动画三角函数

Question

我需要以类似于所示的动画方式绘制 6 个主要三角函数绘制三角函数的动态 gif

然而，

• 我需要的圆圈与这里显示的圆圈相同：https://texample.net/tikz/examples/unit-circle/ 其中每个曲线使用的值将被突出显示（当使用符号曲线时，突出显示圆上的符号曲线的值......等等）

• 我需要波形的曲线与所示的曲线相似如何在 PStricks/Tikz 中制作正弦曲线动画（但角度要以弧度和度为单位，在动画中突出显示曲线和圆上的各 2 个等效角度，还需要显示周期长度......）

• 还需要第七张图来绘制正弦和余弦曲线，并用不同的颜色重叠来强调它们。

• 需要强调所有可能的细节。

我已经将绘图和之前的帖子（MWE）中提出的动画代码作为起点，但修改它并包含所有细节有点让人不知所措。

\documentclass{article}
\usepackage{amsmath} 

\usepackage{tikz} 
    \usetikzlibrary{arrows.meta,arrows,positioning,matrix,quotes, shapes.geometric,calc,decorations.markings,decorations.pathmorphing,
backgrounds,graphs,shapes,shapes.misc,fit,angles,quotes,datavisualization.formats.functions,intersections,hobby} 

\usepackage[bidi=basic,layout=lists.tabular]{babel}
\babelprovide[import=en,maparabic,main]{english}
\babelfont[english]{rm}{Times New Roman}

\begin{document}

\begin{figure}[!htbp]
\begin{center}
\begin{tikzpicture}[scale=5.3,cap=round,>=latex]
 % draw the coordinates
        \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 the unit circle
        \draw[thick] (0cm,0cm) circle(1cm);

        \foreach \x in {0,30,...,360} {
                % lines from center to point
                \draw[gray] (0cm,0cm) -- (\x:1cm);
                % dots at each point
                \filldraw[black] (\x:1cm) circle(0.4pt);
                % draw each angle in degrees
                \draw (\x:0.6cm) node[fill=white] {$\x^\circ$};
        }

        % draw each angle in radians
        \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 {
            % the coordinates for the first quadrant
            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},
            % the coordinates for the second quadrant
            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},
            % the coordinates for the third quadrant
            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},
            % the coordinates for the fourth quadrant
            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 the horizontal and vertical coordinates
        % the placement is better this way
        \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{center}
\caption
{Circle}
\label{fig:angle}
\end{figure}


\foreach \angle in {0,10,...,360}
{
  \begin{tikzpicture}
    % fill circle and plot
    \fill[blue!50] (-1,0) arc (0:\angle:1) -- (-2,0) -- cycle;
    \fill[blue!50] plot[smooth,domain=0:\angle] (pi/180*\x,{sin(\x)}) |- (0,0);
    % draw connection
    \draw (-2,0) +(\angle:1) circle (2pt) -- (pi/180*\angle,{sin(\angle)}) circle (2pt);
    % draw axes an ticks
    \draw (-3.5,0) -- (7,0);
    \foreach \deg in {90, 180, 270, 360}
      \draw (pi/180*\deg,2pt) -- (pi/180*\deg,-2pt) node[below] {$\deg^\circ$};
    \draw (0,-1.2) -- (0,1.2);
    \foreach \y in {-1,-0.5,0.5,1}
      \draw (2pt,\y) -- (-2pt,\y) node[left] {$\y$};
    % draw plot and circle outline
    \draw plot[smooth,domain=0:360] (pi/180*\x,{sin(\x)});
    \draw (-2,0) circle (1);
  \end{tikzpicture}
}
\end{document}

Answer 1

您需要更多，however但您的代码与期望的结果并不是最接近的。

版本渐近线。

import animate;
import graph;
settings.tex="pdflatex"; 
animation Ani;
size(500);

transform t(real x=0){
return shift((-5,x))*scale(3);
}
transform t=t();
transform labelscale=scale(.6);
transform t1=shift((1.5,0))*scale(2,3);

string[][] s={
  {"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"}
};
int[] a={30,45,60,150,135,120,210,225,240,330,315,300};
string[][] z={
  // the coordinates for the first quadrant
  {"\frac{\sqrt{3}}{2}","\frac{1}{2}"},
  {"\frac{\sqrt{2}}{2}","\frac{\sqrt{2}}{2}"},
  {"\frac{1}{2}","\frac{\sqrt{3}}{2}"},
  // the coordinates for the second quadrant
  {"-\frac{\sqrt{3}}{2}","\frac{1}{2}"},
  {"-\frac{\sqrt{2}}{2}","\frac{\sqrt{2}}{2}"},
  {"-\frac{1}{2}","\frac{\sqrt{3}}{2}"},
  // the coordinates for the third quadrant
  {"-\frac{\sqrt{3}}{2}","-\frac{1}{2}"},
  {"-\frac{\sqrt{2}}{2}","-\frac{\sqrt{2}}{2}"},
  {"-\frac{1}{2}","-\frac{\sqrt{3}}{2}"},
  // the coordinates for the fourth quadrant
  {"\frac{\sqrt{3}}{2}","-\frac{1}{2}"},
  {"\frac{\sqrt{2}}{2}","-\frac{\sqrt{2}}{2}"},
  {"\frac{1}{2}","-\frac{\sqrt{3}}{2}"}
};
string[] q={
  "90^\circ(\frac{\pi}{2})",
  "180^\circ(\pi)",
  "270^\circ(\frac{3\pi}{2})",
  "360^\circ(2\pi)",
};
real[] m={pi/2,pi,3*pi/2,2*pi};

for (int j=0; j <= 360; j=j+5){
save();
// sin(x)
if(j != 0) { fill(t*((0,0)--arc((0,0),1,0,j)--cycle),blue+opacity(.4)); }

draw(Label("$x$",EndPoint,filltype=Fill(white)),t*((-1.5,0)--(1.5,0)),Arrow);
draw(Label("$y$",EndPoint,filltype=Fill(white)),t*((0,-1.5)--(0,1.5)),Arrow);

draw(t*circle((0,0),1));

for (int i=0; i<= 360; i=i+30)
{
  draw(t*((0,0)--dir(i)),gray);
  dot(t*dir(i),linewidth(1.5bp));
  if(i != 0)
    label(labelscale*Label(format("$%d^\circ$",i),filltype=Fill(invisible)),
          t*(0.6*dir(i)));
}

for (int i=0; i<s.length; ++i) {
  label(labelscale*Label("$"+s[i][1]+"$",filltype=Fill(invisible)),
        t*(0.85*dir((int) s[i][0]))); 
}
for (int i=0; i<a.length; ++i) { 
  label(labelscale*Label("$("+z[i][0]+","+z[i][1]+")$",filltype=Fill(invisible)),
        t*(1.3*dir(a[i]))); 
}
label(labelscale*"$(-1,0)$",t*(-1.25,0),dir(90));
label(labelscale*"$(1,0)$",t*(1.25,0),dir(90));
label(labelscale*"$(0,-1)$",t*(0,-1.25),Fill(white));
label(labelscale*"$(0,1)$",t*(0,1.25),Fill(white));
//************************
draw(scale(.8)*Label("$x$",EndPoint),t1*((0,0)--(2*pi+0.5,0)),Arrow);
draw(scale(.8)*Label("$y=\sin(t)$",EndPoint),t1*((0,-1.5)--(0,1.5)),Arrow);
for (real a : new real[]{-1,-0.5,0.5,1})
{
draw(scale(0.6)*Label("$"+(string) a+"$",Relative(0)),t1*((0,a)-(0.1,0)--(0,a)+(0.1,0)));
}

for (int i=0; i< q.length; ++i)
{
  draw(scale(0.6)*Label("$"+q[i]+"$",Relative(0),Fill(invisible)),
       t1*((m[i],0)-(0,0.03)--(m[i],0)+(0,0.03)));
}

real f(real x){return sin(x);}
guide F=graph(f,0,2*pi,300);
fill(t1*((0,0)--graph(f,0,radians(j),300)--(radians(j),0)--cycle),blue+opacity(.4));
draw(t1*F,blue);
draw(t*dir(j)--t1*(radians(j),f(radians(j))),(j!=0) ? currentpen : invisible);
draw(t1*(radians(j),f(radians(j)))--t1*(radians(j),0),black+0.4bp);
dot(t*dir(j),Fill(white));
dot(t1*(radians(j),f(radians(j))),Fill(white));

label(Label("Length"+"$="+(string) arclength(graph(f,0,radians(j),1000))+"$"),t1*(4,-2));
label(Label("Length"+"$="+(string) arclength((j!=0) ? Arc((0,0),1,0,j) : nullpath)+"$"),
      t*(0,-2));

Ani.add();
restore();
draw(t1*(radians(j),f(radians(j)))--t1*(radians(j),0),black+0.4bp);
}
erase();
Ani.movie(BBox(2mm,invisible));