%Plotting Curves
%If you modify this file, please indicate here and in the footnote.
%Math263C 

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\Large
Plotting Curves\footnote{Copyright \copyright 2002 Todd Young.
All rights reserved. Please address comments to young@math.ohiou.edu.}
\end{center}

Sketch the graphs to include in your report. Do not print them.
\begin{enumerate}
\item Enter the commands (in the command window): \\
      \verb& ezplot('x^2 + y^2 = 9') & \\
      \verb& ezplot('x^2 + x*y + y^2 = 9') & \\     
      \verb& ezplot('x^2/9 + y^2/4 = 1') & \\
      \verb& ezplot('x^2 - y^2 = 9') & \\
      \verb& ezplot('(x-4)^2 - (y+2)^2 = 9') & \\
      \verb& ezplot('x^2 - y = 9') & \\
What is the geometric object supposed to be in each of the above?
Which ones produce good graphs and which do not?

\item Use \verb& ezplot & to plot the equations: \\
      $x + y = 100$
	\hfill(Use \verb$ ezplot('x + y = 100')$)\\
      $\sin^2 x + \sin^2 y - \ln(xy) = 0$ \hfill 
               (\verb&'sin(x)^2+sin(y)^2-log(x*y)=0'&) \\
      $x^5 + y^5 + xy = 0$ \hfill(\verb&'x^5 + y^5 + x*y = 0'&)\\
Sketch the graphs for your report and discuss any problems
encountered.

\item Try the following commands:\\
      \verb& t = 0:pi/50:2*pi; & \\
      \verb& plot(sin(t)+1, cos(t)-1) & \\
      \verb& plot(3*sin(t)+3,2*cos(t)-2)&\\
What should the geometric object be in each of the above?
Repeat the above commands, but replace 50 in the first
command by 5. What is the effect?

      
\item Try the following commands:\\
      \verb& t = -1.76:.01:1.76; & \\
      \verb& x = cosh(t); & \\
      \verb& y = sinh(t); & \\
      \verb& plot(x,y) & \\
      Use the identity $\cosh^2(t) - \sinh^2(t) = 1$ to
      write the parametric equation in cartesian coordinates.
      What should the plot be?



\item Using complete sentences and standard mathematical notation, 
prepare a brief written report.  Do {\bf not} get a printout.

\end{enumerate}

\vfill

\textsf{\noindent
The user plots curves given both by equations and
by parametric functions. The user also encounters difficulties
with under-sampling and with choice of domain.}


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