# Drawing angles greater than 360º inTikZ

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

• spiral spring in tikz might be of interest here. – Jake Jun 18 '12 at 17:28
• Notice that the spiral here do not start at its center – leo Jun 18 '12 at 17:33
• 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
• @PeterGrill you are absolutely right! thanks for point that – leo Jun 18 '12 at 19:30

## 2 Answers

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

\begin{document}

\newcommand\bigangle[]{%
\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}  • This is exactly what I want. – leo Jun 18 '12 at 21:19
• Incredible, good math skills to achieve the desired output. – azetina Jul 3 '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 4 '13 at 16:04

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: ## 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}