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%
% tikztemplate.tex -- template for standalon tikz images
%
% (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,calc}
\definecolor{darkgreen}{rgb}{0,0.6,0}
\begin{document}
\def\skala{8}
\begin{tikzpicture}[>=latex,thick,scale=\skala]
\def\a{1.6}
\def\w{40}
\pgfmathparse{atan(sin(\w)/(\a*cos(\w)))}
\xdef\v{\pgfmathresult}
\pgfmathparse{cos(\w)}
\xdef\cn{\pgfmathresult}
\pgfmathparse{sin(\w)}
\xdef\sn{\pgfmathresult}
\pgfmathparse{sqrt(\a*\a*cos(\w)*cos(\w)+sin(\w)*sin(\w))}
\xdef\r{\pgfmathresult}
\pgfmathparse{\r/\a}
\xdef\dn{\pgfmathresult}
\draw[color=red,line width=1.4pt] ({\cn},0) -- ({\cn},{\sn});
\node[color=red] at ({\cn},{0.3*\sn})
[above,rotate=90] {$\operatorname{sn}(u,k)$};
\node[color=red] at ({\a*\cn},{0.3*\sn})
[above,rotate=90] {$\operatorname{sn}(u,k)$};
\draw[->,line width=1pt] ({-0.1/\skala},0) -- ({\a+0.4/\skala},0)
coordinate[label={$x$}];
\draw[->,line width=1pt] (0,{-0.1/\skala}) -- (0,{1+0.3/\skala})
coordinate[label={right:$y$}];
\draw[color=gray,line width=1.4pt]
plot[domain=-0.5:90.5,samples=100] ({cos(\x)},{sin(\x)});
\draw[color=gray!50,line width=1.4pt]
plot[domain=-0.5:90.5,samples=100] ({cos(\x)},{sin(\x)/\a});
\draw[color=black,line width=1.4pt]
plot[domain=-0.5:90.5,samples=100] ({\a*cos(\x)},{sin(\x)});
\def\punkt#1#2{
\fill[color=#2] #1 circle[radius={0.10/\skala}];
\fill[color=white] #1 circle[radius={0.06/\skala}];
}
\fill[color=darkgreen!50] (0,0) -- (0:0.35) arc (0:\v:0.35) -- cycle;
%\draw[color=darkgreen] (0:0.35) arc (0:\v:0.35);
\node[color=darkgreen] at ({\v/2}:0.28) {$\vartheta$};
\draw[color=red!40,line width=1.4pt] ({\a*\cn},0) -- ({\a*\cn},{\sn});
\draw[color=darkgreen!40,line width=1.4pt] (0,0) -- ({\a*\cn},{\sn});
\draw[color=darkgreen,line width=1.4pt] (0,0) -- ({\cn},{\sn/\a});
\node[color=darkgreen] at ({0.6*\cn},{0.6*\sn/\a})
[below,rotate=\v] {$\operatorname{dn}(u,k)$};
\punkt{({\cn},{\sn/\a})}{darkgreen}
\node[color=darkgreen] at ({0.87*\a*\cn},{0.87*\sn})
[above,rotate=\v] {$r=a\operatorname{dn}(u,k)$};
\fill[color=gray!50] (0,0) -- (0:0.2) arc (0:\w:0.2) -- cycle;
\node at ({\w/2}:0.15) {$\varphi$};
\draw (0,0) -- (\w:1);
\punkt{({\a*\cn},{\sn})}{black}
\punkt{({\cn},{\sn})}{red!50}
\node at ({\a*\cn},{\sn})
[above right] {$P=(a\cos\varphi,\sin\varphi)$};
\node at ($(\w:1)+({-0.1/\skala},0)$)
[left] {$Q=(\cos\varphi,\sin\varphi)$};
\node at (\a,0) [below] {$a\mathstrut$};
\node at ({-0.1/\skala},1) [left] {$1$};
\node at ({-0.1/\skala},{1/\a}) [left] {$\displaystyle\frac{1}{a}$};
\draw ({-0.1/\skala},{1/\a}) -- ({0.1/\skala},{1/\a});
\draw[color=blue!40,line width=1.4pt] (0,0) -- ({\a*\cn},0);
\draw ({\a*\cn},{-0.1/\skala}) -- ({\a*\cn},{0.1/\skala});
\node[color=blue] at ({\a*\cn},{-0.1/\skala})
[below] {$a\operatorname{cn}(u,k)$};
\draw[color=blue,line width=1.4pt] (0,0) -- ({\cn},0);
\node[color=blue] at ({0.5*\cn},0) [below] {$\operatorname{cn}(u,k)$};
\punkt{({cos(\w)},0)}{blue}
\node at (0,0) [below left] {$O$};
\end{tikzpicture}
\end{document}
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