\frametitle{Angles: Radian}

    In Calculus, the default measurement for angles is \emph{radian}.
  Historical note on radians:
    \item consider a circle with radius $1$, and
    \item<4-> an sector of this circle with angle $\alpha$ (radians)
      \draw (0,0) circle (1cm);
      \draw[<->] (0,0) -- node[right] {radius $1$} (270:1cm);

      \draw[fill=clblue!20] (0,0) to (60:1cm) arc (60:0:1cm) -- cycle;
      \draw[->] (.4cm,0) arc (0:60:.4cm);
      \node at (30:.55cm) {$\alpha$};

      \draw[cred,line width=1mm] (60:1cm) arc (60:0:1cm);
      \node[cred,anchor=west] at (30:1.05cm) {arc has length $\alpha$};
  Then the arc of the sector has length $\alpha$ (equal to the angle).