\documentclass[12pt,letterpaper]{article}
\usepackage[latin1]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{hyperref}
\usepackage{paralist}
\usepackage{gensymb}
\usepackage[all=normal,margins]{savetrees}
\begin{document}
\setlength{\plitemsep}{12ex}
\newtheorem{notation}{Notation}
\begin{center}
Problems PreCal 1508 PLTL Workshop, November 23, 2011\\
PLs: Alex Knaust, Edith Mejia. Lecturer: Yi-Yu Liao\\

\end{center}
Please do the problems that you feel will help your group the most first (you don't have to do them in order). All handouts are available at \url{http://alex.knaust.info/pltlfall2011/}

\begin{enumerate}
\item Give a triple angle formula for $\sin$, $\cos$ and $\tan$ (so that you can find i.e. $\sin{3\theta}$ if you only know $\sin{\theta}$)

\item Find the exact solutions to the equation in the interval $[0, 2\pi)$
\begin{enumerate}
	\item $\sin{2x} - \sin{x} = 0$
	\item $4\sin{x}\cos{x} = 1$
	\item $(\sin{(2x)} + \cos{(2x)})^2 = 1$
	\item $\frac{1}{2}\sec{x} - 1 = 0$
	\item $\tan^2{u} - 6 = 5\tan{u}$
\end{enumerate}

\item Use the power-reducing formulas to rewrite the following as $\cos$ terms of degree one.
\begin{enumerate}
 \item $\cos^4{x}$
 \item $\tan^2{(2x)}\cos^4{(2x)}$
\end{enumerate}

\item Find the following values exactly
\begin{enumerate}
\item $\sin{\left(\frac{\pi}{4} + \frac{\pi}{3}\right)}$
\item $\cos{\left(\frac{\pi}{12}\right)}$
\end{enumerate}

\item Write the following trigonometric expressions as algebraic expressions
\begin{enumerate}
\item $\sin(\arcsin{x} + \arccos{x})$
\item $\cos(\arccos{x} + \arcsin{x})$
\end{enumerate}

\item Use the sum and difference formulae for $\sin$ and $\cos$ to show
\[\tan{(\alpha \pm \beta)} = \frac{\tan{\alpha} \pm \tan{\beta}}{1 \mp \tan{\alpha}\tan{\beta}}\]

\item I'm trying to catch a turkey for my thanksgiving dinner, and have trapped it in a narrow alley. The turkey flies between the two walls at (a fixed height) in a sine wave as follows
\[y = \sin{\frac{1}{3}x - {\pi}{4}}\]
(Think of the $x$ axis as lying parallel to the alley and the $y$ perpendicular). There are three windows at different distances from the beginning of the alley on the left side (positive $y$), which one should my sister open if she wants the turkey to fly in?\\
\begin{inparaenum}
\item $\frac{33\pi}{4}\quad\quad\quad$
\item $\frac{5\pi}{4}\quad\quad\quad$
\item $\frac{17\pi}{3}$
\end{inparaenum}
\begin{center}
Happy Thanksgiving!
\end{center}

\end{enumerate} %final end/enumerate
\end{document}
