Drawing angles greater than 360º inTikZ

Question

When teaching trigonometry, sometimes it is useful to represent angles greater than 360º with some kind of "spiral arc". For example:

angles

the angle of -440º in the figure.

My question is:

How can I do this in nicely TikZ?

I can do it by using several consecutive arcs, but I wish to know if is there a more elegant solution to this.

Yes, it's not an exact duplicate. But the general approach works here too: Try \draw [domain=0:10,variable=\t,smooth,samples=75] plot ({\t r}: {0.05*\t+0.1}); — Jake, Jun 18 '12 at 17:39
BTW, I believe that the -440 angle is incorrectly labelled, it should be 440 degrees (not minus). — Peter Grill, Jun 18 '12 at 18:22

Alain Matthes · Accepted Answer · 2012-06-18T20:53:24.647

27

 \documentclass[11pt]{scrartcl}
 \usepackage{tikz}
 \usetikzlibrary{arrows}

 \begin{document} 

 \newcommand\bigangle[2][]{% 
    \draw[->,domain=0:#2,variable=\t,samples=200,>=latex,#1]
      plot ({(\t+#2)*cos(\t)/(#2)},
           {(\t+#2)*sin(\t)/(#2)}) node[right=.5cm] {$#2^\circ$}
        ;}

 \begin{tikzpicture}
 \draw [thick] ( 0,0) -- (3,0);
 \draw [thick] ( 0,0) -- (0,3); 
 \draw [red,thick] ( 0,0) -- (400:3); 
 \bigangle[blue,dashed]{400}      
 \end{tikzpicture}
 \end{document}

enter image description here

edited Jun 18 '12 at 20:53

answered Jun 18 '12 at 20:45

Alain Matthes

95,075

This is exactly what I want. – leo Jun 18 '12 at 21:19
Incredible, good math skills to achieve the desired output. – azetina Jul 03 '12 at 19:52
The command works great for angles grater than 360. But it looks weird when we pass an angle a with 0 < abs(a) < 360. So far I've managed to fix it by using a conditional construct via the ifthen package. Is it possible to fix this without using any extra package? – leo Sep 04 '13 at 16:04

score 14 · Answer 2 · edited Jun 10 '20 at 12:32

Jake's method is probably simpler, but here I have adapted the standard parametric equation for a spiral and added an offset so that the spiral does not start at the origin to yield:

enter image description here

Notes:

The 440 in the denominator is to normalize the graph so that the arc ends at a y=1.
Polar equations should yield similar results with simpler equations.
There is something wrong with the brown line (even though it is in the correct spot) as it is not ending where I think it should, but this is not related to generating the spiral.

Code:

\documentclass{article}
\usepackage{pgfplots}
\newcommand{\Offset}{360}%
\begin{document}
\begin{tikzpicture}
\begin{axis}[xmin=-2.5,xmax=2.5,ymin=-2.5,ymax=2.5, axis lines=center]
    \addplot[blue,densely dashed,domain=0:440,samples=200,-latex] 
        ({(x+\Offset)cos(x+\Offset)/(440+\Offset)},
         {(x+\Offset)*sin(x+\Offset)/(440+\Offset)});
% Show the 440 degree angle
\pgfmathsetmacro{\XValue}{1.0}%
\pgfmathsetmacro{\YValue}{\XValue*tan(440)}%
\draw [brown, thick] (axis cs: 0,0) -- (axis cs: \XValue,\YValue);

\end{axis}
\end{tikzpicture}
\end{document}

Drawing angles greater than 360º inTikZ

2 Answers2

Notes:

Code:

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