TikZ – Drawing Trigonometric Circle Using TikZ Package

circlesrotatingtikz-nodetikz-pgf

I want to draw below trigonometric circle

I found the websites https://texample.net/tikz/examples/unit-circle/
containing the code.

Please help modify the code to get this image.
Thank you in advance!

\documentclass[landscape]{article}
    \usepackage{tikz}
    \usepackage[active,tightpage]{preview}
    \PreviewEnvironment{tikzpicture}
    \setlength\PreviewBorder{5pt}%
    \usepackage[top=1in,bottom=1in,right=1in,left=1in]{geometry}
    \begin{document}
        \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{document}

Best Answer

With some adjustments and using the rotate around key, here is my attempt. Main changes are indicated by % <--

\documentclass{standalone}
\usepackage{tikz}
\begin{document}
  \begin{tikzpicture}[scale=5.3,cap=round,>=latex]
    \draw[->] (-1.5cm,0cm) -- (1.5cm,0cm) node[right,fill=white] {$x$}; % x axis
    \draw[->] (0cm,-1.5cm) -- (0cm,1.5cm) node[above,fill=white] {$y$}; % y axis
    
    % draw the unit circle
    \draw[thick] (0cm,0cm) circle(1cm);
    
    \foreach \x in {45,135, 225,315,0,30,...,360} { % <-- bissectrices added
      \draw[gray] (0cm,0cm) -- (\x:1cm); % lines from center to point
      \filldraw[black] (\x:1cm) circle(0.4pt); % dots at each point
    }
    
    % for the first and fourth quadrants
    \foreach \adeg/\radtext/\xc/\yc in {
      30/\frac{\pi}{6}/\frac{\sqrt{3}}{2}/\frac{1}{2},
      45/\frac{\pi}{4}/\frac{\sqrt{2}}{2}/\frac{\sqrt{2}}{2},
      60/\frac{\pi}{3}/\frac{1}{2}/\frac{\sqrt{3}}{2},
      300/\frac{5\pi}{3}/\frac{1}{2}/-\frac{\sqrt{3}}{2},
      315/\frac{7\pi}{4}/\frac{\sqrt{2}}{2}/-\frac{\sqrt{2}}{2},
      330/\frac{11\pi}{6}/\frac{\sqrt{3}}{2}/-\frac{1}{2}
    }
    {
      \draw (\adeg:0.6cm) node[fill=white, rotate around={\adeg:(0,0)}] {$\adeg^\circ$}; % <-- rotate around key used
      \draw (\adeg:0.85cm) node[fill=white, rotate around={\adeg:(0,0)}] {$\radtext$}; % <-- rotate around key used
      \draw (\adeg:1.025cm) node[fill=white, rotate around={\adeg:(0,0)}, anchor=west] {$\left(\xc,\yc\right)$}; % <-- rotate around key used, radius changed, anchor key used
    }
  
    % for the second and third quadrants
    \foreach \adeg/\radtext/\xc/\yc in {
      120 / \frac{2\pi}{3} / -\frac{1}{2} / \frac{\sqrt{3}}{2},
      135 / \frac{3\pi}{4} / -\frac{\sqrt{2}}{2} / \frac{\sqrt{2}}{2},
      150 / \frac{5\pi}{6} / -\frac{\sqrt{3}}{2} / \frac{1}{2},
      210 / \frac{7\pi}{6} / -\frac{\sqrt{3}}{2} / -\frac{1}{2},
      225 / \frac{5\pi}{4} / -\frac{\sqrt{2}}{2} / -\frac{\sqrt{2}}{2},
      240 / \frac{4\pi}{3} / -\frac{1}{2} / -\frac{\sqrt{3}}{2}
    }
    {
      \draw (\adeg:0.6cm) node[fill=white, rotate around={\adeg+180:(0,0)}] {$\adeg^\circ$}; % <-- rotate around key used
      \draw (\adeg:0.85cm) node[fill=white, rotate around={\adeg+180:(0,0)}] {$\radtext$}; % <-- rotate around key used
      \draw (\adeg:1.025cm) node[fill=white, rotate around={\adeg+180:(0,0)}, anchor=east] {$\left(\xc,\yc\right)$}; % <-- rotate around key used, radius changed, anchor key used
    }
    
    \foreach \adeg/\radtext/\xc/\yc in {0 / 2\pi / 1 / 0, 180 / \pi / -1 / 0}
    {
      \draw (\adeg:0.6cm) node[fill=white, above=1pt] {$\adeg^\circ$};
      \draw (\adeg:0.85cm) node[fill=white, above=1pt] {$\radtext$};
      \draw (\adeg:1.15cm) node[fill=white, above=1pt] {$\left(\xc,\yc\right)$}; % <-- radius changed
    }
    
    \foreach \adeg/\radtext/\xc/\yc in {90 / \frac{\pi}{2} / 0 / 1, 270 / \frac{3\pi}{2} / 0 / -1}
    {
      \draw (\adeg:0.6cm) node[fill=white, right=1pt] {$\adeg^\circ$};
      \draw (\adeg:0.85cm) node[fill=white, right=1pt] {$\radtext$};
      \draw (\adeg:1.1cm) node[fill=white, right=1pt] {$\left(\xc,\yc\right)$}; % <-- radius changed
    }
  \end{tikzpicture}
\end{document}

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[Tex/LaTex] Want to Draw circle with sector and segment

\documentclass[tikz,border=2mm]{standalone}
\usepackage{lmodern}

\begin{document}
\begin{tikzpicture}[draw=blue!70,thick]
\filldraw[fill=blue!40] circle (2.5cm);
\filldraw[fill=white] 
     (320:2.5cm) node[right] {Q} 
  -- (220:2.5cm) node[left] {P} 
  arc[start angle=220, end angle=320, radius=2.5cm] 
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\node {Major Segment};
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\begin{scope}[xshift=6cm]
\draw circle (2.5cm);
\filldraw[fill=blue!40] 
     (320:2.5cm) node[right] {Q}
  -- (0,0) node[above] {O}
  -- (220:2.5cm) node[left] {P} 
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[Tex/LaTex] Draw circle with three colours in tikz

The problem is that an arc of radius 1 from one coordinate (call it A) which starts at angle X and ends at angle Y will assume that A is at angle of X on the circumference of a circle with radius 1.

So your first arc assumes that (0,0) is at zero degrees on the circumference of a circle with radius 1. This means the centre of the circle must be at (-1,0).

But your second arc assumes that (1,0) is at 120 degrees on the circumference of a circle with radius 1. So the centre must be at (1.5,{.5*(sqrt(3))}.

Finally, your third arc assumes that (0,0) is at 240 degrees on the circumference of a circle with radius 1. So the centre must be at ({cos(60)},{sin(60)}).

[On the improbable assumption that I've not messed up the geometry at this hour of the night.]

I suggest using polar coordinates instead. Then your arcs can start at (0:1), (120:1) and (240:1) which makes things much simpler.

\documentclass[border=10pt,tikz]{standalone}
\begin{document}
\begin{tikzpicture}
  \draw [red] (0:1) arc [radius=1, start angle=0, end angle=120];
  \draw [green] (120:1) arc [radius=1, start angle=120, end angle=240];
  \draw [blue] (240:1) arc [radius=1, start angle=240, end angle=360];
\end{tikzpicture}
\end{document}

Best Answer

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[Tex/LaTex] Want to Draw circle with sector and segment

[Tex/LaTex] Draw circle with three colours in tikz

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