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. (You don’t need a ShareLaTeX account to access these links, but if you’d like to sign up for one, please use this referral link, which lets me earn points toward referral bonuses. Thanks!)