PGF/TikZ 中的范围限制

Question

我目前正在尝试将多个图形放在一个图形中\tikzpicture，但当我尝试放入正切函数时，由于其在 pi/2 处的未定义性质以及我的域被定义为-pi:pi我的 LaTeX 编译器不断出现故障。这是代码

\begin{tikzpicture}[domain=0:pi]
    \draw[very thin, color=gray] (-pi,-1) grid (pi,1);

    \draw[->] (-7.0,0) -- (7.0,0) node[right] {$x$};
    \draw[->] (0,-1.2) -- (0,1.2) node[above] {$f(x)$};

    \draw[color=red]    plot(\x,{sin(\x r)}) node[right] {$f(x) = \sin(x)$};
    \draw[color=blue]   plot(\x,{cos(\x r)}) node[right] {$f(x) = \cos(x)$};
    \draw[color=orange] plot(\x,{tan(\x r)}) node[right] {$f(x) = \tan(x)$};
\end{tikzpicture}

我最大的问题是，我怎样才能在这个图表上设置范围限制，以便绘制正切函数，是否还有其他库可以用来绘制正切函数？

Answer 1

如果没有pgfplots它，会稍微麻烦一些。网格的上边界和下边界分别为 1 和 -1，因此需要计算角度。然后可以显示 tan 函数的可见、允许部分：

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[domain=-pi:pi]
  \draw[very thin, color=gray] (-pi,-1) grid (pi,1);

  \draw[->] (-4,0) -- (6,0) node[right] {$x$};
  \draw[->] (0,-1.2) -- (0,1.2) node[above] {$f(x)$};

  \draw[color=red]    plot(\x,{sin(\x r)})
    node[above right] {$f(x) = \sin(x)$};
  \draw[color=blue]   plot(\x,{cos(\x r)})
    node[right] {$f(x) = \cos(x)$};
  \draw[color=orange]
    plot[domain=-pi:-.75*pi] (\x, {tan(\x r)})
    plot[domain=-.25*pi:.25*pi] (\x, {tan(\x r)})
    plot[domain=.75*pi:pi](\x,{tan(\x r)})
    node[below right] {$f(x) = \tan(x)$};
\end{tikzpicture}
\end{document}

Answer 2

因为您还没有让我们知道您是否已经找到了解决方案，所以这里有一种可能性......

\documentclass[border=2pt]{standalone}
\usepackage{pgfplots}
    \pgfplotsset{compat=1.3}
\begin{document}
    \begin{tikzpicture}
        \begin{axis}[
            % set the labels at the axes
            xlabel=$x$,
            ylabel=$f(x)$,
            % set the domain where the values of the functions should be calculated for
            domain=0:pi,
            % draw the lines "smooth"
            smooth,
            % set limits of the axis
            xmin=0,
            xmax=pi,
            ymin=-2,
            ymax=2,
            % to avoid PGF Math Errors (while calculating the tangent values)
            % restrict the y domain
            % for that the limits should be a bit larger than the axis limits
            % (compare with the result if the limits are equal)
            restrict y to domain=-5:5,
        ]
            \addplot [red]      function {sin(x)};
            \addplot [blue]     function {cos(x)};
            \addplot [orange]   function {tan(x)};
        \end{axis}
    \end{tikzpicture}
\end{document}

Answer 3

您可以以某种方式重新定义tan函数（mytan在示例中命名），以使其在任何地方定义。

\documentclass[tikz,border=7pt]{standalone}
\usetikzlibrary{math}
\tikzmath{
  function mytan(\x) {
    if  abs(cos(\x)) < .001 then {
      return 100;
    } else {
      return tan(\x);
    };
  };
}
\begin{document}
  \begin{tikzpicture}[domain=-pi:pi, samples=100]
      \draw[very thin, color=gray] (-pi,-1) grid (pi,1);
      \clip  (-pi,-2) rectangle (2*pi,2);

      \draw[->] (-7.0,0) -- (7.0,0) node[right] {$x$};
      \draw[->] (0,-1.2) -- (0,1.2) node[above] {$f(x)$};

      \draw[color=red]    plot(\x,{sin(\x r)}) node[above right] {$f(x) = \sin(x)$};
      \draw[color=blue]   plot(\x,{cos(\x r)}) node[right] {$f(x) = \cos(x)$};
      \draw[color=orange] plot(\x,{mytan(\x r)}) node[below right] {$f(x) = \tan(x)$};
  \end{tikzpicture}
\end{document}