用垂直渐近线绘制 f(x)=tan x 的一个周期

Question

我希望图片看起来像手绘的。如能得到帮助我将非常感激，谢谢。

Answer 1

和pgfplots

\documentclass[border=4mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.12}

\begin{document}
\begin{tikzpicture}
\begin{axis}
        [
    ymin=-10,ymax=10,
    xmin=-2,xmax=2,
    %clip=false,
    xtick=\empty,
    ytick={-8,-6,...,8},
    extra x ticks={-1.5708, 1.5708},
    extra x tick labels={$-\frac{\pi}{2}$, $\frac{\pi}{2}$},
    every extra x tick/.style={
            xticklabel style={anchor=north west},
            grid=major,
            major grid style={thick,dashed,red}
    },
    axis lines = center,
    xlabel=$x$,ylabel=$y$,
    domain=-.5*pi:.5*pi,
    samples=200,
    ]
        \addplot [red,thick] {tan(deg(x))};
\end{axis}
\end{tikzpicture}
\end{document}

Answer 2

如果您希望尝试一下 MetaPost，这里有一个包含在 LuaLaTeX 程序中的示例，可以说明它可以解决您的问题：

\documentclass[12pt, border=1bp]{standalone}
\usepackage{amsmath, luamplib}
    \mplibsetformat{metafun}
    \mplibnumbersystem{double}
    \mplibtextextlabel{enable}
\begin{document}
\begin{mplibcode}
vardef function(expr xmin, xmax, xstep)(text f_x) =
    save x; x := xmin;
    (x, f_x) forever:
        hide(x := x + xstep)
        exitif x > xmax;
        .. (x, f_x) 
    endfor
    if x - xstep < xmax: hide(x := xmax) .. (x, f_x) fi
enddef;
numeric u, xmin, xmax, Xmin, Xmax, xstep, ymin, ymax;
u = 1.5cm; Xmax = -Xmin = 2.25; Ymax = -Ymin = 4.75; xstep = 0.05; xmax = -xmin = 1.5;

beginfig(1);
    draw function(xmin, xmax, xstep)(tan x) scaled u;
    clip currentpicture to 
        ((Xmin, Ymin) -- (Xmax, Ymin) -- (Xmax, Ymax) -- (Xmin, Ymax) -- cycle) scaled u;
    draw u*(-pi/2, Ymin) -- u*(-pi/2, Ymax) dashed evenly;
    draw u*(pi/2, Ymin) -- u*(pi/2, Ymax) dashed evenly;
    drawarrow u*(Xmin, 0) -- u*(Xmax, 0);
    drawarrow u*(0, Ymin) -- u*(0, Ymax);
    label.bot("$x$", (Xmax*u, 0)); label.lft("$y$", (0, Ymax*u)); 
    label.ulft("$O$", origin);
    label.llft("$-\dfrac{\pi}{2}$", (-u*pi/2, 0)); 
    label.llft("$\dfrac{\pi}{2}$", (u*pi/2, 0));
    labeloffset := 6bp;
    for i = -4 upto 4: 
        if i<>0: 
            draw (-3bp, i*u) -- (3bp, i*u); label.lft("$" & decimal i & "$", (0, i*u)); 
        fi 
    endfor
endfig;
\end{mplibcode}
\end{document}