\begin{frame}
  \frametitle{Trigonometric Functions: Tangent and Cotangent}
  
  \begin{block}{}
    The tangent and cotangent are defined as:\vspace{-1ex}
    \begin{talign}
      \tan \alpha = \frac{\sin \alpha}{\cos \alpha}
      && \cot \alpha = \frac{\cos \alpha}{\sin \alpha}
    \end{talign}
  \end{block}
  \medskip
  
  \begin{indentation}{-.5cm}{-1cm}
  \scalebox{.7}{
  \begin{tikzpicture}[default,baseline=0cm]
    \diagram{-3.5}{3.5}{-3}{3}{1}
    \begin{scope}[ultra thick]
    \draw[cgreen] plot[smooth,domain=-3.5:-3.2,samples=300] (\x,{tan(\x*90)});
    \draw[cgreen] plot[smooth,domain=-2.8:-1.2,samples=300] (\x,{tan(\x*90)});
    \draw[cgreen] plot[smooth,domain=-0.8:0.8,samples=300] (\x,{tan(\x*90)});
    \draw[cgreen] plot[smooth,domain=1.2:2.8,samples=300] (\x,{tan(\x*90)});
    \draw[cgreen] plot[smooth,domain=3.2:3.5,samples=300] (\x,{tan(\x*90)});
    \end{scope}
    \diagramannotatez
    \diagramannotatexx{-3/$-\frac{3\pi}{2}$,-2/$-\pi$,-1/$-\frac{\pi}{2}$,1/$\frac{\pi}{2}$,2/$\pi$,3/$\frac{3\pi}{2}$}
    \diagramannotatey{1,-1}
    
    \begin{scope}[cred,dashed]
    \draw (-1,-3) -- (-1,3);
    \draw (-3,-3) -- (-3,3);
    \draw (1,-3) -- (1,3);
    \draw (3,-3) -- (3,3);
    \end{scope}
  \end{tikzpicture}
  }\quad
  \scalebox{.7}{
  \begin{tikzpicture}[default,baseline=0cm]
    \diagram{-3.5}{3.5}{-3}{3}{1}
    \begin{scope}[ultra thick]
    \draw[cblue] plot[smooth,domain=-3.5:-2.2,samples=300] (\x,{cot(\x*90)});
    \draw[cblue] plot[smooth,domain=-1.8:-.2,samples=300] (\x,{cot(\x*90)});
    \draw[cblue] plot[smooth,domain=0.2:1.8,samples=300] (\x,{cot(\x*90)});
    \draw[cblue] plot[smooth,domain=2.2:3.5,samples=300] (\x,{cot(\x*90)});
    \end{scope}
    \diagramannotatez
    \diagramannotatexx{-3/$-\frac{3\pi}{2}$,-2/$-\pi$,-1/$-\frac{\pi}{2}$,1/$\frac{\pi}{2}$,2/$\pi$,3/$\frac{3\pi}{2}$}
    \diagramannotatey{1,-1}

    \begin{scope}[cred,dashed]
    \draw (0,-3) -- (0,3);
    \draw (-2,-3) -- (-2,3);
    \draw (2,-3) -- (2,3);
    \end{scope}
  \end{tikzpicture}
  }
  \end{indentation}
  
  \pause
  \begin{itemize}
    \item range = \pause$(-\infty,\infty)$
  \pause
    \item domain of $\tan$ = \pause $\{x \mid \cos x \ne 0\}$ = \pause $\mathbb{R} \setminus \{\pi/2 + z\pi \mid z\in \mathbb{Z}\}$
  \pause
    \item domain of $\cot$ = \pause $\{x \mid \sin x \ne 0\}$ = \pause $\mathbb{R} \setminus \{z\pi \mid z\in \mathbb{Z}\}$
  \end{itemize}
\end{frame}