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\begin{frame}
  \frametitle{Angles: Radian}

  \begin{alertblock}{}
    In Calculus, the default measurement for angles is \emph{radian}.
  \end{alertblock}
  \pause\bigskip  
  
  Historical note on radians:
  \pause
  \begin{itemize}
    \item consider a circle with radius $1$, and
    \item<4-> an sector of this circle with angle $\alpha$ (radians)
  \end{itemize}
  \begin{center}\hspace{2cm}
    \begin{tikzpicture}[default,scale=2]
      \draw (0,0) circle (1cm);
      \draw[<->] (0,0) -- node[right] {radius $1$} (270:1cm);
      \pause

      \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) {$\alpha$};
      \pause

      \draw[cred,line width=1mm] (60:1cm) arc (60:0:1cm);
      \pause
      \node[cred,anchor=west] at (30:1.05cm) {arc has length $\alpha$};
    \end{tikzpicture}
  \end{center}
  \mpause[0]{
  Then the arc of the sector has length $\alpha$ (equal to the angle).
  }
  \vspace{10cm}
\end{frame}