (1.2,0)  node[anchor=west] {$S_0$};

         path (-1.2,0)   node[anchor=west] {$S_3$};

         path (0,1.2)   node[anchor=west] {$S_1$};

         path (0,-1.2)   node[anchor=west] {$S_2$};

         path (-1,2.1)   node[anchor=west] {tiny{$R_1$}};

         clip (0,0) circle[radius=2cm-pgflinewidth/2];

         draw[fill=gray] (0,0) -- (-1.01,2) -- (-1.1547,1.9);

         draw[fill=gray,rotate=120] (0,0) -- (-1.01,2) -- (-1.1547,1.9);

  end{tikzpicture}

end{center}

subsection*{Method 2: compute the polar coordinates of the points and use them}

begin{center}

 begin{tikzpicture}

         draw [rotate=270] (0,0)  arc (180:0:1);

         draw [rotate=270] (-2,0)  arc (180:0:1);

         draw (0,0) circle (2cm);

         draw[dashed] (0,2.5) -- (0,-2.5);

         draw[dashed](-2.5,0) -- (2.5,0);

         draw (0,0) -- (-1.1547,1.9);

         draw (0,0) -- (-1.01,2);

         pgfmathsetmacro{myangleOne}{atan2(1.9,-1.1547)}

         %pgfmathsetmacro{myradius}{veclen(1.9,-1.1547)}

         pgfmathsetmacro{myangleTwo}{atan2(2,-1.01)}

         draw[fill=gray] (0,0) -- (myangleOne:2) arc(myangleOne:myangleTwo:2)

         --cycle;

         %typeout{myangleOne,myangleTwo}

         draw [rotate=120](0,0) -- (-1.1547,1.9);

         draw [rotate=120](0,0) -- (-1.01,2);

         draw[fill=gray,rotate=120] (0,0) -- (myangleOne:2) arc(myangleOne:myangleTwo:2)

         --cycle;

        path (1.2,0)  node[anchor=west] {$S_0$};

        path (-1.2,0)   node[anchor=west] {$S_3$};

        path (0,1.2)   node[anchor=west] {$S_1$};

        path (0,-1.2)   node[anchor=west] {$S_2$};

        path (-1,2.1)  node[anchor=west] {tiny{$R_1$}};

 end{tikzpicture}

end{center}

end{document}