\begin{frame}
  \frametitle{Angles}

  Angles can be measured in \emph{degrees} ($\textdegree$) or in \emph{radians} ($\rad$):
  \begin{itemize}
    \pause
    \item $180\textdegree = \pi\rad$
    \item<3-> $360\textdegree = 2\pi\rad$ is a full revolution
  \end{itemize}
  \begin{center}
    \begin{tikzpicture}[default,nodes={scale=.8}]
      \draw (0,0) circle (1cm);
      \draw[fill=clred!20] (0,0) to (30:1cm) arc (30:0:1cm) -- cycle;
      \draw[->] (.4cm,0) arc (0:30:.4cm);
      \node at (15:.6cm) {$\alpha$};
      \draw[dotted] (180:1.2) -- node [at end,right] {$0\textdegree = 0\rad$} node [at start,left] {$180\textdegree = \pi\rad$} (0:1.2);
      \pause\pause\pause\pause\pause\pause
      \draw[dotted] (180+90:1.2) -- node [at end,above,align=center] {$90\textdegree = $\\$\mpause[1]{\pi/2 \rad}$} node [at start,below] {$\mpause[2]{270\textdegree =} \mpause[3]{3\pi/2 \rad}$} (90:1.2);
      \pause\pause\pause\pause
      \draw[dotted] (180+30:0) -- node [at end,right] {$30\textdegree = \mpause[1]{\pi/6 \rad}$} (30:1.45);
      \pause\pause
      \draw[dotted] (180+45:0) -- node [at end,right] {$45\textdegree = \mpause[1]{\pi/4 \rad}$} (45:1.6);
      \pause\pause
      \draw[dotted] (180+60:0) -- node [at end,right] {$60\textdegree = \mpause[1]{\pi/3 \rad}$} (60:1.8);
      \pause\pause
      \draw[dotted] (180+60:0) -- node [at end,left] {$120\textdegree = 2\pi/3 \rad$} (90+30:1.8);
      \draw[dotted] (180+45:0) -- node [at end,left] {$135\textdegree = 3\pi/4 \rad$} (90+45:1.6);
      \draw[dotted] (180+30:0) -- node [at end,left] {$150\textdegree = 5\pi/6 \rad$} (90+60:1.45);
    \end{tikzpicture}
  \end{center}
  \setcounter{beamerpauses}{4}
  \mpause[0]{
  From $180\textdegree = \pi\rad$ we conclude
  \begin{align*}
    1\textdegree = \frac{\pi}{180} \rad 
    && \mpause[1]{ \text{ and } } &&
    \mpause[1]{ x\textdegree = \frac{x\cdot\pi}{180} \rad  } 
    \\[1ex]
    \mpause[2]{1\rad = \left( \frac{180}{\pi} \right)\textdegree}
    && \mpause[3]{ \text{ and } } &&
    \mpause[3]{ x\rad = \left( \frac{x\cdot 180}{\pi} \right)\textdegree }
  \end{align*}
  }
\end{frame}