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%
% hyperbelflaeche.tex -- Argument der Hyperbelfunktionen
%
% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
%
\documentclass[tikz]{standalone}
\usepackage{amsmath}
\usepackage{times}
\usepackage{txfonts}
\usepackage{pgfplots}
\usepackage{csvsimple}
\usetikzlibrary{arrows,intersections,math}
\begin{document}
\def\skala{2}
\begin{tikzpicture}[>=latex,thick,scale=\skala]
\fill[color=blue!20]
(0,0)
--
plot[domain=0:1,samples=100] ({cosh(\x)},{sinh(\x)})
-- cycle;
\draw[color=blue]
(0,0)
--
plot[domain=0:1,samples=100] ({cosh(\x)},{sinh(\x)})
-- cycle;
\begin{scope}
\clip (-1.8,-2) rectangle (2.5,2);
\draw[color=red,line width=1.4pt] plot[domain=-2:2,samples=100]
({cosh(\x)},{sinh(\x)});
\draw[color=red,line width=1.4pt] plot[domain=-2:2,samples=100]
({-cosh(\x)},{sinh(\x)});
\end{scope}
\fill[color=white] ({cosh(1)},{sinh(1)}) circle[radius=0.03];
\draw ({cosh(1)},{sinh(1)}) circle[radius=0.03];
\node at ({cosh(1)},{sinh(1)}) [right] {$\gamma(t)=(\cosh t,\sinh t)$};
\draw[->] (-1.8,0) -- (3.1,0) coordinate[label={$x$}];
\draw[->] (0,-2) -- (0,2.1) coordinate[label={right:$y$}];
\node[color=blue] at (0.8,0.3) {$t$};
\node at (0,0) [below left] {$O$};
\end{tikzpicture}
\end{document}
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