{VERSION 2 3 "SGI IRIS UNIX" "2.3" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 }{CSTYLE "
" -1 256 "" 1 24 0 0 0 0 1 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 
0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 
0 0 0 0 }{CSTYLE "" -1 259 "" 1 24 0 0 0 0 0 0 1 0 0 0 0 0 0 }{PSTYLE 
"Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 
0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" 
-1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 
}{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 
0 0 0 0 }0 0 0 -1 4 4 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" 
-1 -1 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 
0 }{PSTYLE "" 3 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {PARA 256 "" 0 "" {MPLTEXT 0 21 0 "" }}{PARA 257 "" 0 "" 
{TEXT 256 15 "Calculus Lab 5\n" }{TEXT 259 39 "Parametric curves and p
olar coordinates" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 4 "
" 0 "" {TEXT -1 207 "Parametric plots:\nCalling Sequence:\n   plot([x(
t),y(t),t=range of t], h, v, options)\nParameters:\n   h           - h
orizontal range\n   v           - vertical range\n   [x, y, range] - p
arametric specifications" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "
plot([sin(t),cos(t),t=0..Pi],\nscaling=constrained, thickness=2);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "plot( [(t^2-1)/(t^2+1),2*t/(
t^2+1), t=-infinity..infinity],\nscaling=constrained, thickness=2);" }
}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 27 "Plots in polar coordinates:" }
}{PARA 3 "" 0 "" {TEXT -1 268 "Calling Sequence:\n   plot([r(t),theta(
t),t=range of t ], h, v, coords=polar)\nParameters:\n   r(t)     - the
 distance from the origin as a function of t\n   theta(t) - the angle \+
of rotation in terms of t\n   h        - the horizontal range\n   v   \+
     - the vertical range" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 
"plot([t^2,t,t=0..3*Pi],-8..8,-10..10,coords=polar,\nscaling=constrain
ed, thickness=2);" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 8 "Compare:" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "plot([t,t,t=0..3*Pi],-8..8,-
10..10,coords=polar,\nscaling=constrained, thickness=2);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "plot([t,t,t=0..3*Pi],-8..8,-10..10,
\nscaling=constrained, thickness=2);" }}}}{PARA 0 "" 0 "" {TEXT 257 
188 "\nExplain the difference between the last two plots? Write the an
swer here:\n..........................................................
......................................................." }}}{SECT 0 
{PARA 3 "" 0 "" {TEXT -1 37 "Plot the unit circle as a polar plot." }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "?" }}}}{SECT 0 {PARA 3 "" 0 "
" {TEXT -1 101 "Here is a general animation routine that plots a param
etric curve x=f(t), y=g(t), t=a..b, by tracing:" }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 221 "paint:=(x,y,a,b)->display(\{\nanimate(\n[x(t)*u,y(t)
*u,u=0..1], t=a..b,\ncolor=magenta,frames=30),\nanimate(\n[x(t*u),y(t*
u),u=0..1], t=a..b,numpoints=300,\ncolor=blue,frames=30)\n\}, \nthickn
ess=3, axes=none, scaling=constrained):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "paint(cos,sin,0,Pi);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 31 "f:=t->sin(2*t):\ng:=t->sin(3*t):" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 18 "paint(f,g,0,2*Pi);" }}}{SECT 0 {PARA 4 "" 0 
"" {TEXT -1 78 "Animate the Lissajous curve with f and g redefined wit
h sin(5*t) and sin(9*t):" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "?
" }}}}{PARA 0 "" 0 "" {TEXT -1 1 "\n" }{TEXT 258 71 "What is the diffe
rence in paint between the first and second animation?" }}{PARA 0 "" 
0 "" {TEXT -1 143 "...................................................
......................................................................
......................" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 65 "Plot a
 curve r=f(t) in polar coordinates. Here are some examples:" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "plot([sin(8*t/5),t,t=0..10*Pi],coor
ds=polar,\nscaling=constrained, thickness=2);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 90 "plot([sin(t)+(sin(5*t/2))^3,t,t=0..4*Pi],\ncoord
s=polar,\nscaling=constrained, thickness=2);" }}}{SECT 0 {PARA 4 "" 0 
"" {TEXT -1 66 "Plot the following curves:\nr=sin(t/2), r=t*sin(t), r=
1+4*cos(5*t):" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "?" }}}}}}
{MARK "7 3 1 0 0" 0 }{VIEWOPTS 1 1 0 3 2 1804 }