\documentclass[12pt,fleqn]{article}
\setlength{\topmargin}{-.25in}
\setlength{\oddsidemargin}{-.3in}
\setlength{\textheight}{9in}
\setlength{\textwidth}{7.2in}


\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amsthm}
\usepackage{amstext}
\usepackage{amssymb}


\newcommand{\ra}{\rightarrow}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\E}{\mathbb{E}}

\newtheorem{definition}{Definition}
\newtheorem{formula}[definition]{Formula}

\begin{document}

\begin{center}
\textbf{Review for Test 1 - February 27, 2002}
\end{center}

\begin{enumerate}
\item  The chapter summary and review on pages 440-442 looks quite good as a summary.
\item  Trig functions.  We have thought about these in a couple different ways.
	\begin{enumerate}
	\item  For acute angles ($0 < \theta < 90^\circ$ or $0 < \theta < \pi/2$), 
		we used an acute triangle and talked about ratios of the sides of the triangle.
		This is the SOHCAHTOA stuff in section 5.1.
	\item  For other angles, we drew the angle on the $xy$-plane (with initial ray on the positive $x$-axis)
		and then used ratios of the $x$ and $y$-coordianates (this was in section 5.3).
	\item  Also for any angle, we drew the unit circle (circle with radius 1, centered at the origin).
		We then drew the angle with initial ray on the positive $x$-axis.
		We then looked at where the second ray of the angle hit the unit circle.
		This intersection point gave us the trig functions of the angle (section 5.5).
	\end{enumerate}
\item  Applications of trig functions and triangles:
	\begin{enumerate}
	\item  Using trig, we can ``solve'' any right triangle (and many triangles that aren't right).  (What is a right triangle?)
		See section 5.2 - you should be able to do any of the problems in that section.
	\end{enumerate}
\item  Radians.  We can measure angles using degrees or radians (section 5.4).
	\begin{enumerate}
	\item  Converting between degrees and radians (see the handout on unit conversions as well).
	\item  Arc length - what is the relationship between the angle, the radius of the circle and the length of the arc?
	\item  Angular speed - what is the relationship between angular speed and linear speed (and radius of the circle)?
	\end{enumerate}
\item  Graphs of trig functions.
	\begin{enumerate}
	\item  Be able to graph any trig function.
		You can use your calculator, but many of the important details of a graph are best found without using a calculator
		and I will expect your work and answers to reflect this type of understanding of the graphs.
		Also, you should be able to graph $y=\sin x$ and $y=\cos x$ 
		very well without a calculator (these are the basic graphs to know).
	\item  What do the following terms mean and how can we see these in a graph?
		\begin{enumerate}
		\item  Amplitude
		\item  Period
		\item  Phase shift
		\item  Periodic
		\end{enumerate}
	\end{enumerate}
\item  Studying ideas:
	\begin{enumerate}
	\item  Think about the problems I did in class.
		Try to find similar problems in the book and practice these.  Make sure you can do these well.
	\item  Think about the problems I assigned as homework.
		Again, try to find more problems like these in the book and practice them.
	\item  Try to guess what I will put on the test.
		Think about time problems I have emphasized and make sure you master this sort of problem.
	\item  Go over the concepts you don't feel like you understood very well.
		Try to understand these as well as you can.
	\item  Go see the tutors in Nightengale for help with problems in the book you can't do or concepts you don't understand.
		It is probably best if you have a list of problems that you have tried and thought about when you go in.
	\item  Come see me to discuss any problems and concepts that you are having difficulty with.
	\end{enumerate}
\end{enumerate}



Here is some sort of ``sample test.''
Do not be shocked if the actual test differs substantially.

\begin{enumerate}
\item  Find the following.  If possible, get the exact answer (i.e., a decimal is not correct):
	\begin{enumerate}
	\item  $\sin 30^\circ$
	\item  $\cos (5\pi/3)$
	\item  $\tan 132^\circ$
	\item  $\tan 132$
	\item  $\csc (27\pi/4)$
	\end{enumerate}
\item  Find all angles which satisfy the following:
	\[
	\sin \theta = -.2 \qquad 0 \leq \theta \leq 2\pi
	\]
\item  One or more of numbers 23,24,31 in the review exercises.
\item  One or more of numbers 39,40 in the review exercises.
\item  Graph the following functions.  For each graph, clearly state and identify the amplitude, period, vertical shift, and phase shift.
	\begin{enumerate}
	\item  $y = -3 \sin(4x-\pi)$
	\item  $y = 2 \cos(x/2 - \pi/4) +3$
	\end{enumerate}
\item  The hypoteneuse of a right triangle has a length of 10.  
	One of the acute angles of this right triangle is $12^\circ$.
	Find the measure of all the angles and sides of this triangle.
\end{enumerate}











\end{document}