Tangentas

 \pgfmathsetmacro\myangle{0}
\xdef\angle{\myangle}
\begin{animateinline}[controls,autoplay,loop]{15}
\whiledo{\lengthtest{\angle pt<360pt}}{%
  \begin{tikzpicture}[scale=0.75]
    % fill circle and plot
    \path[use as bounding box] (-5.6,-4.7) rectangle (6.6,4.7);
    \ifthenelse{\lengthtest{\angle pt=90pt}}{}{
    \ifthenelse{\lengthtest{\angle pt=270pt}}{}{
    \fill[blue!50] plot[smooth,domain=0:1.5] (\x-3,{\x*tan(\angle)}) |- (0,0); %goes to; startangle:initialangle:radius; goes from
    \ifthenelse{\lengthtest{\angle pt<90pt}}{\fill[blue!50] plot[smooth,domain=0:\angle] (pi/180*\x,{1.5*tan(\x)}) |- (0,0);}{
    \fill[blue!50] plot[smooth,domain=0:85] (pi/180*\x,{1.5*tan(\x)}) |- (0,0);
     \ifthenelse{\lengthtest{\angle pt<270pt}}{\fill[blue!50] plot[smooth,domain=95:\angle] (pi/180*\x,{1.5*tan(\x)}) |- (9.5*pi/18,0);}{
     \fill[blue!50] plot[smooth,domain=100:265] (pi/180*\x,{1.5*tan(\x)}) |- (9.5*pi/18,0);
     \fill[blue!50] plot[smooth,domain=275:\angle] (pi/180*\x,{1.5*tan(\x)}) |- (27.5*pi/18,0);}}
    % draw connection
    \draw (-1.5,{1.5*tan(\angle)}) circle (3pt) -- (pi/180*\angle,{1.5*tan(\angle)}) circle (3pt);}}
    % draw axes an ticks
    \draw (-5.5,0) -- (7,0);
    \foreach \deg in {45,90,135,180,225,270,315,360}
      \draw (pi/180*\deg,2pt) -- (pi/180*\deg,-2pt) node[below] {$\deg^\circ$};
    \draw (0,-7.6) -- (0,7.6);
    \foreach \y in {-5,-4,-3,-2,-1,-0.5,0.5,1,2,3,4,5}
      \draw (2pt,1.5*\y) -- (-2pt,1.5*\y) node[left] {$\y$};
    %draw blue stick
    \draw[very thick, blue] (-3,0) +(\angle:1.5) -- (-3,0);
    % draw plot and circle outline
    \draw plot[smooth,domain=0:80] (pi/180*\x,{1.5*tan(\x)});
    \draw plot[smooth,domain=100:260] (pi/180*\x,{1.5*tan(\x)});
    \draw plot[smooth,domain=280:360] (pi/180*\x,{1.5*tan(\x)});
    \draw (-3,0) circle (1.5);%
   \pgfmathsetmacro\myangle{\angle+5.0} %myangle can't be used globally
   \xdef\angle{\myangle} %we copy it to global variable
   \end{tikzpicture}
   \ifthenelse{\lengthtest{\angle pt<360pt}}{\newframe}{
   \end{animateinline}
   }
}