\begin{frame}
  \frametitle{Inverse Trigonometric Functions}
  
  We are interested in inverse functions of:
  \medskip
  \begin{center}
  {\small $\sin x$}\quad\scalebox{.7}{
  \begin{tikzpicture}[default,baseline=0cm]
    \diagram{-3}{7}{-1.1}{1.3}{1}
    \begin{scope}[ultra thick]
    \alt<-3>{
    \draw[cred] plot[smooth,domain=-3:7,samples=300] (\x,{sin(\x*90)});
    }{
    \draw[cred,opacity=.2] plot[smooth,domain=-3:7,samples=300] (\x,{sin(\x*90)});
    \draw[cred] plot[smooth,domain=-1:1,samples=300] (\x,{sin(\x*90)});
    }
    \end{scope}
    \diagramannotatez
    \diagramannotatexx{-2/$-\pi$,-1/$-\frac{\pi}{2}$,1/$\frac{\pi}{2}$,2/$\pi$,3/$\frac{3\pi}{2}$,4/$2\pi$,5/$\frac{5\pi}{2}$,6/$3\pi$}
    \diagramannotatey{1,-1}
  \end{tikzpicture}\hspace{1cm}
  }
  \end{center}
  \begin{center}
  {\small $\cos x$}\quad\scalebox{.7}{
  \begin{tikzpicture}[default,baseline=0cm]
    \diagram{-3}{7}{-1.1}{1.3}{1}
    \begin{scope}[ultra thick]
    \alt<-4>{
    \draw[cgreen] plot[smooth,domain=-3:7,samples=300] (\x,{cos(\x*90)});
    }{
    \draw[cgreen,opacity=.2] plot[smooth,domain=-3:7,samples=300] (\x,{cos(\x*90)});
    \draw[cgreen] plot[smooth,domain=0:2,samples=300] (\x,{cos(\x*90)});
    }
    \end{scope}
    \diagramannotatez
    \diagramannotatexx{-2/$-\pi$,-1/$-\frac{\pi}{2}$,1/$\frac{\pi}{2}$,2/$\pi$,3/$\frac{3\pi}{2}$,4/$2\pi$,5/$\frac{5\pi}{2}$,6/$3\pi$}
    \diagramannotatey{1,-1}
  \end{tikzpicture}\hspace{1cm}
  }
  \end{center}
  \pause\medskip
  Problem: \alert{these functions are not one-to-one!}
  \pause\medskip
  
  Solution: we restrict their domain
  \begin{itemize}
  \pause
    \item for $\sin$ we restrict the domain to \alert{$[-\frac{\pi}{2},\frac{\pi}{2}]$}  
  \pause
    \item for $\cos$ we restrict the domain to \alert{$[0,\pi]$}  
  \end{itemize}
  \vspace{10cm}

\end{frame}