LaTeX-examples/tikz/cos-fixpoint/cos-fixpoint.tex

\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{0mm}

\usepackage{pgfplots}
\pgfplotsset{compat=1.9}

\begin{document}
\begin{preview}
\begin{tikzpicture}
    \begin{axis}[
        axis x line=middle,
        axis y line=middle,
        enlarge y limits=true,
        enlarge x limits=true,
        xmin=0, xmax=pi, % x domain
        width=12cm, height=8cm,     % size of the image
        grid = major,
        grid style={dashed, gray!30},
        ymin=-1,      % start the diagram at this y-coordinate
        ymax= 1,      % end   the diagram at this y-coordinate
        % axis background/.style={fill=white},
        ylabel=$y$,
        xlabel=$x$,
        xtick={0,1.5708,3.14159},
        xticklabels={$0$,$\frac{\pi}{2}$,$\pi$},
        legend style={at={(0.2,0.37)}, anchor=north, fill=none}
     ]
      \addplot[domain=-8:8,very thick,samples=200,blue]   {cos(deg(x))};
      \addplot[domain=-8:8,very thick,samples=200,red]   {x};
      \coordinate (a) at (axis cs:0.739085,0.739085);
      \fill[red] (a) circle (3pt);
      \node[label={[label distance=0.1cm]0:$x = y \approx 0.739085$}] at (a) {};
      \legend{$\cos x$, $x$}
    \end{axis}
\end{tikzpicture}
\end{preview}
\end{document}