\begin{frame} \frametitle{Trigonometric Functions: Inverse Cotangent} \begin{minipage}{.4\textwidth} \begin{center} \scalebox{.7}{ \begin{tikzpicture}[default,baseline=0cm] \diagram{-.5}{2.3}{-3}{3}{1} \begin{scope}[ultra thick] \draw[cblue] plot[smooth,domain=0.2:1.8,samples=300] (\x,{cot(\x*90)}); \end{scope} \diagramannotatez \diagramannotatexx{1/$\frac{\pi}{2}$,2/$\pi$} \diagramannotatey{1,-1} \begin{scope}[cred,dashed] \draw (0,-3) -- (0,3); \draw (2,-3) -- (2,3); \end{scope} \end{tikzpicture} }\\[.5ex] $\cot x$ restricted to $(0,\pi)$ \end{center} \end{minipage}\pause \begin{minipage}{.59\textwidth} \begin{center} \scalebox{.7}{ \begin{tikzpicture}[default,baseline=0cm] \diagram{-3}{3}{-.5}{2.3}{1} \begin{scope}[ultra thick] \draw[cgreen] plot[smooth,domain=0.2:1.8,samples=300] ({cot(\x*90)},\x); \end{scope} \diagramannotatez \diagramannotatex{1,-1} \diagramannotateyy{1/$\frac{\pi}{2}$,2/$\pi$} \end{tikzpicture} }\\[.5ex] $\cot^{-1} x$ \end{center} \end{minipage} \pause\medskip \begin{block}{} \begin{malign} \cot^{-1} y = x \;\;\iff\;\; \cot x = y \text{ and } 0 < x < \pi \end{malign} \end{block} \pause The function $\cot^{-1}$ has domain \pause $(-\infty,\infty)$ and range \pause$(0,\pi)$. \end{frame}