anim.tex

\documentclass[tikz]{standalone}
\usepackage{tikz}
\begin{document}
\foreach \angle in {0,10,...,360}
{
  \begin{tikzpicture}
    % fill circle and plot
    \fill[blue!50] (-1,0) arc (0:\angle:1) -- (-2,0) -- cycle;
    \fill[blue!50] plot[smooth,domain=0:\angle] (pi/180*\x,{sin(\x)}) |- (0,0);
    % draw connection
    \draw (-2,0) +(\angle:1) circle (2pt) -- (pi/180*\angle,{sin(\angle)}) circle (2pt);
    % draw axes an ticks
    \draw (-3.5,0) -- (7,0);
    \foreach \deg in {90, 180, 270, 360}
      \draw (pi/180*\deg,2pt) -- (pi/180*\deg,-2pt) node[below] {$\deg^\circ$};
    \draw (0,-1.2) -- (0,1.2);
    \foreach \y in {-1,-0.5,0.5,1}
      \draw (2pt,\y) -- (-2pt,\y) node[left] {$\y$};
    % draw plot and circle outline
    \draw plot[smooth,domain=0:360] (pi/180*\x,{sin(\x)});
    \draw (-2,0) circle (1);
  \end{tikzpicture}
}
\end{document}

%convert -density 300 -delay 8 -loop 0 -background white -alpha remove anim.pdf anim.gif