\begin{frame}
  \frametitle{Inverse Trigonometric: Examples}
    
  \begin{indentation}{-.7cm}{-1cm}  
  \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|}
    \hline 
    $\alpha$ & $0$ & $\frac{\pi}{6}$ & $\frac{\pi}{4}$ & $\frac{\pi}{3}$ & $\frac{\pi}{2}$ & $\frac{2\pi}{3}$ & $\frac{3\pi}{4}$ & $\frac{5\pi}{6}$ & $\pi$ & $\frac{3\pi}{2}$ & $2\pi$
    \\
    \hline 
    $\sin \alpha$ & $0$ & $\frac{1}{2}$ & $\frac{1}{\sqrt{2}}$ & $\frac{\sqrt{3}}{2}$ & $1$ & $\frac{\sqrt{3}}{2}$ & $\frac{1}{\sqrt{2}}$ & $\frac{1}{2}$ & $0$ & $-1$ & $0$   
    \\
    \hline 
    $\cos \alpha$ & $1$ & $\frac{\sqrt{3}}{2}$ & $\frac{1}{\sqrt{2}}$ & $\frac{1}{2}$ & $0$ & $-\frac{1}{2}$ & $-\frac{1}{\sqrt{2}}$ & $-\frac{\sqrt{3}}{2}$ & $-1$ & $0$ & $1$
    \\
    \hline 
  \end{tabular}
  \end{indentation}
  
  \begin{talign}
    \sin^{-1}(y) = x \quad&\iff\quad \sin(x) = y \text{ and } -\frac{\pi}{2} \le x \le \frac{\pi}{2}\\
    \cos^{-1}(y) = x \quad&\iff\quad \cos(x) = y \text{ and } 0 \le x \le \pi
  \end{talign}
  \vspace{-3ex}
  
  \begin{exampleblock}{}
    Evaluate the following:
    \begin{itemize}
      \item $\sin^{-1}(\frac{1}{2}) = \pause \frac{\pi}{6}$\pause
      \item $\tan(\arcsin(\frac{1}{3})) = \pause \frac{\sin(\arcsin(\frac{1}{3}))}{\cos(\arcsin(\frac{1}{3}))} =
        \mpause[6]{ \frac{\frac{1}{3}}{\frac{2}{3}\sqrt{2}} = }
        \mpause[7]{ \frac{1}{3} \cdot \frac{3}{2} \cdot \frac{1}{\sqrt{2}} = }
        \mpause[8]{ \frac{1}{2\sqrt{2}}}
        $
        \begin{center}
        \scalebox{.8}{
        \mpause[1]{%
        \begin{tikzpicture}[default,scale=1.1]
          \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:.65cm) {$\alpha$};
          \draw[dotted] (-1.2,0) -- (1.2,0);
          \draw[dotted] (0,-1.2) -- (0,1.2);
          
          \draw[<->] (0,-.1) -- node[below] {{\tiny radius $1$}} (1,-.1);
           
          \draw[dotted] (30:1cm) -- ({sqrt(3/4)},1.2);
          \draw[cgreen,<->] (0,1.2) -- node[above,inner sep=1mm] {$\cos \alpha$} ({sqrt(3/4)},1.2);
          \draw[dotted] (30:1cm) -- (1.2,1/2);
          \draw[cred,<->] (1.2,0) -- node[right,inner sep=1mm] {$\sin \alpha$} (1.2,1/2);
        \end{tikzpicture}
        }
        \hspace{1cm}
        \mpause[2]{%
        \begin{tikzpicture}[default,scale=2]
          \node[anchor=west] at (-.5,1) {Let $\alpha = \arcsin (\frac{1}{3})$, then};
          \draw (0,0) -- node[below,xshift=10mm] {\alert{$\cos \alpha = \mpause[3]{ \sqrt{1 - (\frac{1}{3})^2} =}  \mpause[4]{ \sqrt{\frac{8}{9} } = } \mpause[5]{ \frac{2}{3}\sqrt{2} }$}} (2,0) -- node[right] {$\sin \alpha = \frac{1}{3}$} ++(0,1) -- node[above] {$1$} (0,0);
          \draw[fill=clred!20] (0,0) to (26.5:1cm) arc (26.5:0:1cm) -- cycle;
          \draw[->] (.4cm,0) arc (0:26.5:.4cm);
          \node at (13:.65cm) {$\alpha$};
        \end{tikzpicture}
        }
        }
        \end{center}
    \end{itemize}
  \end{exampleblock}
\end{frame}