A unit circle with automation (based on http://mathdancing.wordpress.com/2013/10/22/tikz-unit-circle/)

unitcircle.tex

\documentclass[border=4pt]{standalone}
\usepackage{amsmath,mathpazo,gensymb}
\usepackage{tikz}

\makeatletter
\pgfarrowsdeclare{centre*}{centre*}
{
  \pgfarrowsleftextend{+-.5\pgflinewidth}
  \pgfutil@tempdima=0.4pt%
  \advance\pgfutil@tempdima by.2\pgflinewidth%
  \pgfarrowsrightextend{4.5\pgfutil@tempdima}
}
{
  \pgfutil@tempdima=0.4pt%
  \advance\pgfutil@tempdima by.2\pgflinewidth%
  \pgfsetdash{}{+0pt}
  \pgfpathcircle{\pgfqpoint{4.5\pgfutil@tempdima}{0bp}}{4.5\pgfutil@tempdima}
  \pgfusepathqfillstroke
}
\makeatother

\newcommand\unitcirclepts{%
  {%
    {},%
    {%
      {"(\noexpand\frac{\noexpand\sqrt{3}}{2},\noexpand\frac12)"},%
      {"(-\noexpand\frac12,\noexpand\frac{\noexpand\sqrt{3}}{2})"},%
      {"(-\noexpand\frac{\noexpand\sqrt{3}}{2},-\noexpand\frac12)"},%
      {"(\noexpand\frac12,-\noexpand\frac{\noexpand\sqrt{3}}{2})"},%
    },%
    {
      {"(\noexpand\frac{\noexpand\sqrt{2}}{2},\noexpand\frac{\noexpand\sqrt{2}}{2})"},%
      {"(-\noexpand\frac{\noexpand\sqrt{2}}{2},\noexpand\frac{\noexpand\sqrt{2}}{2})"},%
      {"(-\noexpand\frac{\noexpand\sqrt{2}}{2},-\noexpand\frac{\noexpand\sqrt{2}}{2})"},%
      {"(\noexpand\frac{\noexpand\sqrt{2}}{2},-\noexpand\frac{\noexpand\sqrt{2}}{2})"},%
    },%
    {%
      {"(\noexpand\frac12,\noexpand\frac{\noexpand\sqrt{3}}{2})"},%
      {"(-\noexpand\frac{\noexpand\sqrt{3}}{2},\noexpand\frac12)"},%
      {"(-\noexpand\frac12,-\noexpand\frac{\noexpand\sqrt{3}}{2})"},%
      {"(\noexpand\frac{\noexpand\sqrt{3}}{2},-\noexpand\frac12)"},%
    },%
    {},%
    {%
      {"(0,1)"},%
      {"(-1,0)"},%
      {"(0,-1)"},%
      {"(1,0)"},%
    },%
  }
}


\begin{document}

\begin{tikzpicture} [>=stealth, scale=2.5,
% Toggle commenting on the next four lines for the completed unit circle:
angle/.style={node contents={\(\label\)}},
point/.style={node contents={\(\pgfmathparse{\unitcirclepts[\nang-1][\ang]}\pgfmathresult\)};
  },
%angle/.style={minimum height=1cm, minimum width=1cm,draw,node contents={}},
%point/.style={node contents={}},
]
    \useasboundingbox (-3.6,-3.6) rectangle (3.6,3.6);
    \draw [thick] (0,0) circle[radius=3cm];
    \draw [thick] (-3.3,0) -- (-3,0);
    \draw [thick] (3.3,0) -- (3,0);
    \draw [thick] (0,-3.3) -- (0,-3);
    \draw [thick] (0,3.3) -- (0,3);
\foreach \nang/\pos in {2/.75,3/.5,4/.75,6/.5}
{
  \foreach \ang/\offset in {0/above right,1/above left,2/below left,3/below right}
  {
    \pgfmathtruncatemacro\angle{\nang + 6*\ang}
    \pgfmathsetmacro\numerator{\angle/gcd(\angle,12) == 1 ? "" : int(\angle/gcd(\angle,12))}
    \pgfmathtruncatemacro\denominator{12/gcd(\angle,12)}
    \pgfmathsetmacro\label{\denominator == 1 ? "\numerator \noexpand\pi" : "\noexpand\frac{\numerator \noexpand\pi}{\denominator}"}
    \node[font=\tiny] (deg) at (15*\angle:1)  {\(\pgfmathparse{int(15*\angle)}\pgfmathresult\degree\)};
    \node[name=rad,at=(15*\angle:3*\pos),angle];
    \draw[-centre*] (0,0) -- (deg) -- (rad) -- (15*\angle:3) node[\offset,point];
}
}
\end{tikzpicture}
\end{document}