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如何在表格中显示所有三角函数图？

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如何在表格中显示所有三角函数图？

为了我的数学总结，我试图制作一个表格，其中包含所有三角函数的函数图（类似于下图，但包括反函数）。由于我的空间仅限于 12 页，我希望其中一些垂直对齐以节省一些空间，就像图中一样。我对 Latex 还不太熟悉，我尝试使用 来做到这一点tabular。但是这些图有点太靠右了 - 我希望它们完全居中。我该怎么做？

我的另一个问题是，如果我尝试绘制诸如tan、csc、sec、arcsin、等函数arccos，它们要么产生错误，要么搞乱一切。我该如何绘制这些函数？

我也找不到任何总结了所有三角函数的模板，我觉得这很奇怪，因为我认为我不是第一个需要它的人。是否有一个秘密的地方可以共享此类文件？

下面是三个函数的代码（我包含了两次余弦，以便有东西可以显示）：

\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}

这

答案1

我主张使用该pgfplots包来制作此类图形。

它允许您使用以下内容，例如

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

这里有几个演示；请根据需要进行调整。作为参考，另请参阅PGFPlots 中带有三角标签的轴， 例如。

六个三角函数图的屏幕截图

选项 1：使用小页面和单独的图

% 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}

选项 2：与选项 1 类似，但带有标题

如果您想添加标题，我们可以使用以下内容，例如；您会看到上面的新部分是

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

然后，在代码中，我使用了\begin{axis}[title={$y=\sin(x)$}]。

6 个三角函数的屏幕截图

% 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}

选项 3：使用 groupplot

输出与选项 2 相同，但输入可能更令人满意；请注意，这需要groupplots在下方代码中注释的库。

% 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}

如果您需要对图形进行编号/引用，那么我建议使用命令\caption，或许使用subfigure包。

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