%% This document created by Scientific Notebook (R) Version 3.0


\documentclass[12pt,thmsa]{article}
\usepackage{amssymb}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{makeidx}
\usepackage{sw20jart}

%TCIDATA{TCIstyle=article/art4.lat,jart,sw20jart}

%TCIDATA{<META NAME="ViewSettings" CONTENT="31">}
%TCIDATA{<META NAME="GraphicsSave" CONTENT="32">}
%TCIDATA{<META NAME="Title" CONTENT="2D Plots of Functions and Expressions">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Thu Feb 13 17:04:00 1997}
%TCIDATA{Language=American English}
%TCIDATA{CSTFile=MathHelp.cst}
%TCIDATA{<LINK REL="author" HREF="DM0-1.tex">}
%TCIDATA{<LINK REL="begin" HREF="DM6-1.tex">}
%TCIDATA{<LINK REL="contents" HREF="DM0-0.tex">}
%TCIDATA{<LINK REL="copyright" HREF="DM0-2.tex">}
%TCIDATA{<LINK REL="end" HREF="DM6-7.tex">}
%TCIDATA{<LINK REL="index" HREF="DMIndex.tex">}
%TCIDATA{<LINK REL="next" HREF="DM6-5.tex">}
%TCIDATA{<LINK REL="parent" HREF="DM6.tex">}
%TCIDATA{<LINK REL="previous" HREF="DM6-3.tex">}
%TCIDATA{<LINK REL="top" HREF="DM0-0.tex">}

\input{tcilatex}
\begin{document}


\section{2D Plots\label{Plot expression} of Functions and Expressions}

In the equation $f(x)=x\sin x$, each of the two sides---$f(x)$ and $x\sin x$%
---is an \emph{expression} while $f$ is a \emph{function}. The function $f$
is a rule that assigns to each number the product of that number and the
sine of that number. Thus the function $f$ defined by the equation $%
f(x)=x\sin x$ is the same function as the function $g$ defined by the
equation $g(t)=t\sin t$. The expression $x\sin x$ (or $f(x)$) is different
from the expression $t\sin t$ (or $f(t)$), since $x\sin x$ is tied to the
variable $x$, and $t\sin t$ is tied to the variable $t$.

\strut

\subsection{\ Expressions\label{Plot multiple expressions}}

\begin{quote}
$\blacktriangleright $ To plot one or more expressions 
\index{Plot expression}involving a single variable
\end{quote}

\begin{itemize}
\begin{enumerate}
\item[1.]  Enter the expression(s) in your document. If you want to plot
several expressions 
\index{Plot 2D@Plot 2D!multiple expressions@multiple expressions}at once,
enter them separated by (red) commas.

\item[2.]  With the insertion point in an expression or list of expressions,
click 
\FRAME{itbpF}{0.3009in}{0.3009in}{0.0701in}{}{}{2dplot.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 0.3009in;height 0.3009in;depth 0.0701in;original-width
17.8125pt;original-height 16.9375pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename '2dplot.wmf';file-properties "XNPEU";}}, or from
the \textsf{Plot 2D} submenu choose \textsf{Rectangular}.\medskip 
\end{enumerate}
\end{itemize}

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Rectangular}
\end{quote}

\begin{quotation}
$x\sin \dfrac{1}{x}$
\end{quotation}

\FRAME{dtbpFU}{3in}{2.0003in}{0pt}{\Qcb{$y=x\sin \dfrac{1}{x}\protect%
\medskip $}}{\Qlb{sam}}{Figure }{\special{language "Scientific Word";type
"MAPLEPLOT";width 3in;height 2.0003in;depth 0pt;display "PICT";function
\TEXUX{$x\sin \dfrac{1}{x}$};linecolor "black";linestyle 1;linethickness
1;pointstyle "point";xmin "-1";xmax "1";xviewmin "-1.04";xviewmax
"1.041";yviewmin "-0.2383";yviewmax "0.8631";rangeset"X";phi 45;theta
45;plottype 4;numpoints 99;axesstyle "normal";xis \TEXUX{x};var1name
\TEXUX{$x$};}}\bigskip Add the Label $y=x\sin \frac{1}{x}$ by typing it into
the \textsf{Plot Properties + Labelling} tabbed dialog in the \textsf{%
Caption Text} entry field.

\begin{quote}
$\blacktriangleright $ To add an expression to a 2D plot\label%
{Add expression to Plot 2D}
\end{quote}

\begin{itemize}
\item  Select the expression with the mouse and drag it onto the
plot.\medskip
\end{itemize}

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Rectangular}
\end{quote}

\begin{quotation}
$x\sin \frac{1}{x}$
\end{quotation}

\begin{quote}
$\blacktriangleright $ Select and drag to the frame
\end{quote}

\begin{quotation}
$x$ and $-x$
\end{quotation}

\begin{quote}
$\blacktriangleright $ Revise \textsf{Plot Components} page,\textsf{\ Item
Number: 2, Line Color: Red}, \textsf{Item Number: 3, Line Color: Blue}
\end{quote}

\FRAME{dtbpFU}{3in}{2.0003in}{0pt}{\Qcb{$y=x\sin \frac{1}{x},$ $y=x,$ $y=-x$}%
}{}{}{\special{language "Scientific Word";type "MAPLEPLOT";width 3in;height
2.0003in;depth 0pt;display "PICT";function \TEXUX{$x\sin
\frac{1}{x}$};linecolor "black";linestyle 1;linethickness 1;pointstyle
"point";function \TEXUX{$x$};linecolor "red";linestyle 1;linethickness
1;pointstyle "point";function \TEXUX{$-x$};linecolor "blue";linestyle
1;linethickness 1;pointstyle "point";xmin "-0.1001326";xmax
"0.1070383";xviewmin "-0.1043";xviewmax "0.1113";yviewmin "-0.1113";yviewmax
"0.1114";rangeset"X";phi 45;theta 45;plottype 4;numpoints 49;axesstyle
"normal";xis \TEXUX{x};var1name \TEXUX{$x$};}}\bigskip

\medskip You can also add expressions with \textsf{Add Item} in the \textsf{%
Plot Properties} tabbed dialogs, as described earlier.

\begin{quote}
$\blacktriangleright $ To plot trigonometric functions of degrees\label%
{Plot with degrees}
\end{quote}

\begin{itemize}
\begin{enumerate}
\item[1.]  Enter the expression(s) in your document. If you want to plot
several expressions 
\index{Plot 2D@Plot 2D!multiple expressions@multiple expressions}at once,
enter them separated by (red) commas.

\item[2.]  With the insertion point in an expression or list of expressions,
click 
\FRAME{itbpF}{0.3009in}{0.3009in}{0.0701in}{}{}{2dplot.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 0.3009in;height 0.3009in;depth 0.0701in;original-width
17.8125pt;original-height 16.9375pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename '2dplot.wmf';file-properties "XNPEU";}}, or from
the \textsf{Plot 2D} submenu choose \textsf{Rectangular}.\medskip

\item  With the plot selected, click \FRAME{itbpF}{0.3009in}{0.3009in}{%
0.0701in}{}{}{property.wmf}{\special{language "Scientific Word";type
"GRAPHIC";display "PICT";valid_file "F";width 0.3009in;height 0.3009in;depth
0.0701in;original-width 17.8125pt;original-height 16.9375pt;cropleft
"0";croptop "1";cropright "1";cropbottom "0";filename
'Property.wmf';file-properties "XNPEU";}} or choose \textsf{Edit + Properties%
}. Click \textsf{Plot Components} tab. Change \textsf{Domain Interval(s)} to 
$-180<x<180$ (or other limits as appropriate). Choose \textsf{OK}.
\end{enumerate}
\end{itemize}

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Rectangular}
\end{quote}

\begin{quotation}
$\sin x^{\circ },\cos 2x^{\circ }$
\end{quotation}

\FRAME{dtbpFU}{3in}{2.0003in}{0pt}{\Qcb{$y=\sin x^{\circ }$, $y=\cos
2x^{\circ }$}}{}{}{\special{language "Scientific Word";type
"MAPLEPLOT";width 3in;height 2.0003in;depth 0pt;display "PICT";function
\TEXUX{$\sin x^{\circ }$};linecolor "black";linestyle 1;linethickness
1;pointstyle "point";function \TEXUX{$\cos 2x^{\circ }$};linecolor
"red";linestyle 1;linethickness 1;pointstyle "point";xmin "-180";xmax
"180";xviewmin "-187.2";xviewmax "187.3";yviewmin "-1.04";yviewmax
"1.041";rangeset"X";phi 45;theta 45;plottype 4;numpoints 49;axesstyle
"normal";xis \TEXUX{x};var1name \TEXUX{$x$};}}

\strut

\subsection{\ Defined Functions\label{Plot function}}

You can plot a defined function in two different ways. Recall that you
define a function such as $f(x)=x\sin x$ by placing the insertion point in
the expression and choosing \textsf{New Definition} from the \textsf{Define}
submenu.

\begin{quote}
$\blacktriangleright $ To plot a defined function $f$ of one variable
\end{quote}

\begin{itemize}
\begin{enumerate}
\item[1.]  Select the function name $f$ or select the expression $f(x)$.

\item[2.]  From the \textsf{Plot 2D} submenu, choose \textsf{Rectangular}%
.\medskip
\end{enumerate}
\end{itemize}

\index{Plot 2D@Plot 2D!piecewise-defined functions@piecewise-defined functions}%
\label{Plot piecewise-defined function}To plot a 
\hyperref{piecewise-defined function}{}{}{DM3-2.tex#Piecewise-defined
function} $f$, you may use either the function name $f$ or the expression $%
f(x)$ to create the plot. If the function is not continuous, these two
choices will give different plots as illustrated in the second example
below. In the first example, the function is 
\[
f(x)=\left\{ 
\begin{array}{ccc}
x^{2}-1 & \text{if} & x<-1 \\ 
1-x^{2} & \text{if} & -1\leq x\leq 1 \\ 
x^{2}-1 & \text{if} & 1<x
\end{array}
\right. 
\]

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Rectangular}
\end{quote}

\begin{quotation}
$f$
\end{quotation}

\FRAME{dtbpF}{3.0459in}{2.0392in}{0pt}{}{}{piecews3.wmf}{\special{language
"Scientific Word";type "GRAPHIC";maintain-aspect-ratio TRUE;display
"PICT";valid_file "F";width 3.0459in;height 2.0392in;depth
0pt;original-width 216.8125pt;original-height 144.5625pt;cropleft
"0";croptop "1";cropright "1";cropbottom "0";filename
'piecews3.wmf';file-properties "XNPEU";}}

In the following example the function is 
\[
g(x)=\left\{ 
\begin{array}{ccc}
x^{2}-1 & \text{if} & x<-1 \\ 
20-x^{2} & \text{if} & -1\leq x\leq 1 \\ 
x^{2}-1 & \text{if} & 1<x
\end{array}
\right. 
\]
Observe that plotting the expression $g(x)$ gives the graph of the function $%
y=g(x)$, while plotting the function name $g$ adds vertical lines at
discontinuities to make a continuous graph.

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Rectangular}
\end{quote}

\begin{quotation}
$g$
\end{quotation}

\FRAME{dtbpF}{3.0277in}{2.028in}{0pt}{}{}{pcwscont.wmf}{\special{language
"Scientific Word";type "GRAPHIC";display "PICT";valid_file "F";width
3.0277in;height 2.028in;depth 0pt;original-width 216.8125pt;original-height
144.5625pt;cropleft "0";croptop "1";cropright "1";cropbottom "0";filename
'Pcwscont.wmf';file-properties "XNPEU";}}

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Rectangular}
\end{quote}

\begin{quotation}
$g(x)$
\end{quotation}

\FRAME{dtbpF}{3.0277in}{2.028in}{0pt}{}{}{pcwsdisc.wmf}{\special{language
"Scientific Word";type "GRAPHIC";display "PICT";valid_file "F";width
3.0277in;height 2.028in;depth 0pt;original-width 216.8125pt;original-height
144.5625pt;cropleft "0";croptop "1";cropright "1";cropbottom "0";filename
'Pcwsdisc.wmf';file-properties "XNPEU";}}

\begin{quote}
$\blacktriangleright $ To add a defined function $f$ to a 2D plot
\end{quote}

\begin{enumerate}
\item[1.]  Select the name $f$ of the function or select the expression $%
f(x) $.

\item[2.]  Drag your selection onto the plot.\medskip
\end{enumerate}

\subsection{\ Special Functions\label{Special Functions}}

\strut

\begin{quotation}
You can enter the \textsl{greatest integer function} 
\index{Greatest integer@Greatest integer}\label{Greatest integer}or 
\index{Floor function@Floor function}\label{Floor function}\textsl{floor
function} $f(x)=\left\lfloor x\right\rfloor $ by clicking the brackets icon 
\FRAME{itbpF}{0.3001in}{0.3001in}{0.0701in}{}{}{fences.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 0.3001in;height 0.3001in;depth
0.0701in;original-width 24.0625pt;original-height 22.5625pt;cropleft
"0";croptop "1";cropright "1";cropbottom "0";filename
'FENCES.WMF';file-properties "XNPEU";}} and choosing \FRAME{itbpF}{0.1989in}{%
0.3001in}{0.0692in}{}{}{lfloor.wmf}{\special{language "Scientific Word";type
"GRAPHIC";maintain-aspect-ratio TRUE;display "PICT";valid_file "F";width
0.1989in;height 0.3001in;depth 0.0692in;original-width
15.0625pt;original-height 24.0625pt;cropleft "0";croptop "1.0119";cropright
"0.9983";cropbottom "0";filename 'lfloor.wmf';file-properties "XNPEU";}}
(see \hyperref{floor}{}{}{DM2-4.tex#Floor}).
\end{quotation}

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Rectangular}
\end{quote}

\begin{quotation}
$\left\lfloor x\right\rfloor $
\end{quotation}

\FRAME{dtbpF}{2.9992in}{1.9995in}{0pt}{}{}{Plot }{\special{language
"Scientific Word";type "MAPLEPLOT";width 2.9992in;height 1.9995in;depth
0pt;display "PICT";function \TEXUX{$\left\lfloor x\right\rfloor $};linecolor
"green";linestyle 1;linethickness 2;pointstyle "point";xmin "-5";xmax
"5";xviewmin "-5.2";xviewmax "5.204";yviewmin "-5.18";yviewmax
"4.184";rangeset"X";phi 45;theta 45;plottype 4;numpoints 49;axesstyle
"normal";xis \TEXUX{x};var1name \TEXUX{$x$};}}\medskip

\begin{quotation}
In a similar fashion, you can enter the 
\index{Absolute value@Absolute value}\label{Absolute value function}\textsl{%
absolute value function} $f(x)=\left| x\right| $ by choosing vertical
brackets from%
\FRAME{itbpF}{0.3009in}{0.3009in}{0.0701in}{}{}{brackets.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 0.3009in;height 0.3009in;depth 0.0701in;original-width
24.0625pt;original-height 23.3125pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'Brackets.wmf';file-properties "XNPEU";}}. The
following shows the graph of $f(x)=\left| \sin x\right| .$
\end{quotation}

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Rectangular}
\end{quote}

\begin{quotation}
$\left| \sin x\right| $
\end{quotation}

\FRAME{dtbpF}{2.9992in}{1.9995in}{0pt}{}{}{Plot }{\special{language
"Scientific Word";type "MAPLEPLOT";width 2.9992in;height 1.9995in;depth
0pt;display "PICT";function \TEXUX{$\left| \sin x\right| $};linecolor
"green";linestyle 1;linethickness 1;pointstyle "point";xmin "-5";xmax
"5";xviewmin "-5.2";xviewmax "5.204";yviewmin "-0.01497";yviewmax
"1.02";rangeset"X";phi 45;theta 45;plottype 4;numpoints 49;axesstyle
"normal";xis \TEXUX{x};var1name \TEXUX{$x$};}}\medskip

The 
\index{Gamma function@Gamma function}\label{Gamma function}\textsl{Gamma
function} $\Gamma (x)$ extends the factorial function in the sense that for
each nonnegative integer $n$ the identity $\Gamma (n+1)=n!$ holds. The plot
of the Gamma function displays the vertical asymptotes with the graph.

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Rectangular}
\end{quote}

\begin{quotation}
$\Gamma (x)$
\end{quotation}

\FRAME{dtbpF}{2.9992in}{1.9995in}{0pt}{}{}{Plot }{\special{language
"Scientific Word";type "MAPLEPLOT";width 2.9992in;height 1.9995in;depth
0pt;display "PICT";function \TEXUX{$\Gamma (x)$};linecolor "red";linestyle
1;linethickness 1;pointstyle "point";xmin "-5";xmax "5";xviewmin
"-5";xviewmax "5";yviewmin "-25";yviewmax "25";viewset"XY";rangeset"X";phi
45;theta 45;plottype 4;numpoints 106;axesstyle "normal";xis
\TEXUX{x};var1name \TEXUX{$x$};}}\medskip

The \textsl{Heaviside function} 
\index{Heaviside function@Heaviside function}\label{Heaviside function}is
defined by 
\[
H(x)=\left\{ 
\begin{array}{ccc}
0 & 
\text{if} & x<0 \\ 
1 & \text{if} & x\geq 0
\end{array}
\right. 
\]
You can also call it directly from Maple by choosing \textsf{Define + Define
Maple Name }and filling in \texttt{Heaviside(x)} for the \textsf{Maple Name}
and $H(x)$ for the \textsf{Scientific Notebook Name} in the dialog box.%
\FRAME{dtbpF}{3.0096in}{3.6936in}{0pt}{}{}{mapdefin.wmf}{\special{language
"Scientific Word";type "GRAPHIC";display "PICT";valid_file "F";width
3.0096in;height 3.6936in;depth 0pt;original-width 267.25pt;original-height
329.75pt;cropleft "0";croptop "1";cropright "1";cropbottom "0";filename
'Mapdefin.wmf';file-properties "XNPEU";}}The Heaviside function provides an
alternative method for creating piecewise-defined functions. Note that $%
H(x-2)\sin (x)+H(-x)\cos x$ is $\cos x$ for $x\leq 0$, $\sin x$ for $x\geq 2$%
, and $0$ for $0\leq x\leq 2$.

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Rectangular }
\end{quote}

\begin{quotation}
$H(x-2)\sin x+H(-x)\cos x$
\end{quotation}

\FRAME{dtbpF}{3.0277in}{2.028in}{0pt}{}{}{heavisid.wmf}{\special{language
"Scientific Word";type "GRAPHIC";display "PICT";valid_file "F";width
3.0277in;height 2.028in;depth 0pt;original-width 216.8125pt;original-height
144.5625pt;cropleft "0";croptop "1";cropright "1";cropbottom "0";filename
'Heavisid.wmf';file-properties "XNPEU";}}

\medskip

\subsection{\ Polygons\label{Polygon plots} and Point Plots}

You can plot the 
\index{Polygons@Polygons}\label{Plot polygons} 
\index{Point plot@Point plot}points $\{\left( x_{1},y_{1}\right) ,\left(
x_{2},y_{2}\right) ,\left( x_{3},y_{3}\right) ,\ldots ,\left(
x_{n},y_{n}\right) \}$, or a polygon whose vertices lie at these points, by
typing the vector $\left( x_{1},y_{1},x_{2},y_{2},x_{3},y_{3},\ldots
,x_{n},y_{n}\right) $ or by entering the matrix $\left[ 
\begin{array}{cc}
x_{1} & y_{1} \\ 
x_{2} & y_{2} \\ 
x_{3} & y_{3} \\ 
\vdots & \vdots \\ 
x_{n} & y_{n}
\end{array}
\right] $ and choosing \textsf{Plot 2D + Rectangular}.

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Rectangular}
\end{quote}

\begin{quotation}
$\left( 1,1,2,1,2,2,1,2,1,1\right) $
\end{quotation}

\FRAME{dtbpF}{1.9995in}{1.299in}{0pt}{}{}{Figure }{\special{language
"Scientific Word";type "MAPLEPLOT";width 1.9995in;height 1.299in;depth
0pt;display "PICT";function \TEXUX{$\left( 1,1,2,1,2,2,1,2,1,1\right)
$};linecolor "blue";linestyle 1;linethickness 1;pointstyle "point";xmin
"0";xmax "3";xviewmin "0";xviewmax "3";yviewmin "-0.005788";yviewmax
"2.994212";viewset"XY";rangeset"X";phi 45;theta 45;plottype 4;constrained
TRUE;numpoints 49;axesstyle "normal";xis \TEXUX{x};var1name \TEXUX{$x$};}}

The default is to connect the points with straight-line segments. To plot
points alone, choose \textsf{Point Plot} in the \textsf{Plot Properties}
dialog box.

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Rectangular, Edit + Properties,
Point, Circle}
\end{quote}

\begin{quotation}
$\left[ 
\begin{array}{cc}
1 & 1 \\ 
2 & 1 \\ 
2 & 2 \\ 
1 & 2
\end{array}
\right] $
\end{quotation}

\FRAME{dtbpF}{1.9986in}{1.2981in}{0pt}{}{}{Figure }{\special{language
"Scientific Word";type "MAPLEPLOT";width 1.9986in;height 1.2981in;depth
0pt;display "PICT";function \TEXUX{$\left( 1,1,2,1,2,2,1,2\right)
$};linecolor "black";linestyle 1;linethickness 1;pointstyle
"circle";pointplot TRUE;xmin "0";xmax "3";xviewmin "0";xviewmax "3";yviewmin
"0";yviewmax "3";viewset"XY";rangeset"X";phi 45;theta 45;plottype
4;constrained TRUE;numpoints 4;axesstyle "normal";xis \TEXUX{x};var1name
\TEXUX{$x$};}}\medskip

\begin{example}
You can generate a regular pentagon with an enclosed five-point star by
using the points $\left( \cos \frac{2\pi k}{5},\sin \frac{2\pi k}{5}\right) $
as $k$ ranges from $0$ to $5.$

Place the insertion point in the vector 
\[
\left[ 1,0,\cos \frac{2\pi }{5},\sin \frac{2\pi }{5},\cos \frac{4\pi }{5}%
,\sin \frac{4\pi }{5},\cos \frac{6\pi }{5},\sin \frac{6\pi }{5},\cos \frac{%
8\pi }{5},\sin \frac{8\pi }{5},1,0\right] 
\]

Choose \textsf{Plot 2D + Rectangular.}

Choose\textbf{\ }\textsf{Edit + Plot Properties} or\textsf{\ }double-click
the frame and click the dialog box tool.

Choose \textsf{Equal Scaling Along Each Axis}

Select the vector 
\[
\left[ 1,0,\cos \frac{4\pi }{5},\sin \frac{4\pi }{5},\cos \frac{8\pi }{5}%
,\sin \frac{8\pi }{5},\cos \frac{2\pi }{5},\sin \frac{2\pi }{5},\cos \frac{%
6\pi }{5},\sin \frac{6\pi }{5},1,0\right] 
\]
with the mouse and drag it to the frame.\FRAME{dtbpF}{0.9496in}{0.6287in}{0pt%
}{}{}{Plot }{\special{language "Scientific Word";type "MAPLEPLOT";width
0.9496in;height 0.6287in;depth 0pt;display "PICT";function \TEXUX{$\left[
1,0,.30902,.95106,-.80902,.58779,-.80902,-.58779,.30902,-.95106,1,0\right]
$};linecolor "blue";linestyle 1;linethickness 1;pointstyle "point";function
\TEXUX{$\left[
1,0,-.80902,.58779,.30902,-.95106,.30902,.95106,-.80902,-.58779,1,0\right]
$};linecolor "blue";linestyle 1;linethickness 1;pointstyle "point";xmin
"-0.82057";xmax "1.17943";xviewmin "-0.8452";xviewmax "1.037";yviewmin
"-0.9891";yviewmax "0.9899";rangeset"X";phi 45;theta 45;plottype
4;constrained TRUE;numpoints 49;axesstyle "none";xis \TEXUX{x};var1name
\TEXUX{$x$};}}\medskip
\end{example}

You may find it convenient to combine \textsf{Line} and \textsf{Point}
styles, as in the following plot that combines a data cloud with a line of
best fit. (See the chapter on Statistics for information on \hyperref{curves
of best fit.}{}{}{DM11.tex})

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Rectangular, Edit + Properties,
Point, Circle}, select and drag $\frac{2792}{647}+\frac{957}{647}x$ to the
view
\end{quote}

\begin{quotation}
$\left[ 
\begin{array}{ll}
1 & 8 \\ 
3 & 7 \\ 
4 & 9 \\ 
6 & 12 \\ 
7 & 15 \\ 
7 & 16 \\ 
10 & 19 \\ 
11 & 21
\end{array}
\right] $
\end{quotation}

\FRAME{dtbpF}{3in}{2.0003in}{0pt}{}{}{}{\special{language "Scientific
Word";type "MAPLEPLOT";width 3in;height 2.0003in;depth 0pt;display
"PICT";function \TEXUX{$\left[
\MATRIX{2,8}{c}\VR{,,l,,,}{,,l,,,}{,,,,,}\HR{,,,,,,,,}\CELL{1}\CELL{8}%
\CELL{3}\CELL{7}\CELL{4}\CELL{9}\CELL{6}\CELL{12}\CELL{7}\CELL{15}\CELL{7}%
\CELL{16}\CELL{10}\CELL{19}\CELL{11}\CELL{21}\right] $};linecolor
"black";linestyle 1;linethickness 1;pointstyle "circle";pointplot
TRUE;function \TEXUX{$\frac{2792}{647}+\frac{957}{647}x$};linecolor
"red";linestyle 1;linethickness 1;pointstyle "point";xmin "0";xmax
"12";xviewmin "-0.24";xviewmax "12.24";yviewmin "3.96";yviewmax
"22.43";rangeset"X";phi 45;theta 45;plottype 4;numpoints 49;axesstyle
"normal";xis \TEXUX{x};var1name \TEXUX{$x$};}}

\strut

\subsection{\ \label{Log scaling}Log and Log-Log Plots}

Options for both \textsf{Log} and \textsf{Log-Log} plots\label%
{Log-Log scaling} 
\index{Plot type@Plot type!log@log} 
\index{Plot type@Plot type!log-log@log-log}are listed on the\textsf{\ Axes }%
page of the \textsf{Plot Properties} tabbed dialog. Power functions $%
f(x)=ax^{n}$ plot as straight lines on a \textsf{Log-Log} coordinate system
since $\log (f(x))=\log (ax^{n})=\ln a+n\ln x$ is of the form $Y=A+MX.$

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Rectangular, }set \textsf{Axes
Scaling} to \textsf{Log-Log, Domain Interval }$0.1<x<1.1$
\end{quote}

\begin{quotation}
$5x^{2/3}$
\end{quotation}

\FRAME{dtbpF}{3.8744in}{1.9995in}{0pt}{}{}{Plot }{\special{language
"Scientific Word";type "MAPLEPLOT";width 3.8744in;height 1.9995in;depth
0pt;display "PICT";function \TEXUX{$5x^{2/3}$};linecolor "blue";linestyle
1;linethickness 1;pointstyle "point";xmin "0.1";xmax "1.1";xviewmin
"-1.021";xviewmax "0.06264";yviewmin "0.01842";yviewmax
"0.7407";rangeset"X";phi 45;theta 45;plottype 21;num-x-ticks 2;num-y-ticks
3;numpoints 49;axesstyle "normal";xis \TEXUX{x};var1name \TEXUX{$x$};}}

Exponential functions $f(x)=cb^{x}$ plot as straight lines on a \textsf{Log}
coordinate system because $\log f(x)=x\log b+\log c=Bx+C.$

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Rectangular, }set \textsf{\ Axes
Scaling} to \textsf{Log}
\end{quote}

\begin{quotation}
$y=5\times 2^{x}$
\end{quotation}

\FRAME{dtbpF}{3in}{2.0003in}{0pt}{}{}{}{\special{language "Scientific
Word";type "MAPLEPLOT";width 3in;height 2.0003in;depth 0pt;display
"PICT";function \TEXUX{$5\times 2^{x}$};linecolor "blue";linestyle
1;linethickness 1;pointstyle "point";xmin "-5";xmax "5";xviewmin
"-5.2";xviewmax "5.204";yviewmin "-0.8664";yviewmax "2.266";rangeset"X";phi
45;theta 45;plottype 20;numpoints 49;axesstyle "normal";xis
\TEXUX{x};var1name \TEXUX{$x$};}}

\subsection{\ 
\index{Parametric plots@Parametric plots}\label{Parametric plots}Parametric
Plots}

A 2D parametric curve 
\index{Plot 2D@Plot 2D!parametric@parametric}is defined by a pair of
equations $x=f(t)$, $y=g(t)$. The curve is the set of points $(f(t),g(t))$,
where $t$ ranges over an interval.

\begin{quote}
$\blacktriangleright $ To plot a 2D parametric curve
\end{quote}

\begin{itemize}
\begin{enumerate}
\item[1.]  Make the two defining expressions the components of a vector. You
can use any of the standard notations for a vector, including the forms $%
\left[ \sin 2t,\cos 3t\right] $, $\left( \sin 2t,\cos 3t\right) $, $\left[ 
\begin{array}{cc}
\sin 2t & \cos 3t
\end{array}
\right] $, $\left( 
\begin{array}{cc}
\sin 2t & \cos 3t
\end{array}
\right) $, $\left[ 
\begin{array}{c}
\sin 2t \\ 
\cos 3t
\end{array}
\right] $, or $\left( 
\begin{array}{c}
\sin 2t \\ 
\cos 3t
\end{array}
\right) $. (The latter four expressions are $1\times 2$ and $2\times 1$
matrices, respectively.)

\item[2.]  With the insertion point in the vector, from the \textsf{Plot 2D}
menu choose \textsf{Parametric}.\medskip
\end{enumerate}
\end{itemize}

The following plot shows the parametric curve defined by $x=\sin 2t$, $%
y=\cos 3t$ as the parametric plot of the vector $\left[ \sin 2t,\cos
3t\right] $ with $0\leq t\leq 2\pi $ and \textsf{Equal Scaling Along Each
Axis}.

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Parametric }
\end{quote}

\begin{quotation}
$\left( \sin 2t,\cos 3t\right) $
\end{quotation}

\FRAME{dtbpF}{2.9992in}{1.9995in}{0pt}{}{}{Plot }{\special{language
"Scientific Word";type "MAPLEPLOT";width 2.9992in;height 1.9995in;depth
0pt;display "PICT";function \TEXUX{$\left( \sin 2t,\cos 3t\right)
$};linecolor "blue";linestyle 1;linethickness 1;pointstyle "point";xmin
"-5";xmax "5";xviewmin "-1.04";xviewmax "1.041";yviewmin "-1.04";yviewmax
"1.041";rangeset"X";phi 45;theta 45;plottype 19;constrained TRUE;numpoints
49;axesstyle "normal";xis \TEXUX{t};var1name \TEXUX{$x$};}}\label%
{Inverse function}\label{Inverse relation}\label{Plotting cube root}\label%
{Cube root}You can make a parametric plot of the pair $\left( f(x),x\right) $
to plot the inverse function or inverse relation of a function $y=f(x)$. For
example, to plot the cube root function $y=x^{\frac{1}{3}}$, observe that it
is the inverse function to $y=x^{3}$ and do a parametric plot.

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Parametric }
\end{quote}

\begin{quotation}
$\left( x^{3},x\right) $\FRAME{dtbpFU}{4.3647in}{2.0003in}{0pt}{\Qcb{$y=x^{%
\frac{1}{3}}$}}{}{}{\special{language "Scientific Word";type
"MAPLEPLOT";width 4.3647in;height 2.0003in;depth 0pt;display "PICT";function
\TEXUX{$\left( x^{3},x\right) $};linecolor "blue";linestyle 1;linethickness
1;pointstyle "point";xmin "-5";xmax "5";xviewmin "-50";xviewmax
"50";yviewmin "-5.2";yviewmax "5.204";viewset"XY";rangeset"X";phi 45;theta
45;plottype 19;numpoints 49;axesstyle "normal";xis \TEXUX{x};var1name
\TEXUX{$x$};}}\bigskip
\end{quotation}

The inverse relation of $\sin x$ follows. You can adjust the view to get the
plot of the inverse function $\sin ^{-1}x$.

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Parametric }
\end{quote}

\begin{quotation}
$\left( \sin x,x\right) $\FRAME{dtbpF}{3in}{2.3021in}{0pt}{}{}{}{%
\special{language "Scientific Word";type "MAPLEPLOT";width 3in;height
2.3021in;depth 0pt;display "PICT";function \TEXUX{$\left( \sin x,x\right)
$};linecolor "blue";linestyle 1;linethickness 1;pointstyle "point";xmin
"-5";xmax "5";xviewmin "-1.04";xviewmax "1.041";yviewmin "-5.2";yviewmax
"5.204";rangeset"X";phi 45;theta 45;plottype 19;numpoints 49;axesstyle
"normal";xis \TEXUX{x};var1name \TEXUX{$x$};}}
\end{quotation}

\subsection{\ Envelopes\label{Envelope}\label{Carrier waves}}

An interesting phenomenon occurs when simple curves are displayed as the
``envelope'' 
\index{Envelope@Envelope} of a more complicated function. Such things happen
in practice when low-frequency waves (say, frequencies in the audible range
for the human ear) ride carrier waves broadcast from a radio station.

The following example shows the curve $y=4\sin x+3\cos 3x$ ``riding'' on top
of the carrier $y=\sin 30x$.

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Rectangular}
\end{quote}

\begin{quotation}
$4\sin x+3\cos 3x,(4\sin x+3\cos 3x)\sin 30x$
\end{quotation}

\FRAME{dtbpF}{3in}{2.0003in}{0pt}{}{}{}{\special{language "Scientific
Word";type "MAPLEPLOT";width 3in;height 2.0003in;depth 0pt;display
"PICT";function \TEXUX{$4\sin x+3\cos 3x,(4\sin x+3\cos 3x)\sin
30x$};linecolor "red";linestyle 1;linethickness 1;pointstyle
"point";function \TEXUX{$4\sin x+3\cos 3x$};linecolor "black";linestyle
1;linethickness 1;pointstyle "point";xmin "-5";xmax "5";xviewmin
"-5.2";xviewmax "5.204";yviewmin "-6.79";yviewmax "6.796";rangeset"X";phi
45;theta 45;plottype 4;numpoints 49;axesstyle "normal";xis
\TEXUX{x};var1name \TEXUX{$x$};}}

\medskip

You can generate this plot by plotting $4\sin x+3\cos 3x$, and then dragging
the expression $(4\sin x+3\cos 3x)\sin 30x$ into the frame.

\subsection{\ Implicit Plots\label{Implicit equations}\label{Circle}}

The equation of a circle 
\index{Circle}cannot be rewritten as a function of one variable. You can
plot the set of points satisfying such an equation using the 2D implicit
plot feature.

\begin{quote}
$\blacktriangleright $ To plot an equation
\end{quote}

\begin{itemize}
\begin{enumerate}
\item[1.]  Enter the equation.

\item[2.]  With the insertion point in the equation, from the \textsf{Plot 2D%
} submenu, choose \textsf{Implicit}.\medskip
\end{enumerate}
\end{itemize}

The \textsf{Domain Intervals} for the following plot were set to $-3\leq
x\leq 7$ and $-2\leq y\leq 8$.

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Implicit}
\end{quote}

\begin{quotation}
$\left( x-2\right) ^{2}+\left( y-3\right) ^{2}=25$
\end{quotation}

\begin{center}
\FRAME{itbpF}{2.0064in}{1.3361in}{0in}{}{}{Figure }{\special{language
"Scientific Word";type "MAPLEPLOT";width 2.0064in;height 1.3361in;depth
0in;display "PICT";function \TEXUX{$\left( x-2\right) ^{2}+\left( y-3\right)
^{2}=25$};linecolor "red";linestyle 1;linethickness 1;pointstyle
"point";xmin "-3";xmax "7";ymin "-2";ymax "8";xviewmin "-3.2";xviewmax
"7.204";yviewmin "-2.2";yviewmax "8.204";rangeset"XY";phi 45;theta
45;plottype 12;num-x-gridlines 25;num-y-gridlines 25;plotstyle
"wireframe";axesstyle "normal";xis \TEXUX{x};yis \TEXUX{y};var1name
\TEXUX{$x$};var2name \TEXUX{$y$};}}\FRAME{itbpF}{2.0046in}{1.3353in}{0in}{}{%
}{Figure }{\special{language "Scientific Word";type "MAPLEPLOT";width
2.0046in;height 1.3353in;depth 0in;display "PICT";function \TEXUX{$\left(
x-2\right) ^{2}+\left( y-3\right) ^{2}=25.$};linecolor "red";linestyle
1;linethickness 1;pointstyle "point";xmin "-3";xmax "7";ymin "-2";ymax
"8";xviewmin "-3.2";xviewmax "7.204";yviewmin "-2.2";yviewmax
"8.204";rangeset"XY";phi 45;theta 45;plottype 12;constrained
TRUE;num-x-gridlines 25;num-y-gridlines 25;plotstyle "wireframe";axesstyle
"normal";xis \TEXUX{x};yis \TEXUX{y};var1name \TEXUX{$x$};var2name
\TEXUX{$y$};}}\medskip \FRAME{itbpF}{2.0046in}{1.3353in}{0in}{}{}{Figure }{%
\special{language "Scientific Word";type "MAPLEPLOT";width 2.0046in;height
1.3353in;depth 0in;display "PICT";function \TEXUX{$\left( x-2\right)
^{2}+\left( y-3\right) ^{2}=25.$};linecolor "red";linestyle 1;linethickness
1;pointstyle "point";xmin "-3";xmax "7";ymin "-2";ymax "8";xviewmin
"-10";xviewmax "10";yviewmin "-10";yviewmax
"10";viewset"XY";rangeset"XY";phi 45;theta 45;plottype 12;constrained
TRUE;num-x-gridlines 25;num-y-gridlines 25;plotstyle "wireframe";axesstyle
"normal";xis \TEXUX{x};yis \TEXUX{y};var1name \TEXUX{$x$};var2name
\TEXUX{$y$};}}
\end{center}

\begin{itemize}
\item  Unequal scales on the $x$- and $y$-axes can cause distortion of
geometric figures. Click the \textsf{Equal Scaling Along Each Axis }box to
make the figure on the left look like the circle (middle figure).

\item  With the \textsf{Domain Intervals} unchanged, click to remove the
check mark from the \textsf{View Intervals + Default} and edit the \textsf{%
View Intervals} to $-10\leq x\leq 10$ and $-10\leq y\leq 10$ in order to
generate the plot above on the right. This again illustrates the difference
between \textsf{Domain Intervals} (in this case, $-3\leq x\leq 7$ and $%
-2\leq y\leq 8$) and \textsf{View Intervals} (in this case, $-10\leq x\leq
10 $ and $-10\leq y\leq 10$).
\end{itemize}

\label{Inverse function (2)}\label{Inverse relation (2)}\label{Cube root (2)}%
\label{Plotting cube root (2)}You can make an implicit plot of the equation $%
x=f(y)$ to plot the inverse function or inverse relation of a function $%
y=f(x)$. For example, to plot the cube root function $y=x^{\frac{1}{3}}$,
observe that it is the inverse function to $y=x^{3}$ and do an implicit plot
of $x=y^{3}.$

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Implicit }
\end{quote}

\begin{quotation}
$y^{3}=x$\FRAME{dtbpF}{4.1355in}{2.0003in}{0pt}{}{}{}{\special{language
"Scientific Word";type "MAPLEPLOT";width 4.1355in;height 2.0003in;depth
0pt;display "PICT";function \TEXUX{$y^{3}=x$};linecolor "blue";linestyle
1;linethickness 1;pointstyle "point";xmin "-5";xmax "5";ymin "-5";ymax
"5";xviewmin "-5.2";xviewmax "5.204";yviewmin "-1.77";yviewmax
"1.771";rangeset"X";phi 45;theta 45;plottype 12;num-x-gridlines
25;num-y-gridlines 25;axesstyle "normal";xis \TEXUX{x};yis
\TEXUX{y};var1name \TEXUX{$x$};var2name \TEXUX{$y$};}}
\end{quotation}

For the inverse relation of the sine function, do an implicit plot of $%
x=\sin y$. Changing the view appropriately will give the plot of the inverse
sine function.

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Implicit }
\end{quote}

\begin{quotation}
$x=\sin y$\FRAME{dtbpF}{3in}{2.0003in}{0pt}{}{}{}{\special{language
"Scientific Word";type "MAPLEPLOT";width 3in;height 2.0003in;depth
0pt;display "PICT";function \TEXUX{$x=\sin y$};linecolor "blue";linestyle
1;linethickness 1;pointstyle "point";xmin "-5";xmax "5";ymin "-5";ymax
"5";xviewmin "-1.035";xviewmax "1.036";yviewmin "-5.2";yviewmax
"5.204";rangeset"X";phi 45;theta 45;plottype 12;num-x-gridlines
25;num-y-gridlines 25;axesstyle "normal";xis \TEXUX{x};yis
\TEXUX{y};var1name \TEXUX{$x$};var2name \TEXUX{$y$};}}
\end{quotation}

\strut

\subsection{\ \label{Polar coordinates (2)}Polar Coordinates}

In polar coordinates, you specify 
\index{Polar coordinates@Polar coordinates}a 
\index{Plot 2D@Plot 2D!polar coordinates@polar coordinates}point $P$ by
giving the angle $\theta $ that the ray from the origin to the point $P$
makes with the polar axis and the distance $r$ from the origin. The
equations that relate rectangular coordinates to polar coordinates are given
by 
\[
x=r\cos \theta ,\qquad y=r\sin \theta 
\]
or equivalently, 
\[
x^{2}+y^{2}=r^{2},\qquad \tan \theta =%
\dfrac{y}{x} 
\]

\begin{quote}
$\blacktriangleright $ To make a plot in polar coordinates
\end{quote}

\begin{enumerate}
\item[1.]  Type an expression for the radius in terms of the angle $\theta .$

\item[2.]  With the insertion point in the expression,\textsf{\ }from the 
\textsf{Plot 2D} submenu choose \textsf{Polar}.\ \medskip
\end{enumerate}

To obtain the view shown in the following two plots, select the frame and
choose \textsf{Edit + Properties}. Click the \textsf{Axes} tab, check 
\textsf{Equal Scaling on Both Axes}, and choose \textsf{OK}.

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Polar}
\end{quote}

\begin{quotation}
$\sin 2\theta $
\end{quotation}

\FRAME{dtbpF}{2.4993in}{1.9995in}{0pt}{}{}{Figure }{\special{language
"Scientific Word";type "MAPLEPLOT";width 2.4993in;height 1.9995in;depth
0pt;display "PICT";function \TEXUX{$\sin 2\theta $};linecolor
"blue";linestyle 1;linethickness 1;pointstyle "point";xmin "-3.1416";xmax
"3.1416";xviewmin "-0.8";xviewmax "0.8";yviewmin "-0.8";yviewmax
"0.8";viewset"XY";rangeset"X";phi 45;theta 45;plottype 8;constrained
TRUE;numpoints 49;axesstyle "normal";xis \TEXUX{v952};var1name
\TEXUX{$\theta $};}}\ 

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Polar}
\end{quote}

\begin{quotation}
$1-\cos \theta $
\end{quotation}

\FRAME{dtbpF}{3in}{2.0003in}{0pt}{}{}{}{\special{language "Scientific
Word";type "MAPLEPLOT";width 3in;height 2.0003in;depth 0pt;display
"PICT";function \TEXUX{$1-\cos \theta $};linecolor "blue";linestyle
1;linethickness 1;pointstyle "point";xmin "-3.1416";xmax "3.1416";xviewmin
"-2.045";xviewmax "0.2959";yviewmin "-1.351";yviewmax
"1.352";rangeset"X";phi 45;theta 45;plottype 8;constrained TRUE;numpoints
49;axesstyle "normal";xis \TEXUX{v952};var1name \TEXUX{$\theta $};}}

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Polar}
\end{quote}

\begin{quotation}
$1-\sin \theta +2\sin 3\theta $
\end{quotation}

\FRAME{dtbpF}{3in}{2.0003in}{0pt}{}{}{}{\special{language "Scientific
Word";type "MAPLEPLOT";width 3in;height 2.0003in;depth 0pt;display
"PICT";function \TEXUX{$1-\sin \theta +2\sin 3\theta $};linecolor
"cyan";linestyle 1;linethickness 1;pointstyle "point";xmin "-3.1416";xmax
"3.1416";xviewmin "-2.37";xviewmax "2.372";yviewmin "-4.107";yviewmax
"1.473";rangeset"X";phi 45;theta 45;plottype 8;numpoints 49;axesstyle
"normal";xis \TEXUX{v952};var1name \TEXUX{$\theta $};}}

\subsection{\ \label{Parametric polar plots}Parametric Polar Plots}

The polar plot of $\theta =r^{2}$ is obtained as the 2D polar plot 
\index{Plot 2D!parametric polar}of the vector $\left( r,r^{2}\right) $. To
get the following plot, revise the first plot that appears, choosing \textsf{%
Polar} and setting the parameter range to $0$ to $5$.

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Parametric, Edit + Properties,} 
\textsf{Polar}
\end{quote}

\begin{quotation}
$\left( r,r^{2}\right) $
\end{quotation}

\FRAME{dtbpF}{2.9992in}{1.9995in}{0pt}{}{}{Figure }{\special{language
"Scientific Word";type "MAPLEPLOT";width 2.9992in;height 1.9995in;depth
0pt;display "PICT";function \TEXUX{$\left( r,r^{2}\right) $};linecolor
"navy";linestyle 1;linethickness 1;pointstyle "point";xmin "0";xmax
"5";xviewmin "-4.876";xviewmax "5.153";yviewmin "-5.041";yviewmax
"4.706";rangeset"X";phi 45;theta 45;plottype 22;constrained TRUE;numpoints
49;axesstyle "normal";xis \TEXUX{r};var1name \TEXUX{$x$};}}\medskip

Both the radius $r$ and the angle $\theta $ may be defined in terms of some
third variable $t$. You can make the polar plot of the parametric curve
defined by the equations $r=1-\sin t$, $\theta =\cos t$ as the polar plot of
the vector\textsf{\ }$\left( 1-\sin t,\cos t\right) $, using \textsf{%
Parametric} from the \textsf{Plot 2D} submenu. Revise the first plot,
choosing \textsf{Polar} and parameter range $0\leq t\leq 2\pi $.

\begin{quote}
$\blacktriangleright $ \textsf{Plot 2D + Parametric,} \textsf{Edit +
Properties, Polar}
\end{quote}

\begin{quotation}
$(1-\sin t,\cos t)$
\end{quotation}

\FRAME{dtbpF}{3in}{2.0003in}{0pt}{}{}{}{\special{language "Scientific
Word";type "MAPLEPLOT";width 3in;height 2.0003in;depth 0pt;display
"PICT";function \TEXUX{$(1-\sin t,\cos t)$};linecolor "navy";linestyle
1;linethickness 1;pointstyle "point";xmin "-0";xmax "6.28";xviewmin
"-0.04";xviewmax "2.041";yviewmin "-1.193";yviewmax "1.192";rangeset"X";phi
45;theta 45;plottype 22;numpoints 49;axesstyle "normal";xis
\TEXUX{t};var1name \TEXUX{$x$};}}

\subsection{\ Related topics}

\begin{itemize}
\item  \hyperref{Plotting Curves and Surfaces}{}{}{DM6-1.tex#Plotting}

\item  \hyperref{Frame Properties}{}{}{DM6-2.tex#Frame Properties}

\item  \hyperref{The View for 2D Plots}{}{}{DM6-3.tex#View intervals}

\item  \hyperref{3D Plots of Functions and Expressions}{}{}{DM6-6.tex#3D
Plots}

\item  \hyperref{Exercises and Solutions}{}{}{DM6-7.tex#Exercises}
\end{itemize}

\rule{0.67in}{0.01in}

\hyperref{\FRAME{itbpF}{38.875pt}{24.5pt}{6pt}{}{}{index.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 38.875pt;height 24.5pt;depth
6pt;original-width 36.875pt;original-height 22.5625pt;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'index.wmf';file-properties
"XNPEU";}}}{}{}{DMIndex.tex#Math Index}\quad {\small Index entries: 
\hyperref{Curve fitting}{}{}{DMIndex.tex#Curves in space}, \hyperref{%
Envelopes}{}{}{DMIndex.tex#Envelopes}, \hyperref{Expressions}{}{}{%
DMIndex.tex#Expressions}, \hyperref{Implicit plots}{}{}{DMIndex.tex#Implicit}%
, \hyperref{Log and log log plots}{}{}{DMIndex.tex#Log and log log plots}, 
\hyperref{Parametric plots}{}{}{DMIndex.tex#Parametric plots}, \hyperref{%
Plotting}{}{}{DMIndex.tex#Plotting}, \hyperref{Polar coordinates}{}{}{%
DMIndex.tex#Polar coordinates}, \hyperref{Polygons}{}{}{DMIndex.tex#Polygons}%
, \hyperref{Statistics}{}{}{DMIndex.tex#Statistics}}

\end{document}
