使用 tikz 绘制 arctan 和 arccot 的图形？

Question

绘制已知函数的反函数不需要任何特殊的东西f(x)。要理解这一点，回想一下的图f(x)可以看作的参数图

 (x,f(x))

立即致电x=f^{-1}(t)。那么这块地将

 (f^{-1}(t),t) .

由此可见，一个阴谋

 (f(t),t)

是相同的

 (t,f^{-1}(t))

当然，我们必须适当调整域。因此，为了绘制arctan(x)（该函数的 pgf 名称是atan，请参阅JairoAraujo 的评论，或者atan2，处理象限），我们可以绘制

 (tan(t),t)

以及arccot

 (cot(t),t) .

本 MWE 对此进行了说明

\documentclass[tikz,border=3mm]{standalone}
\usepackage{amsmath}
\DeclareMathOperator{\arccot}{arccot}
\begin{document}
\begin{tikzpicture}[trig format=rad,samples=101]
\draw[blue,thick] plot[variable=\t,domain=-pi/2+0.1:pi/2-0.1] ({tan(\t)},\t);
\draw[red,dashed,thick] plot[variable=\t,domain=-10:10] (\t,{atan(\t)});
\path (8,pi/2) node[above]{$y=\arctan(x)$};
\draw plot[variable=\t,domain=-pi/2+0.1:-0.1] ({cot(\t)},\t);
\draw plot[variable=\t,domain=0.1:pi/2-0.1] ({cot(\t)},\t);
\path (8,0) node[below]{$y=\arccot(x)$};
\end{tikzpicture}
\end{document}

红色虚线只是为了表明“它有效”。

当然，用来绘制这个图非常有意义pgfplots。

\documentclass[tikz,border=3mm]{standalone}
\usepackage{amsmath}
\DeclareMathOperator{\arccot}{arccot}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\begin{document}
\begin{tikzpicture}
\begin{axis}[trig format plots=rad,
    samples=101,
    unbounded coords=jump,
    xmin=-10,xmax=10,ymax=pi/2+0.5
    ]
\addplot[blue,thick,variable=\t,domain=-pi/2+0.1:pi/2-0.1] ({tan(\t)},\t);
\path (10,pi/2) node[above left]{$y=\arctan(x)$};
\addplot[red,dashed,thick,variable=\t,domain=-10:10] (\t,{atan(\t)});
\addplot[green!60!black,variable=\t,domain=-pi/2+0.1:pi/2-0.1] ({cot(\t)},\t);
\draw[green!60!black,dashed] (0,-2) -- (0,2);
\path (10,0) node[below left]{$y=\arccot(x)$};
\end{axis}
\end{tikzpicture}
\end{document}

或者，根据要求，不带盒子，但带有网格。

\documentclass{article}
\usepackage{amsmath}
\DeclareMathOperator{\arccot}{arccot}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\begin{document}
\begin{figure}
\centering
\begin{tikzpicture}
\begin{axis}[axis lines=middle,xlabel={$x$},ylabel={$y$},
    width=0.9\textwidth,
    trig format plots=rad,
    samples=101,
    unbounded coords=jump,
    xmin=-pi,xmax=pi,
    ymin=-pi/2-0.2,ymax=pi/2+0.5,
    xtick={-pi/2,pi/2},xticklabels={$-\frac{\pi}{2}$,$\frac{\pi}{2}$},
    ytick={-pi/2,pi/2},yticklabels={$-\frac{\pi}{2}$,$\frac{\pi}{2}$},
    grid=major,grid style={densely dashed},
    legend style={at={(0.01,0.99)},anchor=north west}
    ]
\addplot[blue,thick,variable=\t,domain=-pi/2+0.1:pi/2-0.1] ({tan(\t)},\t);
\addlegendentry{$y=\arctan(x)$}
%\addplot[red,dashed,thick,variable=\t,domain=-10:10] (\t,{atan(\t)});
\addplot[green!60!black,variable=\t,domain=-pi/2+0.1:pi/2-0.1] ({cot(\t)},\t);
\draw[green!60!black,dashed] (0,-2) -- (0,2);
\addlegendentry{$y=\arccot(x)$}
\end{axis}
\end{tikzpicture}
\caption{``Standard'' branches of the multivalued functions $\arctan$ and $\arccot$.}
\end{figure}
\end{document}

Answer 1