\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 Final}
\end{center}

\begin{enumerate}
\item  Same format as the other tests.
	You can have one $3 \times 5$ note card with formulas on it.
\item  Final will cover all of Chapter~5, Chapter~6, and Chapter~7 (except 7.5, 7.6).
\item  Trig functions.
	\begin{enumerate}
	\item  SOHCAHTOA
	\item  Unit circle
	\item  Solving right triangles
	\end{enumerate}
\item  Radians.
	\begin{enumerate}
	\item  Converting between degrees and radians.
	\item  Arc length.
	\item  Angular speed.
	\end{enumerate}
\item  Graphs of trig functions.
	\begin{enumerate}
	\item  Amplitude
	\item  Period
	\item  Phase shift
	\item  Periodic
	\end{enumerate}
\item  Identities:
	\begin{enumerate}
	\item  Be familiar with them.
	\item  Use identities to simplify trigonometric expressions.
	\item  Be able to prove (or disprove) trigonometric identities. (How do you disprove an identity?)
	\end{enumerate}
\item  Inverse trig functions
	\begin{enumerate}
	\item  Evaluating inverse trig functions
	\item  Simplifying composition of trig functions and inverse trig functions 
	\item  Using inverse trig functions to find angles (remember sometimes you end up in the wrong quadrant)
	\end{enumerate}
\item  Solving trig equations
	\begin{enumerate}
	\item  Know how to solve algebraically and graphically (graphing checks your work)
	\item  Remember the first step is to get trig functions by themselves.
	\item  Remember that once you get a trig function by itself, you take the inverse trig function and use the unit circle.
	\item  Don't forget the $+2k\pi$, and remember to put it in the right spot.
	\end{enumerate}
\item  Solving triangles.
	\begin{enumerate}
	\item  Law of sines.
	\item  Law of cosines.
	\item  When are there two triangles with the given data.
	\item  When are there no triangles with the given data.
	\item  Area of triangles.
	\end{enumerate}
\item  Complex numbers.
	\begin{enumerate}
	\item  Standard form and trigonmetric form of a complex number.
	\item  Using trig form of a complex number.
	\item  Solving equations with complex numbers in it.
	\end{enumerate}
\item  Polar coordinates
	\begin{enumerate}
	\item  Converting between polar coordinates and rectangular coordinates
	\item  Graphing
	\end{enumerate}
\end{enumerate}


\newpage

Sample test.  As usual, the actual final may differ significantly.

\begin{enumerate}
\item  Suppose your car has wheels that are $1.75$ feet in diameter and you are travelling $41$ miles per hour ($60$ feet per second).
	How fast are your wheels turning (in revolutions per second)?
\item  Graph one of the following functions.
	Identify all the important points of the graph.
	\begin{eqnarray*}
	y & = & -4 \sin(\pi x/3 -\pi/6) +3 \\
	y & = & -4 \cos(3x/4 + \pi/12) -2
	\end{eqnarray*}
\item  Prove or dispove the identities
	\begin{eqnarray*}
	\frac{1-\sin x}{\cos x} & = & \frac{\cos x}{1- \sin x} \\
	\frac{\tan y + \sin y}{2\tan y} & = & \cos^2 \frac{y}{2} \\
	\frac{1+\cos 2\theta}{\sin 2\theta} & = & \tan \theta
	\end{eqnarray*}
\item  Solve the following equations
	\begin{eqnarray*}
	2 \cos^2x + 3 \cos x & = & -1 \\
	\csc^2x - 2 \cot^2x & = & 0
	\end{eqnarray*}
\item  Find all angles satisfying $\tan \theta=-\sqrt{3}$ and $\pi \leq \theta \leq 4 \pi$.
\item  Solve some triangles as in test 3.
	Find the areas of these triangles too.
\item  Solve the following equation for $x$:
	\[
	x^2 - 2(1+i)x = -1+(\sqrt{3}-2)i
	\]
\item  Find all fifth roots of $32$.
\item  Graph the polar equations.  Convert the equations to rectangular form too.
	\begin{eqnarray*}
	r & = & 1+ \cos \theta \\
	r & = & 3 \sin(2\theta)
	\end{eqnarray*}
\end{enumerate}













\end{document}


