TikZ code generated by GeoGebra improperly scales the plot

Question

I'm new to both GeoGebra and TikZ so my question might be silly.

I used GeoGebra to draw the distribution function of a Cauchy distribution, which is F(x) = 1/\pi \arctan(10(x-0.5))+0.5.

Here is the plot I did in GeoGebra

and this is the TikZ code generated by the GeoGebra

or

\documentclass[10pt]{article}
\usepackage{pgf,tikz}
\usetikzlibrary{arrows}
\pagestyle{empty}
\begin{document}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
\draw[->,color=black] (-0.6,0.) -- (1.6,0.);
\foreach \x in {-0.4,-0.2,0.2,0.4,0.6,0.8,1.,1.2,1.4,1.6}
\draw[shift={(\x,0)},color=black] (0pt,2pt) -- (0pt,-2pt);
\draw[->,color=black] (0.,-0.6) -- (0.,1.2);
\foreach \y in {-0.5,-0.4,-0.3,-0.2,-0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.,1.1}
\draw[shift={(0,\y)},color=black] (2pt,0pt) -- (-2pt,0pt);
\clip(-0.6,-0.1) rectangle (1.6,1.2);
\draw[smooth,samples=100,domain=-0.6:1.6] plot(\x,{1.0/3.1415926535* rad(atan(10.0*((\x)-0.5)))+0.5});
\draw [dash pattern=on 1pt off 1pt,domain=-0.6:1.6] plot(\x,{(-1.-0.*\x)/-1.});
\draw [->,dash pattern=on 1pt off 1pt] (0.,0.688120318294) -- (0.568235782686,0.690599882462);
\draw [->,dash pattern=on 1pt off 1pt] (0.568235782686,0.690599882462) -- (0.57,0.);
\draw (-0.10792616721,1.20729312763) node[anchor=north west] {$F(x)$};
\draw (-0.0673181324647,0.722300140252) node[anchor=north west] {$U$};
\draw (0.534636264929,0.0039270687237) node[anchor=north west] {$X$};
\draw (1.47339847991,0.0112201963534) node[anchor=north west] {$x$};
\draw (-0.0553745928339,1.01767180926) node[anchor=north west] {$1$};
\end{tikzpicture}
\end{document}

Note. I've add the function rad in front of atan as TikZ uses degrees instead of radians; see the discussion here

Finally, this is the plot I got after compiling the code in LaTex

What is the problem? Am I missing something?

Answer 1

Using pgfplots, the job is considerably simpler:

The code:

\documentclass{article}
\usepackage{pgfplots}

\begin{document}

\begin{tikzpicture}
\begin{axis}[
  axis lines=middle,
  samples=200,
  xtick=\empty,
  ytick=\empty,
  width=.8\linewidth,
  domain=-3:3
]
\addplot+[no marks,blue] {1/pi*atan(10*(x-0.5))+0.5};
\node[circle,fill,inner sep=1.5pt] 
  (aux) at (axis cs:0.75,{1/pi*atan(10*(0.75-0.5))+0.5}) {};
\draw[dotted,->]
  (axis cs:0.75,0) node[below] {$x$} -- (aux);  
\draw[dotted,->]
  (axis cs:0,{1/pi*atan(10*(0.75-0.5))+0.5})  node[left] {$v$} -- (aux);  
\end{axis}
\end{tikzpicture}

\end{document}

Change 0.75 (which I used just for the example) to the desired value to locate the point on the path.

Answer 2

(note: I just noticed that my solution was mentioned before by Harish Kumar in the commnets)

The tikzpicture enviroment has options that allow you to control the scale (e.g. relative to the text size). Looks like the code generated by GeoGebra miscalculates this scale, even with respect to locations where it puts the labels.

I solved it by specifying these options x=10.0cm,y=10.0cm, as below. Now the result looks almost equal your GeoGebra window screenshot.

\documentclass[10pt]{article} 
\usepackage{pgf,tikz} 
\usetikzlibrary{arrows}
\pagestyle{empty}
\begin{document} 

\scalebox{0.5}{
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=10.0cm,y=10.0cm] 
\draw[->,color=black] (-0.6,0.) -- (1.6,0.); 
\foreach \x in `{-0.4,-0.2,0.2,0.4,0.6,0.8,1.,1.2,1.4,1.6} 
\draw[shift={(\x,0)},color=black] (0pt,2pt) -- (0pt,-2pt); 
\draw[->,color=black] (0.,-0.6) -- (0.,1.2); 
\foreach \y in {-0.5,-0.4,-0.3,-0.2,-0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.,1.1}    
\draw[shift={(0,\y)},color=black] (2pt,0pt) -- (-2pt,0pt); 
\clip(-0.6,-0.1) rectangle (1.6,1.2); 
\draw[smooth,samples=100,domain=-0.6:1.6] plot(\x,{1.0/3.1415926535* rad(atan(10.0*((\x)-0.5)))+0.5}); 
\draw [dash pattern=on 1pt off 1pt,domain=-0.6:1.6] plot(\x,{(-1.-0.*\x)/-1.}); 
\draw [->,dash pattern=on 1pt off 1pt] (0.,0.688120318294) -- (0.568235782686,0.690599882462); 
\draw [->,dash pattern=on 1pt off 1pt] (0.568235782686,0.690599882462) -- (0.57,0.); 
\draw (-0.10792616721,1.20729312763) node[anchor=north west] {$F(x)$}; 
\draw (-0.0673181324647,0.722300140252) node[anchor=north west] {$U$}; 
\draw (0.534636264929,0.0039270687237) node[anchor=north west] {$X$}; 
\draw (1.47339847991,0.0112201963534) node[anchor=north west] {$x$}; 
\draw (-0.055374592`8339,1.01767180926) node[anchor=north west] {$1$}; 
\end{tikzpicture} 
}
\end{document}