How to color a zone in Tikz

Question

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.

Answer 1

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}