\documentclass[12pt,letterpaper]{article}
\usepackage{graphicx}

\title{Math 235 Lab 2 Sample}
\author{Your Names Here}
\begin{document}

\maketitle

In this discussion, we define a curve in the plane via a set of parametric
equations,
$$
x(t)=3\sin(2\pi t)-2\cos^5(2\pi t) \qquad y(t)=\cos(2\pi t)-3\sin(2\pi t) \qquad 0\leq t \leq 1
$$


\begin{enumerate}
\item Plot the curve.  Plot the points on the curve where $t=0, 0.1, 0.2, \cdots, 1.0$.
Combine the two plots into one using \verb+display+.

SOLUTION:
We used the \verb+seq+ command to generate the point plot, and then
we overlapped our two graphs using \verb+display+.  The result is seen
in Figure \ref{Q1}.

\begin{figure}
\centering
\includegraphics[width=3.0in]{XYgraph}  %The name of the plot file is XYgraph.eps
\caption{The graph for Question 1 gives the parametric equations
as a plot in the $(x,y)$ plane.}
\label{Q1}
\end{figure}

\item Determine the points $(x,y)$ where the curve crosses the line $x=1$.  

SOLUTION:

\item Determine the points $(x,y)$ where the curve crosses the line $y=2x$.

SOLUTION:

\item Find the point(s) $(x,y)$ where the tangent line is horizontal.  Plot one tangent line together with the curve to illustrate your solution.

SOLUTION:

\item Find the point(s) $(x,y)$ where the tangent line is has slope $-2/3$.  Plot one tangent line together with the curve to illustrate your solution.

SOLUTION:

\item Find the point(s) $(x,y)$ where the curve crosses itself. 

SOLUTION:

\item Extra Credit:  Find the angle in degrees
between the two branches of the curve.  

\end{enumerate}

\end{document}