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使用 TikZ 绘制单位圆和正弦波图表

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使用 TikZ 绘制单位圆和正弦波图表

我怎样才能将此图表（附件）表达为 TikZ 图片以用于 LaTeX 文档？我已经研究了一段时间，但没有成功。

感谢您的帮助。

图表

\documentclass{article}% guessing (cfr)
\usepackage{tikz}
\usepackage[top=1in,bottom=1in,right=1in,left=1in]{geometry}
\begin{document}% added - surely necessary! (cfr)
\begin{tikzpicture}[scale=5.3,cap=round,>=latex]
        \draw[->] (-1.5cm,0cm) -- (1.5cm,0cm) node[right,fill=white] {$x$};
        \draw[->] (0cm,-1.5cm) -- (0cm,1.5cm) node[above,fill=white] {$y$};

        \draw[thick] (0cm,0cm) circle(1cm);

        \foreach \x in {0,30,...,360} {
                \draw[gray] (0cm,0cm) -- (\x:1cm);
                \filldraw[black] (\x:1cm) circle(0.4pt);
                \draw (\x:0.6cm) node[fill=white] {$\x^\circ$};
        }

        \foreach \x/\xtext in {
            30/\frac{\pi}{6},
            45/\frac{\pi}{4},
            60/\frac{\pi}{3},
            90/\frac{\pi}{2},
            120/\frac{2\pi}{3},
            135/\frac{3\pi}{4},
            150/\frac{5\pi}{6},
            180/\pi,
            210/\frac{7\pi}{6},
            225/\frac{5\pi}{4},
            240/\frac{4\pi}{3},
            270/\frac{3\pi}{2},
            300/\frac{5\pi}{3},
            315/\frac{7\pi}{4},
            330/\frac{11\pi}{6},
            360/2\pi}
                \draw (\x:0.85cm) node[fill=white] {$\xtext$};

        \foreach \x/\xtext/\y in {
            30/\frac{\sqrt{3}}{2}/\frac{1}{2},
            45/\frac{\sqrt{2}}{2}/\frac{\sqrt{2}}{2},
            60/\frac{1}{2}/\frac{\sqrt{3}}{2},
            150/-\frac{\sqrt{3}}{2}/\frac{1}{2},
            135/-\frac{\sqrt{2}}{2}/\frac{\sqrt{2}}{2},
            120/-\frac{1}{2}/\frac{\sqrt{3}}{2},
            210/-\frac{\sqrt{3}}{2}/-\frac{1}{2},
            225/-\frac{\sqrt{2}}{2}/-\frac{\sqrt{2}}{2},
            240/-\frac{1}{2}/-\frac{\sqrt{3}}{2},
            330/\frac{\sqrt{3}}{2}/-\frac{1}{2},
            315/\frac{\sqrt{2}}{2}/-\frac{\sqrt{2}}{2},
            300/\frac{1}{2}/-\frac{\sqrt{3}}{2}}
                \draw (\x:1.25cm) node[fill=white] {$\left(\xtext,\y\right)$};

        \draw (-1.25cm,0cm) node[above=1pt] {$(-1,0)$}
              (1.25cm,0cm)  node[above=1pt] {$(1,0)$}
              (0cm,-1.25cm) node[fill=white] {$(0,-1)$}
              (0cm,1.25cm)  node[fill=white] {$(0,1)$};
    \end{tikzpicture}
\end{document}

结果是 单位圆图像

答案1

也许，这只是一个开始。

编辑此版本结合了我在原始版本中使用的两张图片，并用来backgrounds演示如何添加虚线。绘制了两条这样的线来说明该方法。（虽然不是很整齐，但线条确实出现在预期的位置。）

编辑2此版本通过循环绘制更多线条，并将垂直线添加到X轴。

正弦波

\documentclass[a4paper]{article}% guessing (cfr)
\usepackage[landscape,scale=.9]{geometry}
\usepackage{tikz}
\usetikzlibrary{datavisualization.formats.functions,backgrounds,calc}
\def\mytypesetter#1{% page 813
  \pgfmathparse{#1/pi}%
  \pgfmathprintnumber{\pgfmathresult}$\pi$%
}
\begin{document}% added - surely necessary! (cfr)
  \centering
  \begin{tikzpicture}[scale=4,cap=round,>=latex,baseline={(0,0)}]
    \draw[->] (-1.5cm,0cm) -- (1.5cm,0cm) node[right,fill=white] {$x$};
    \draw[->] (0cm,-1.5cm) -- (0cm,1.5cm) node[above,fill=white] {$y$};

    \draw[thick] (0cm,0cm) circle(1cm);

    \foreach \x in {0,30,...,360} {
      \draw[gray] (0cm,0cm) -- (\x:1cm);
      \filldraw[black] (\x:1cm) coordinate (x\x) circle (0.4pt);
      \draw (\x:0.6cm) node[fill=white] {$\x^\circ$};
    }

    \foreach \x/\xtext in {
      30/\frac{\pi}{6},
      45/\frac{\pi}{4},
      60/\frac{\pi}{3},
      90/\frac{\pi}{2},
      120/\frac{2\pi}{3},
      135/\frac{3\pi}{4},
      150/\frac{5\pi}{6},
      180/\pi,
      210/\frac{7\pi}{6},
      225/\frac{5\pi}{4},
      240/\frac{4\pi}{3},
      270/\frac{3\pi}{2},
      300/\frac{5\pi}{3},
      315/\frac{7\pi}{4},
      330/\frac{11\pi}{6},
      360/2\pi}
    \draw (\x:0.85cm) node[fill=white] {$\xtext$};

    \foreach \x/\xtext/\y in {
      30/\frac{\sqrt{3}}{2}/\frac{1}{2},
      45/\frac{\sqrt{2}}{2}/\frac{\sqrt{2}}{2},
      60/\frac{1}{2}/\frac{\sqrt{3}}{2},
      150/-\frac{\sqrt{3}}{2}/\frac{1}{2},
      135/-\frac{\sqrt{2}}{2}/\frac{\sqrt{2}}{2},
      120/-\frac{1}{2}/\frac{\sqrt{3}}{2},
      210/-\frac{\sqrt{3}}{2}/-\frac{1}{2},
      225/-\frac{\sqrt{2}}{2}/-\frac{\sqrt{2}}{2},
      240/-\frac{1}{2}/-\frac{\sqrt{3}}{2},
      330/\frac{\sqrt{3}}{2}/-\frac{1}{2},
      315/\frac{\sqrt{2}}{2}/-\frac{\sqrt{2}}{2},
      300/\frac{1}{2}/-\frac{\sqrt{3}}{2}}
    \draw (\x:1.25cm) node {$\left(\xtext,\y\right)$};

    \draw (-1.25cm,0cm) node[above=1pt] {$(-1,0)$}
    (1.25cm,0cm)  node[above=1pt] {$(1,0)$}
    (0cm,-1.25cm) node[fill=white] {$(0,-1)$}
    (0cm,1.25cm)  node[fill=white] {$(0,1)$};
    \begin{scope}[xshift=20mm]
      \datavisualization
      [
      school book axes,
      y axis={unit length=10mm},
      x axis={unit length=2.5mm, ticks={step=(.5*pi), tick typesetter/.code=\mytypesetter{##1}}},
      visualize as smooth line,
      ]
      data [format=function] {
        var x : interval [0:4*pi];
        func y = sin(\value x r);
      };
    \end{scope}
    \begin{scope}[on background layer]
      \coordinate (o) at (0,0);
      \foreach \i in {90,120,...,270}
        {
          \draw [densely dashed, opacity=.25, color=blue!50!cyan] (x\i) -- ({x\i} -| o) -- ++(20mm,0) -- ++(pi*\i/720,0) coordinate (xx\i) edge (xx\i |- o)  -- ++(.5*pi,0) coordinate (xxx\i) edge (xxx\i |- o);
        }
    \end{scope}
  \end{tikzpicture}
\end{document}

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