{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "" -1 256 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 257 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 262 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 266 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 267 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 271 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 272 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 273 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 274 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 275 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 276 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 277 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Normal" -1 257 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {PARA 256 "" 0 "" {TEXT 266 63 "Precalculus Exploration 5: Int roduction to Sinusoidal Functions" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 257 "" 0 "" {TEXT -1 229 "Visual exploration of the combined plo t of different sinusoidal function, including function variation movie s (animations). The students should perform these explorations themsel ves in groups of two using Maple on the computers. " }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 25 "asin(bx + c) + \+ d, vary a." }}{EXCHG {PARA 0 "" 0 "" {TEXT 258 24 "Sine Functions: a*s in(x)" }}{PARA 0 "" 0 "" {TEXT 267 40 "Click in the red area and press [Enter]." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 614 "restart:\na:=1: # En ter the a in a*sin(bx + c) + d\nn:=5: # Enter n = the number of funct ions that you want of the form a*sin(x).\nxleft:=0:\nxright:=2*Pi:\nyb ot:=-n:\nytop:=n:\nf:=(a,b,c,d,x)->a*sin(b*x+c)+d:\nList:=[]:\nfor i f rom 1 to n do\nF[i]:=f(i*a,1,0,0,x):\np[i]:=plot(F[i],x=xleft..xright, y=ybot..ytop,color=blue):\nList:=[op(List),F[i]]:\nod:\nSinPlot1:=plot s[display](\n [seq(p[i],i=1..n)],\n labels=[``,``] ,\n tickmarks=[5,9],\n #view=[x_left..x_right,y_ve rtex-20..y_vertex+20],\n titlefont=[HELVETICA,DEFAULT,14],\n title=` Sine Functions: a*sin(x) Plot`):\nSinPlot1;\nop(List);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 259 30 "Sine Functions: a*sin(x) Movie" }{TEXT -1 1 "\n" }{TEXT 268 173 "Click in the red area and press [Enter].\nThen click on the plot \+ to see VCR type controls for the movie.\nYou should slow the movie dow n to about 3 fps using the [<<] control." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 951 "restart:\na:=1: # Enter the a in a*sin(bx + c) + d \nn:=5: # Enter n = the number of functions that you want of the form a*sin(x).\nxleft:=0:\nxright:=2*Pi:\nybot:=-n:\nytop:=n:\nf:=(a,b,c,d ,x)->a*sin(b*x+c)+d:\nList:=[]:\nfor i from 1 to n do\nF[i]:=f(i*a,1,0 ,0,x):\nif a >= 0 then\nTitle[i]:=`Sine Functions: `||i||`sin(x) Plot `:\nelif a < 0 then\nTitle[i]:=`Sine Functions: -`||i||`sin(x) Plot`: \nfi:\np[i]:=plot(F[i],x=xleft..xright,\n y=ybot..ytop, \n color=blue,\n titlefont=[HELVETICA,DEF AULT,14],\n title=Title[i]):\n#combp[i]:=plots[display]( [seq(p[j],j=1..i)]):\nList:=[op(List),F[i]]:\nod:\nSinPlot1Movie:=plot s[display](\n [seq(p[i],i=1..5)],\n insequence=tr ue,\n labels=[``,``],\n tickmarks=[5,9]\n \+ #view=[x_left..x_right,y_vertex-20..y_vertex+20]):\n #titlefont=[HE LVETICA,DEFAULT,14],\n #title=`Sine Functions: a*sin(x) Plot`\n):\nS inPlot1Movie;\nop(List);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 25 "asin(bx + c) + d, vary b." }}{EXCHG {PARA 0 "" 0 "" {TEXT 260 23 "Sine Functions: sin(bx)" }} {PARA 0 "" 0 "" {TEXT 270 40 "Click in the red area and press [Enter]. " }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 613 "restart:\nb:=1: # Enter the b in a*sin(bx + c) + d\nn:=2: # Enter n = the number of functions that you want of the form sin(bx).\nxleft:=0:\nxright:=2*Pi :\nybot:=-n:\nytop:=n:\nf:=(a,b,c,d,x)->a*sin(b*x+c)+d:\nList:=[]:\nfo r i from 1 to n do\nF[i]:=f(1,i*b,0,0,x):\np[i]:=plot(F[i],x=xleft..xr ight,y=ybot..ytop,color=blue):\nList:=[op(List),F[i]]:\nod:\nSinPlot2: =plots[display](\n [seq(p[i],i=1..n)],\n labels=[` `,``],\n tickmarks=[5,9],\n #view=[x_left..x_right ,y_vertex-20..y_vertex+20],\n titlefont=[HELVETICA,DEFAULT,14],\n ti tle=`Sine Functions: sin(b*x) Plot`):\nSinPlot2;\nop(List);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 261 29 "Sine Functions: sin(bx) Movie" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 274 173 "Click in the red area and press [Enter].\nThen \+ click on the plot to see VCR type controls for the movie.\nYou should \+ slow the movie down to about 3 fps using the [<<] control." }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 903 "restart:\nb:=1: # Enter th e b in a*sin(bx + c) + d\nn:=5: # Enter n = the number of functions t hat you want of the form sin(bx).\nxleft:=0:\nxright:=2*Pi:\nybot:=-n: \nytop:=n:\nf:=(a,b,c,d,x)->a*sin(b*x+c)+d:\nList:=[]:\nfor i from 1 t o n do\nF[i]:=f(1,i*b,0,0,x):\nif b >= 0 then\nTitle[i]:=`Sine Functio ns: sin(`||i||`x) Plot`:\nelif b < 0 then\nTitle[i]:=`Sine Functions: sin(-`||i||`x) Plot`:\nfi:\np[i]:=plot(F[i],x=xleft..xright,\n \+ y=ybot..ytop,\n color=blue,\n t itlefont=[HELVETICA,DEFAULT,14],\n title=Title[i]):\nLis t:=[op(List),F[i]]:\nod:\nSinPlot2Movie:=plots[display](\n [ seq(p[i],i=1..n)],\n insequence=true,\n labels=[` `,``],\n tickmarks=[5,9]\n #view=[x_left..x_right, y_vertex-20..y_vertex+20]):\n #titlefont=[HELVETICA,DEFAULT,14],\n # title=`Sine Functions: a*sin(x) Plot`\n):\nSinPlot2Movie;\nop(List); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 " " 0 "" {TEXT -1 25 "asin(bx + c) + d, vary c." }}{EXCHG {PARA 0 "" 0 " " {TEXT 262 26 "Sine Functions: sin(x + c)" }}{PARA 0 "" 0 "" {TEXT 271 40 "Click in the red area and press [Enter]." }{TEXT -1 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 704 "restart:\nc:=Pi/2:\nc2:=pi/2:\nn:= 1: # Enter n = the number of functions that you want of the form sin( x + c), c != 0.\nxleft:=-2*Pi:\nxright:=2*Pi:\nybot:=-2*n:\nytop:=2*n: \nf:=(a,b,c,d,x)->a*sin(b*x+c)+d:\nList:=[]:\nfor i from 0 to n do\nF[ i]:=f(1,1,c*i,0,x):\nF2[i]:=f(1,1,c2*i,0,x):\nif modp(i,2)=0 then\nsin color:=`red`:\nelse\nsincolor:=`blue`:\nfi:\np[i]:=plot(F[i],x=xleft.. xright,y=ybot..ytop,color=sincolor):\nList:=[op(List),F2[i]]:\nod:\nSi nPlot3:=plots[display](\n [seq(p[i],i=0..n)],\n la bels=[``,``],\n tickmarks=[5,9],\n #view=[x_left.. x_right,y_vertex-20..y_vertex+20],\n titlefont=[HELVETICA,DEFAULT,14] ,\n title=`Sine Functions: sin(x + c) Plot`):\nSinPlot3;\nop(List); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 263 32 "Sine Functions: sin(x + c) Movie" }{TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 275 173 "Click in the red area and press [Enter] .\nThen click on the plot to see VCR type controls for the movie.\nYou should slow the movie down to about 3 fps using the [<<] control." } {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1123 "restart:\nc:=Pi/2 :\nc2:=pi/2:\nn:=1: # Enter n = the number of functions that you want of the form sin(x + c), c != 0.\nxleft:=-2*Pi:\nxright:=2*Pi:\nybot:= -2*n:\nytop:=2*n:\nf:=(a,b,c,d,x)->a*sin(b*x+c)+d:\nList:=[]:\nfor i f rom 0 to n do\nF[i]:=f(1,1,c*i,0,x):\nF2[i]:=f(1,1,c2*i,0,x):\nif modp (i,2)=0 then\nsincolor:=`red`:\nelse\nsincolor:=`blue`:\nfi:\nctxt:=co nvert(evalf((i)*c,5),string);\nctxt:=``||ctxt;\nif length(ctxt) = 2 th en\nctxt:=``||ctxt||`0000`:\nfi:\nif evalf(c) >= 0 then\nTitle[i]:=`Si ne Functions: sin(x + `||ctxt||`) Plot`:\nelif evalf(c) < 0 then\nTit le[i]:=`Sine Functions: sin(x -`||ctxt||`) Plot`:\nfi:\np[i]:=plot(F[ i],x=xleft..xright,\n y=ybot..ytop,\n co lor=sincolor,\n titlefont=[HELVETICA,DEFAULT,14],\n \+ title=Title[i]):\nList:=[op(List),F2[i]]:\nod:\nSinPlot3Movi e:=plots[display](\n [seq(p[i],i=0..n)],\n insequ ence=true,\n labels=[``,``],\n tickmarks=[5,9]\n \+ #view=[x_left..x_right,y_vertex-20..y_vertex+20]):\n #titlef ont=[HELVETICA,DEFAULT,14],\n #title=`Sine Functions: a*sin(x) Plot` \n):\nSinPlot3Movie;\nop(List);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 25 "asin(bx + c) + d, va ry d." }}{EXCHG {PARA 0 "" 0 "" {TEXT 264 26 "Sine Functions: sin(x) + d" }}{PARA 0 "" 0 "" {TEXT 272 40 "Click in the red area and press [E nter]." }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 631 "restart: \nd:=1: # Enter the d in a*sin(bx + c) + d\nn:=4: # Enter n = the numb er of functions that you want of the form sin(x) + d, d != 0.\nxleft:= 0:\nxright:=2*Pi:\nybot:=-(n+1):\nytop:=n+1:\nf:=(a,b,c,d,x)->a*sin(b* x+c)+d:\nList:=[]:\nfor i from 0 to n do\nF[i]:=f(1,1,0,i*d,x):\np[i]: =plot(F[i],x=xleft..xright,y=ybot..ytop,color=blue):\nList:=[op(List), F[i]]:\nod:\nSinPlot1:=plots[display](\n [seq(p[i],i=0..n)], \n labels=[``,``],\n tickmarks=[5,9],\n \+ #view=[x_left..x_right,y_vertex-20..y_vertex+20],\n titlefont=[HELVET ICA,DEFAULT,14],\n title=`Sine Functions: sin(x) + d Plot`):\nSinPl ot1;\nop(List);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 265 33 "Sine Functions: sin(x) + d Movie " }}{PARA 0 "" 0 "" {TEXT 276 173 "Click in the red area and press [En ter].\nThen click on the plot to see VCR type controls for the movie. \nYou should slow the movie down to about 3 fps using the [<<] control ." }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 927 "restart:\nd:=1 : # Enter the d in a*sin(bx + c) + d\nn:=4: # Enter n = the number o f functions that you want of the form sin(x) + d, d != 0.\nxleft:=0:\n xright:=2*Pi:\nybot:=-(n+1):\nytop:=n+1:\nf:=(a,b,c,d,x)->a*sin(b*x+c) +d:\nList:=[]:\nfor i from 0 to n do\nF[i]:=f(1,1,0,i*d,x):\nif d >= 0 then\nTitle[i]:=`Sine Functions: sin(x) + `||i||` Plot`:\nelif d < \+ 0 then\nTitle[i]:=`Sine Functions: sin(x) - `||i||` Plot`:\nfi:\np[i ]:=plot(F[i],x=xleft..xright,\n y=ybot..ytop,\n \+ color=blue,\n titlefont=[HELVETICA,DEFAULT,14], \n title=Title[i]):\nList:=[op(List),F[i]]:\nod:\nSinPlo t4Movie:=plots[display](\n [seq(p[i],i=0..n)],\n \+ insequence=true,\n labels=[``,``],\n tickmarks=[5, 9]\n #view=[x_left..x_right,y_vertex-20..y_vertex+20]):\n # titlefont=[HELVETICA,DEFAULT,14],\n #title=`Sine Functions: a*sin(x) Plot`\n):\nSinPlot4Movie;\nop(List);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 34 "asin(bx + c ) + d, vary a, b, c, d." }}{EXCHG {PARA 0 "" 0 "" {TEXT 256 33 "Sine F unctions: a*sin(bx + c) + d" }}{PARA 0 "" 0 "" {TEXT 273 40 "Click in \+ the red area and press [Enter]." }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1043 "restart:\na:=1: # Enter the a in a*sin(bx + c) + d \nb:=3: # Enter the b in a*sin(bx + c) + d\nc:=0: # Enter the c in a *sin(bx + c) + d\nd:=-1: # Enter the d in a*sin(bx + c) + d\nk:=1: # \+ Enter k = the number of intervals of +2*Pi on the x-axis that you want .\nm:=5: # Enter m = the positive height of the y-axis that you want. \nn:=2: # Enter n = the number of new functions that you want differe nt from sin(x). \nxleft:=-2*k*Pi:\nxright:=2*k*Pi:\nybot:=-m:\nytop:= m:\nf:=(a,b,c,d,x)->a*sin(b*x+c)+d:\nList:=[]:\nfor i from 0 to n do\n #F[i]:=f(i*a,i*b,i*c,i*d,x):\nif i = 0 then\nF[i]:=f(1,1,0,0,x):\np[i] :=plot(F[i],x=xleft..xright,y=ybot..ytop,color=red):\nelse\nF[i]:=f(i* a,b,c,d,x):\np[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,color=blue): \nfi:\nList:=[op(List),F[i]]:\nod:\nSinPlot1:=plots[display](\n \+ [seq(p[i],i=0..n)],\n labels=[``,``],\n tickma rks=[5,9],\n #view=[x_left..x_right,y_vertex-20..y_vertex+20 ],\n titlefont=[HELVETICA,DEFAULT,14],\n title=`Sine Functions: a*s in(bx + c) + d Plot`):\nSinPlot1;\nop(List);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 257 39 "Sine Fu nctions Movie: a*sin(bx + c) + d" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 277 173 "Click in the red area and press [Enter].\nThen click on the plot to see VCR type controls for the movie.\nYou should slow the movie down to about 3 fps using the [<<] control." }{TEXT -1 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 1124 "restart:\na:=1: # Enter the a in a*sin(bx + c) + d\nb:=3: # Enter the b in a*sin(bx + c) + d\nc:=0: \+ # Enter the c in a*sin(bx + c) + d\nd:=-1: # Enter the d in a*sin(bx + c) + d\nk:=1: # Enter k = the number of intervals of +2*Pi on the x- axis that you want.\nm:=5: # Enter m = the positive height of the y-a xis that you want.\nn:=2: # Enter n = the number of new functions tha t you want different from sin(x). \nxleft:=-2*k*Pi:\nxright:=2*k*Pi: \nybot:=-m:\nytop:=m:\nf:=(a,b,c,d,x)->a*sin(b*x+c)+d:\nList:=[]:\nfor i from 0 to n do\n#F[i]:=f(i*a,i*b,i*c,i*d,x):\nif i = 0 then\nF[i]:= f(1,1,0,0,x):\np[i]:=plot(F[i],x=xleft..xright,y=ybot..ytop,color=red) :\nelse\nF[i]:=f(i*a,b,c,d,x):\np[i]:=plot(F[i],x=xleft..xright,y=ybot ..ytop,color=blue):\nfi:\ncombp[i]:=plots[display]([seq(p[j],j=0..i)]) :\nList:=[op(List),F[i]]:\nod:\nSinPlot1:=plots[display](\n \+ [seq(combp[i],i=0..n)],\n insequence = true,\n la bels=[``,``],\n tickmarks=[5,9],\n #view=[x_left.. x_right,y_vertex-20..y_vertex+20],\n titlefont=[HELVETICA,DEFAULT,14] ,\n title=`Sine Functions: a*sin(bx + c) + d Plot`):\nSinPlot1;\nop (List);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 37 "____________________ _________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 30 "Filename: ExplorePrecalc05.mws" }}{PARA 0 "" 0 "" {TEXT -1 36 "Copyright 2005, All Rights Reserved." }}{PARA 0 "" 0 "" {TEXT -1 44 "Permission is granted to use and modify for " }}{PARA 0 "" 0 " " {TEXT -1 37 "academic and non-commercial purposes." }}{PARA 0 "" 0 " " {TEXT -1 13 "Dr. John Pais" }}{PARA 0 "" 0 "" {TEXT -1 28 "Mathemati cs Department-MICDS" }}{PARA 0 "" 0 "" {TEXT -1 45 "E-mail: pais@micds .org or pais@kinetigram.com" }}{PARA 0 "" 0 "" {TEXT -1 33 "URL: http ://kinetigram.com/micds" }}{PARA 0 "" 0 "" {TEXT -1 37 "______________ _______________________" }}}{MARK "8" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }