\documentclass [12pt] {article}

\usepackage{graphicx}
\usepackage{amssymb}
\usepackage{epstopdf}
\usepackage{amsmath}
\DeclareGraphicsRule{.tif}{png}{.png}{`convert #1 `dirname #1`/`basename #1 .tif`.png}

\newenvironment{packed_itemize}{
\begin{itemize}
  \setlength{\itemsep}{1pt}
  \setlength{\parskip}{0pt}
  \setlength{\parsep}{0pt}
}{\end{itemize}}

\topmargin 0pt
\advance \topmargin by -\headheight
\advance \topmargin by -\headsep
\textheight 8.9in
\oddsidemargin 0pt
\evensidemargin \oddsidemargin
\marginparwidth 0.5in
\textwidth 6.5in

\begin{document}

\begin{center}
\Huge{Trigonometric Integration}
\end{center}


While working in a group make sure you:
\begin{packed_itemize}
\item Expect to make mistakes but be sure to reflect/learn from them!
\item Are civil and are aware of your impact on others.
\item Assume and engage with the strongest argument while assuming best intent.
\end{packed_itemize}


\begin{enumerate}
\item Find:

%$\displaystyle{\int \cos(x)\sin^2(x) \,dx}$

 %$\displaystyle{\int \cos^2(x)\sin^3(x)\,dx}$ \hspace{2.2in} 
 $\displaystyle{\int \cos^3(x)\sin^4(x) \,dx}$



\vfill
 %$\displaystyle{\int \cos^4(x)\sin(x) \,dx}$ \hspace{2.2in} 


\vfill



\newpage
\item Recall the Pythagorean Theorem (the trigonometric version of $a^2+b^2=c^2$) $$\sin^2(x)+\cos^2(x)=1.$$ \noindent \begin{enumerate}
\item Use the above theorem to write down a relationship between $\tan(x)$ \& $\sec(x)$.
\vspace{.3in}
\item Use the above theorem to write down a relationship between $\cot(x)$ and $\csc(x)$.
\vspace{.3in}
\end{enumerate}

\item Consider the strategy we developed to integrate expressions with sines and cosines.  Try and develop a parallel strategy when working the following examples:


 $\displaystyle{\int \tan^6(y)\sec^4(y)\,dy}$ \hspace{2.2in} $\displaystyle{\int \tan^4(x)\,dx}$

\vfill
 $\displaystyle{\int \tan(\theta)\sec^4(\theta)\,d\theta}$
 \vfill

\item Record your strategy by finishing the following sentences:  Given $\int \tan^m(x)\sec^n(x)\,dx$,
\begin{enumerate}
\item if $n$ is even...
\vspace{.4in}
\item if $m$ is odd...
\vspace{.4in} 
\end{enumerate}

\end{enumerate}

\end{document}
