tikz-pgf – How to Display All Trigonometric Function Plots in a Table Using TikZ

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For my maths summary I am trying to make a table with all function plots of the trigonometric functions (Something like the picture below, but including the inverses). Since my space is limited to 12 pages I want some of them to be vertically aligned to save some space, just like in the picture. I am fairly new to Latex and I tried doing this using tabular. However the plots are bit too far on the right – I want them perfectly centered. How can I do this?

My other problem is that if I try to plot functions like tan, csc, sec, arcsin,arccos,… they either produce an error or mess everything up. How can I plot these functions?

I also couldn't find any templates with all the trig functions summarized, which I found odd since I thought that would be something I am not the first person in need of. Is there a secret place where such files are shared?

Here is my code for three functions (I included cosine twice so I have something to display):

\documentclass{article}
\usepackage[utf8]{inputenc}

\title{testtt}

\usepackage{amsmath}    \usepackage{amsfonts}   \usepackage{amssymb}
\usepackage{amsthm}     \usepackage{latexsym}   \usepackage{mathtools}

\usepackage{tikz}

\begin{document}


\newcommand*{\xMin}{-9}
\newcommand*{\xMax}{9}
\newcommand*{\yMin}{-3}
\newcommand*{\yMax}{3}
\begin{tabular}{ c c }

\begin{tikzpicture}[>=stealth,scale=0.4]
    \draw[very thin,color=gray,scale={pi/2}] ({\xMin*((1)/(2))+0.01},-6/pi+0.01) grid ({\xMax*(1/2)-0.01},7/pi-0.01);
    \draw node at ({pi},0) [below] {${\pi}$};
    \draw node at ({2*pi},0) [below] [xshift=1pt] {${2\pi}$};
    \draw node at ({-pi},0) [below] [xshift=-2pt]  {${-\pi}$};
    \draw node at ({-2*pi},0) [below] [xshift=-2pt] {${-2\pi}$};

    \draw node at (0,1) [left] {$1$};
    \draw node at (0,2) [left] {$2$};
    \draw node at (0,-1) [left] {$-1$};
    \draw node at (0,-2) [left] {$-2$};


    \draw [->] [thick] ({\xMin*(pi/4)},0) -- ({\xMax*(pi/4)+0.5},0) 
        node [right] {$x$};
    \draw [->] [thick] (0,-3) -- (0,3.5)
        node [above] {$y$};

    \draw [-,thin,black,domain={-2*pi}:{2*pi},samples=100] 
    plot (\x, {sin(\x*180/pi)}) node[above] {$f(x) = \sin(x)$};

\end{tikzpicture} &

\begin{tikzpicture}[>=stealth,scale=0.4]
    \draw[very thin,color=gray,scale={pi/2}] ({\xMin*((1)/(2))+0.01},-6/pi+0.01) grid ({\xMax*(1/2)-0.01},7/pi-0.01);
    \draw node at ({pi},0) [below] {${\pi}$};
    \draw node at ({2*pi},0) [below] [xshift=1pt] {${2\pi}$};
    \draw node at ({-pi},0) [below] [xshift=-2pt]  {${-\pi}$};
    \draw node at ({-2*pi},0) [below] [xshift=-2pt] {${-2\pi}$};

    \draw node at (0,1) [left] {$1$};
    \draw node at (0,2) [left] {$2$};
    \draw node at (0,-1) [left] {$-1$};
    \draw node at (0,-2) [left] {$-2$};


    \draw [->] [thick] ({\xMin*(pi/4)},0) -- ({\xMax*(pi/4)+0.5},0) 
        node [right] {$x$};
    \draw [->] [thick] (0,-3) -- (0,3.5)
        node [above] {$y$};

    \draw [-,thin,black,domain={-2*pi}:{2*pi},samples=100] 
    plot (\x, {cos(\x*180/pi)}) node[above] {$f(x) = \cos(x)$};

\end{tikzpicture} \\

\begin{tikzpicture}[>=stealth,scale=0.4]
    \draw[very thin,color=gray,scale={pi/2}] ({\xMin*((1)/(2))+0.01},-6/pi+0.01) grid ({\xMax*(1/2)-0.01},7/pi-0.01);
    \draw node at ({pi},0) [below] {${\pi}$};
    \draw node at ({2*pi},0) [below] [xshift=1pt] {${2\pi}$};
    \draw node at ({-pi},0) [below] [xshift=-2pt]  {${-\pi}$};
    \draw node at ({-2*pi},0) [below] [xshift=-2pt] {${-2\pi}$};

    \draw node at (0,1) [left] {$1$};
    \draw node at (0,2) [left] {$2$};
    \draw node at (0,-1) [left] {$-1$};
    \draw node at (0,-2) [left] {$-2$};


    \draw [->] [thick] ({\xMin*(pi/4)},0) -- ({\xMax*(pi/4)+0.5},0) 
        node [right] {$x$};
    \draw [->] [thick] (0,-3) -- (0,3.5)
        node [above] {$y$};

    \draw [-,thin,black,domain={-2*pi}:{2*pi},samples=100] 
    plot (\x, {cos(\x*180/pi)}) node[above] {$f(x) = \cos(x)$};

\end{tikzpicture}
    
    
\end{tabular}

\end{document}

this

Best Answer

I would advocate using the pgfplots package for this type of graphic.

It allows you to use the following, for example

  \begin{tikzpicture}
    \begin{axis}
      \addplot[timtam]expression[domain=-3.5:3.5]{sin(x)};
    \end{axis}
  \end{tikzpicture}

Here's a couple of demonstrations; adjust as you see fit. For reference, see also Axis with trigonometric labels in PGFPlots, for example.

screenshot of six trigonometric graphs

option 1 : using minipages, and individual plots

% arara: pdflatex
\documentclass{article}
\usepackage{geometry}
\usepackage{pgfplots}
\pgfplotsset{
  % framing the graphs
  framed/.style={
      axis background/.style ={draw=blue,fill=yellow!20,rounded corners=3ex}},
  % line style
  timtam/.style={
      color=red,mark=none,line width=1pt},
  % every axis
  every axis/.append style={
      axis x line=middle,    % put the x axis in the middle
      axis y line=middle,    % put the y axis in the middle
      axis line style={->},  % arrows on the axis
      xlabel={$x$},          % default put x on x-axis
      ylabel={$y$},          % default put y on y-axis
      scale only axis,       % otherwise width won't be as intended: http://tex.stackexchange.com/questions/36297/pgfplots-how-can-i-scale-to-text-width
      xtick={-3.14159265359,-1.57079632679,1.57079632679,3.14159265359},
      xticklabels={$-\pi$,$-\pi/2$,$\pi/2$,$\pi$},
      xmin=-3.5, xmax=3.5,
      ymin=-2.3, ymax=2.3,
      trig format=rad,       % use radians
      framed,
      grid=both,
      width=\textwidth,
    },
  % not needed in the below, but you might like them for future
  asymptote/.style={
      color=red,mark=none,line width=1pt,dashed},
  soldot/.style={
      color=red,only marks,mark=*},
  holdot/.style={
      color=red,fill=white,only marks,mark=*},
}


% arrow style
\tikzset{>=stealth}

\begin{document}

\begin{minipage}{.33\textwidth}
  \begin{tikzpicture}
    \begin{axis}
      \addplot[timtam]expression[domain=-3.5:3.5]{sin(x)};
    \end{axis}
  \end{tikzpicture}
\end{minipage}
\begin{minipage}{.33\textwidth}
  \begin{tikzpicture}
    \begin{axis}
      \addplot[timtam]expression[domain=-3.5:3.5]{cos(x)};
    \end{axis}
  \end{tikzpicture}
\end{minipage}
\begin{minipage}{.33\textwidth}
  \begin{tikzpicture}
    \begin{axis}
      \addplot[timtam]expression[domain=-4.5:-1.58]{tan(x)};
      \addplot[timtam]expression[domain=-1.56:1.55]{tan(x)};
      \addplot[timtam]expression[domain=1.58:4.5]{tan(x)};
    \end{axis}
  \end{tikzpicture}
\end{minipage}%

\vspace{1cm}

\begin{minipage}{.33\textwidth}
  \begin{tikzpicture}
    \begin{axis}
      \addplot[timtam]expression[domain=-3.5:-3.2]{1/sin(x)};
      \addplot[timtam]expression[domain=-3.1:-0.1]{1/sin(x)};
      \addplot[timtam]expression[domain=0.1:3.1]{1/sin(x)};
      \addplot[timtam]expression[domain=3.2:4.5]{1/sin(x)};
    \end{axis}
  \end{tikzpicture}
\end{minipage}
\begin{minipage}{.33\textwidth}
  \begin{tikzpicture}
    \begin{axis}
      \addplot[timtam]expression[domain=-4.5:-1.58]{1/cos(x)};
      \addplot[timtam]expression[domain=-1.56:1.56]{1/cos(x)};
      \addplot[timtam]expression[domain=1.58:4.5]{1/cos(x)};
    \end{axis}
  \end{tikzpicture}
\end{minipage}
\begin{minipage}{.33\textwidth}
  \begin{tikzpicture}
    \begin{axis}
      \addplot[timtam]expression[domain=-3.5:-3.2]{cot(x)};
      \addplot[timtam]expression[domain=-3.1:-0.1]{cot(x)};
      \addplot[timtam]expression[domain=0.1:3.1]{cot(x)};
      \addplot[timtam]expression[domain=3.2:4.5]{cot(x)};
    \end{axis}
  \end{tikzpicture}
\end{minipage}%
\end{document}

option 2: just like option 1, but with titles

If you'd like to add titles, we can use the following, for example; you'll see that the new part to the above is

      title style={at={(axis cs:0,-3.2)}}, %<------  NEW BIT

and then, within the code, I've used \begin{axis}[title={$y=\sin(x)$}].

screenshot of 6 trigonometric functions

% arara: pdflatex
\documentclass{article}
\usepackage{geometry}
\usepackage{pgfplots}
\pgfplotsset{
  % framing the graphs
  framed/.style={
      axis background/.style ={draw=blue,fill=yellow!20,rounded corners=3ex}},
  % line style
  timtam/.style={
      color=red,mark=none,line width=1pt},
  % every axis
  every axis/.append style={
      axis x line=middle,    % put the x axis in the middle
      axis y line=middle,    % put the y axis in the middle
      axis line style={->},  % arrows on the axis
      xlabel={$x$},          % default put x on x-axis
      ylabel={$y$},          % default put y on y-axis
      scale only axis,       % otherwise width won't be as intended: http://tex.stackexchange.com/questions/36297/pgfplots-how-can-i-scale-to-text-width
      xtick={-3.14159265359,-1.57079632679,1.57079632679,3.14159265359},
      xticklabels={$-\pi$,$-\pi/2$,$\pi/2$,$\pi$},
      xmin=-3.5, xmax=3.5,
      ymin=-2.3, ymax=2.3,
      trig format=rad,       % use radians
      framed,
      grid=both,
      width=\textwidth,
      title style={at={(axis cs:0,-3.2)}}, %<------  NEW BIT
    },
  % not needed in the below, but you might like them for future
  asymptote/.style={
      color=red,mark=none,line width=1pt,dashed},
  soldot/.style={
      color=red,only marks,mark=*},
  holdot/.style={
      color=red,fill=white,only marks,mark=*},
}


% arrow style
\tikzset{>=stealth}

\begin{document}

\begin{minipage}{.33\textwidth}
  \begin{tikzpicture}
    \begin{axis}[title={$y=\sin(x)$}]
      \addplot[timtam]expression[domain=-3.5:3.5]{sin(x)};
    \end{axis}
  \end{tikzpicture}
\end{minipage}
\begin{minipage}{.33\textwidth}
  \begin{tikzpicture}
    \begin{axis}[title={$y=\cos(x)$}]
      \addplot[timtam]expression[domain=-3.5:3.5]{cos(x)};
    \end{axis}
  \end{tikzpicture}
\end{minipage}
\begin{minipage}{.33\textwidth}
  \begin{tikzpicture}
    \begin{axis}[title={$y=\tan(x)$}]
      \addplot[timtam]expression[domain=-4.5:-1.58]{tan(x)};
      \addplot[timtam]expression[domain=-1.56:1.55]{tan(x)};
      \addplot[timtam]expression[domain=1.58:4.5]{tan(x)};
    \end{axis}
  \end{tikzpicture}
\end{minipage}%

\vspace{1cm}

\begin{minipage}{.33\textwidth}
  \begin{tikzpicture}
    \begin{axis}[title={$y=\csc(x)$}]
      \addplot[timtam]expression[domain=-3.5:-3.2]{1/sin(x)};
      \addplot[timtam]expression[domain=-3.1:-0.1]{1/sin(x)};
      \addplot[timtam]expression[domain=0.1:3.1]{1/sin(x)};
      \addplot[timtam]expression[domain=3.2:4.5]{1/sin(x)};
    \end{axis}
  \end{tikzpicture}
\end{minipage}
\begin{minipage}{.33\textwidth}
  \begin{tikzpicture}
    \begin{axis}[title={$y=\sec(x)$}]
      \addplot[timtam]expression[domain=-4.5:-1.58]{1/cos(x)};
      \addplot[timtam]expression[domain=-1.56:1.56]{1/cos(x)};
      \addplot[timtam]expression[domain=1.58:4.5]{1/cos(x)};
    \end{axis}
  \end{tikzpicture}
\end{minipage}
\begin{minipage}{.33\textwidth}
  \begin{tikzpicture}
    \begin{axis}[title={$y=\cot(x)$}]
      \addplot[timtam]expression[domain=-3.5:-3.2]{cot(x)};
      \addplot[timtam]expression[domain=-3.1:-0.1]{cot(x)};
      \addplot[timtam]expression[domain=0.1:3.1]{cot(x)};
      \addplot[timtam]expression[domain=3.2:4.5]{cot(x)};
    \end{axis}
  \end{tikzpicture}
\end{minipage}%
\end{document}

option 3: using groupplot

The output is as in option 2, but the input is, perhaps, more pleasing; note that this requires the groupplots library, annotated in the code below.

% arara: pdflatex
\documentclass{article}
\usepackage{geometry}
\usepackage{pgfplots}
\usepgfplotslibrary{groupplots}  %<------------ NEW BIT
\pgfplotsset{
  % framing the graphs
  framed/.style={
      axis background/.style ={draw=blue,fill=yellow!20,rounded corners=3ex}},
  % line style
  timtam/.style={
      color=red,mark=none,line width=1pt},
  % every axis
  every axis/.append style={
      axis x line=middle,    % put the x axis in the middle
      axis y line=middle,    % put the y axis in the middle
      axis line style={->},  % arrows on the axis
      xlabel={$x$},          % default put x on x-axis
      ylabel={$y$},          % default put y on y-axis
      scale only axis,       % otherwise width won't be as intended: http://tex.stackexchange.com/questions/36297/pgfplots-how-can-i-scale-to-text-width
      xtick={-3.14159265359,-1.57079632679,1.57079632679,3.14159265359},
      xticklabels={$-\pi$,$-\pi/2$,$\pi/2$,$\pi$},
      xmin=-3.5, xmax=3.5,
      ymin=-2.3, ymax=2.3,
      trig format=rad,       % use radians
      framed,
      grid=both,
      width=\textwidth,
      title style={at={(axis cs:0,-3.2)}},
    },
  % not needed in the below, but you might like them for future
  asymptote/.style={
      color=red,mark=none,line width=1pt,dashed},
  soldot/.style={
      color=red,only marks,mark=*},
  holdot/.style={
      color=red,fill=white,only marks,mark=*},
}


% arrow style
\tikzset{>=stealth}

\begin{document}

\begin{tikzpicture}
  \begin{groupplot}[
      group style={
          group name=my plots,
          group size=3 by 2,
        },
      width=.33\textwidth,
    ]
    \nextgroupplot[title={$y=\sin(x)$}]
      \addplot[timtam]expression[domain=-3.5:3.5]{sin(x)};
    \nextgroupplot[title={$y=\cos(x)$}]
      \addplot[timtam]expression[domain=-3.5:3.5]{cos(x)};
    \nextgroupplot[title={$y=\tan(x)$}]
      \addplot[timtam]expression[domain=-4.5:-1.58]{tan(x)};
      \addplot[timtam]expression[domain=-1.56:1.55]{tan(x)};
      \addplot[timtam]expression[domain=1.58:4.5]{tan(x)};
    \nextgroupplot[title={$y=\csc(x)$}]
      \addplot[timtam]expression[domain=-3.5:-3.2]{1/sin(x)};
      \addplot[timtam]expression[domain=-3.1:-0.1]{1/sin(x)};
      \addplot[timtam]expression[domain=0.1:3.1]{1/sin(x)};
      \addplot[timtam]expression[domain=3.2:4.5]{1/sin(x)};
    \nextgroupplot[title={$y=\sec(x)$}]
      \addplot[timtam]expression[domain=-4.5:-1.58]{1/cos(x)};
      \addplot[timtam]expression[domain=-1.56:1.56]{1/cos(x)};
      \addplot[timtam]expression[domain=1.58:4.5]{1/cos(x)};
    \nextgroupplot[title={$y=\cot(x)$}]
      \addplot[timtam]expression[domain=-3.5:-3.2]{cot(x)};
      \addplot[timtam]expression[domain=-3.1:-0.1]{cot(x)};
      \addplot[timtam]expression[domain=0.1:3.1]{cot(x)};
      \addplot[timtam]expression[domain=3.2:4.5]{cot(x)};
  \end{groupplot}
\end{tikzpicture}
\end{document}

If you need to number/reference the figures, then I'd recommend using the \caption command, perhaps employing the subfigure package.

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