\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}