After getting several requests from IRL folks for my unit circle, I figured I’d make it a post here. (Seriously, when I get tackled in the hall for a unit circle handout, it means that there’s a real need out there, even though I would have figured that there’s enough unit circles in the world.)

### Blank unit circle

blank unit circle as pdf

latex code on sharelatex.

latex code:

\documentclass[border=4pt]{standalone}
\usepackage{amsmath,mathpazo,gensymb}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture} [>=stealth, scale=2.5,
% Toggle commenting on the next four lines for the completed unit circle:
angle/.style={draw,text=white,fill=white,minimum height=1cm, minimum width=1cm},
point/.style={white},
%angle/.style={fill=white},
%point/.style={},
]
\draw [white] (-3.6,-3.6) rectangle (3.6,3.6);
\draw [thick,fill=white] (0,0) circle (3cm);
\draw [thick, ] (-3.3,0) -- (3.3,0);
\draw [thick, ] (0,-3.3) -- (0,3.3);
\draw (0,0) -- node [angle] {$\frac{\pi}{2}$} (90:3)
node[point, above right] {$ \left(0,1\right) $};
\draw (0,0) -- node [angle] {\footnotesize{$\pi$}} (180:3)
node[point, above left] {$ \left(-1,0\right) $};
\draw (0,0) -- node [angle] {$\frac{3\pi}{2}$} (270:3)
node[point, below right] {$ \left(0,-1\right) $};
\draw (0,0) -- node [angle] {\footnotesize{$2\pi$}} (0:3)
node[point, above right] {$ \left(1,0\right) $};
\draw (0,0) -- node [angle] {$\frac{\pi}{4}$} (45:3)
node [point, above right] {$ \left( \frac{\sqrt2}{2} , \frac{\sqrt2}{2} \right) $};
\draw (0,0) -- node [angle] {$\frac{3\pi}{4}$} (135:3)
node [point, above left] {$ \left( -\frac{\sqrt2}{2} , \frac{\sqrt2}{2} \right) $};
\draw (0,0) -- node [angle] {$\frac{5\pi}{4}$} (225:3)
node [point, below left] {$ \left( -\frac{\sqrt2}{2} , -\frac{\sqrt2}{2} \right) $};
\draw (0,0) -- node [angle] {$\frac{7\pi}{4}$} (315:3)
node [point, below right] {$ \left( \frac{\sqrt2}{2} , -\frac{\sqrt2}{2} \right) $};
\draw (0,0) -- node [near end, angle] {$\frac{\pi}{6}$} (30:3)
node [point, above right] {$ \left( \frac{\sqrt3}{2} , \frac{1}{2} \right) $};
\draw (0,0) -- node [near end, angle] {$\frac{\pi}{3}$} (60:3)
node [point, above right] {$ \left( \frac{1}{2} , \frac{\sqrt3}{2} \right) $};
\draw (0,0) -- node [near end, angle] {$\frac{2\pi}{3}$} (120:3)
node [point, above left] {$ \left( -\frac{1}{2} , \frac{\sqrt3}{2} \right) $};
\draw (0,0) -- node [near end, angle] {$\frac{5\pi}{6}$} (150:3)
node [point, above left] {$ \left(- \frac{\sqrt3}{2} , \frac{1}{2} \right) $};
\draw (0,0) -- node [near end, angle] {$\frac{7\pi}{6}$} (210:3)
node [point, below left] {$ \left(- \frac{\sqrt3}{2} , -\frac{1}{2} \right) $};
\draw (0,0) -- node [near end, angle] {$\frac{4\pi}{3}$} (240:3)
node [point, below left] {$ \left( -\frac{1}{2} , -\frac{\sqrt3}{2} \right) $};
\draw (0,0) -- node [near end, angle] {$\frac{5\pi}{3}$} (300:3)
node [point, below right] {$ \left( \frac{1}{2} , -\frac{\sqrt3}{2} \right) $};
\draw (0,0) -- node [near end, angle] {$\frac{11\pi}{6}$} (330:3)
node [point, below right] {$ \left( \frac{\sqrt3}{2} , -\frac{1}{2} \right) $};
\foreach \n in {1,2,3,4}
\foreach \t in {0,30,45,60}
\fill (\n*90+\t:3) circle (0.03cm);
\foreach \t in {30,45,60, 120,135,150, 210,225,240, 300,315,330}
\node [font=\tiny, fill=white,inner sep=1pt] at (\t:.75) {$ \t\degree $};
\end{tikzpicture}
\end{document}

### Completed Unit Circle

completed unit circle as pdf

latex code on sharelatex

Get the latex code here.

\documentclass[border=4pt]{standalone}
\usepackage{amsmath,mathpazo,gensymb}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture} [>=stealth, scale=2.5,
% Toggle commenting on the next four lines for the completed unit circle:
%angle/.style={draw,text=white,fill=white,minimum height=1cm, minimum width=1cm},
%point/.style={white},
angle/.style={fill=white},
point/.style={},
]
\draw [white] (-3.6,-3.6) rectangle (3.6,3.6);
\draw [thick,fill=white] (0,0) circle (3cm);
\draw [thick, ] (-3.3,0) -- (3.3,0);
\draw [thick, ] (0,-3.3) -- (0,3.3);
\draw (0,0) -- node [angle] {$\frac{\pi}{2}$} (90:3)
node[point, above right] {$ \left(0,1\right) $};
\draw (0,0) -- node [angle] {\footnotesize{$\pi$}} (180:3)
node[point, above left] {$ \left(-1,0\right) $};
\draw (0,0) -- node [angle] {$\frac{3\pi}{2}$} (270:3)
node[point, below right] {$ \left(0,-1\right) $};
\draw (0,0) -- node [angle] {\footnotesize{$2\pi$}} (0:3)
node[point, above right] {$ \left(1,0\right) $};
\draw (0,0) -- node [angle] {$\frac{\pi}{4}$} (45:3)
node [point, above right] {$ \left( \frac{\sqrt2}{2} , \frac{\sqrt2}{2} \right) $};
\draw (0,0) -- node [angle] {$\frac{3\pi}{4}$} (135:3)
node [point, above left] {$ \left( -\frac{\sqrt2}{2} , \frac{\sqrt2}{2} \right) $};
\draw (0,0) -- node [angle] {$\frac{5\pi}{4}$} (225:3)
node [point, below left] {$ \left( -\frac{\sqrt2}{2} , -\frac{\sqrt2}{2} \right) $};
\draw (0,0) -- node [angle] {$\frac{7\pi}{4}$} (315:3)
node [point, below right] {$ \left( \frac{\sqrt2}{2} , -\frac{\sqrt2}{2} \right) $};
\draw (0,0) -- node [near end, angle] {$\frac{\pi}{6}$} (30:3)
node [point, above right] {$ \left( \frac{\sqrt3}{2} , \frac{1}{2} \right) $};
\draw (0,0) -- node [near end, angle] {$\frac{\pi}{3}$} (60:3)
node [point, above right] {$ \left( \frac{1}{2} , \frac{\sqrt3}{2} \right) $};
\draw (0,0) -- node [near end, angle] {$\frac{2\pi}{3}$} (120:3)
node [point, above left] {$ \left( -\frac{1}{2} , \frac{\sqrt3}{2} \right) $};
\draw (0,0) -- node [near end, angle] {$\frac{5\pi}{6}$} (150:3)
node [point, above left] {$ \left(- \frac{\sqrt3}{2} , \frac{1}{2} \right) $};
\draw (0,0) -- node [near end, angle] {$\frac{7\pi}{6}$} (210:3)
node [point, below left] {$ \left(- \frac{\sqrt3}{2} , -\frac{1}{2} \right) $};
\draw (0,0) -- node [near end, angle] {$\frac{4\pi}{3}$} (240:3)
node [point, below left] {$ \left( -\frac{1}{2} , -\frac{\sqrt3}{2} \right) $};
\draw (0,0) -- node [near end, angle] {$\frac{5\pi}{3}$} (300:3)
node [point, below right] {$ \left( \frac{1}{2} , -\frac{\sqrt3}{2} \right) $};
\draw (0,0) -- node [near end, angle] {$\frac{11\pi}{6}$} (330:3)
node [point, below right] {$ \left( \frac{\sqrt3}{2} , -\frac{1}{2} \right) $};
\foreach \n in {1,2,3,4}
\foreach \t in {0,30,45,60}
\fill (\n*90+\t:3) circle (0.03cm);
% \foreach \t in {30,45,60, 120,135,150, 210,225,240, 300,315,330}
% \node [font=\tiny, fill=white,inner sep=1pt] at (\t:.75) {$ \t\degree $};
\end{tikzpicture}
\end{document}

As a sidenote, ~~I am really pleased that WordPress’s code tags seem to have improved greatly since the last time I tried to use them.~~ Never mind. It’s better than it was, but it’s changing < and > to `<`

and `>`

. And it took the <-> away entirely. For the actual code, you can check out the versions on sharelatex, as well as this document, that has them both embedded in it.