{VERSION 5 0 "IBM INTEL NT" "5.0" } {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 "" 0 1 0 128 0 1 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 257 "" 0 1 0 128 0 1 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 128 128 128 1 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 128 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 128 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 0 1 0 0 128 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 128 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 263 "" 0 1 0 0 128 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 128 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 128 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 266 "" 0 1 0 0 128 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 0 1 0 0 128 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 268 "" 0 1 0 0 128 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 269 "" 0 1 0 128 128 1 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 270 "" 0 1 0 128 128 1 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 271 "" 0 1 0 128 128 1 0 0 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 "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 }} {SECT 0 {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 257 55 "High School Modul es > Trigonometry by Gregory A. Moore " }}{PARA 3 "" 0 "" {TEXT -1 4 " " }{TEXT 256 34 "Visualizing Inverse Trig Functions" }}{PARA 0 "" 0 "" {TEXT -1 66 "\nA graphic view of what the inverse trig functions \+ are computing.\n" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 32 " 1. Visualizi ng the Inverse Sine" }}{PARA 0 "" 0 "" {TEXT -1 1 "\n" }{TEXT 269 118 "[ Execute the code resource section. Although there will be no output immediately, these definitions are used below.]\n" }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 970 "restart: with(plots):\narcsinplot := proc( \+ asin)\n local A,B,C,E,F,G, H,J, theta, c1, c2, c3;\n theta := arcs in(asin);\n c1 := COLOR(RGB, 1, .75, .2 );\n c2 := COLOR(RGB, .7, \+ .4, .1);\n c3 := COLOR(RGB, 1, .2, .1);\n A := plot(sin(x), x = - Pi..Pi, color = c3, tickmarks = [1,1]);\n B := plot(sin(x), \+ x = -Pi/2..Pi/2, color = c2, thickness = 4);\n C := polygonplot( [[-Pi/2,-1],[Pi/2,-1],[Pi/2,1],[-Pi/2,1],[-Pi/2,-1]], \n \+ color = c1, style = patchnogrid );\n E := plot( [[-Pi/2,-1],[Pi/ 2,-1],[Pi/2,1],[-Pi/2,1],[-Pi/2,-1]], \n color = orang e, linestyle = 3);\n F := plottools[arrow]( [0,asin], [theta, asin] , .05, .10, .15, \n color = red);\n G := plottools[arrow]( \+ [theta,asin], [theta, 0],.10,.20,.10, \n color = red);\n H : = textplot([theta, -.15, evalf(theta,3)],align=\{ABOVE, CENTER\});\n \+ J := textplot([ -.2, asin, evalf(asin, 3)],align=\{ABOVE, LEFT\}); \ndisplay([F,G,A,B,C,E,H,J ]);\nend proc:" }}}{PARA 0 "" 0 "" {TEXT 267 25 " \n Example 1.1" }{TEXT -1 24 ": Compute arcsin( 0. 5 )\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "arcsinplot( .5);\na rcsin( .5 );" }}}{PARA 0 "" 0 "" {TEXT -1 1 "\n" }}{PARA 0 "" 0 "" {TEXT 265 23 " Example 1.2" }{TEXT -1 25 ": Compute arccsin ( 0.9 )\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "arcsinplot(.9); \narcsin( .9);" }}}{PARA 0 "" 0 "" {TEXT -1 1 "\n" }}{PARA 0 "" 0 "" {TEXT 266 24 " Example 1.3 " }{TEXT -1 26 ": Simplify arcsi n( -0.3).\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "arcsinplot(-. 8);\narcsin(-.8);" }}}{PARA 0 "" 0 "" {TEXT -1 1 "\n" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 34 " 2. Visualizin g the Inverse Cosine" }}{PARA 0 "" 0 "" {TEXT -1 1 "\n" }{TEXT 270 118 "[ Execute the code resource section. Although there will be no ou tput immediately, these definitions are used below.]\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 942 "restart: with(plots):\narccosplot \+ := proc( acos )\n local A,B,C,E,F,G, H,J, theta, c1, c2, c3;\n the ta := arccos(acos);\n c1 := COLOR(RGB, .6, .6, .85 );\n c2 := COLO R(RGB, .3, .4, .87);\n c3 := COLOR(RGB, .1, .2, .6);\n A := plot( cos(x), x = -Pi/2..3*Pi/2, color = c3, tickmarks = [0,0]);\n B := p lot(cos(x), x = 0..Pi, color = c2, thickness = 4);\n C := polyg onplot( [[0,-1],[Pi,-1],[Pi,1],[0,1],[0,-1]], \n color \+ = c1, style = patchnogrid );\n E := plot( [[0,-1],[Pi,-1],[Pi,1],[0 ,1],[0,-1]], \n color = navy, linestyle = 3);\n F : = plottools[arrow]( [0,acos], [theta, acos], .05, .10, .15, \n \+ color = navy);\n G := plottools[arrow]( [theta,acos], [theta, 0], .10, .20, .18, \n color = navy);\n H := textplot([theta, -. 15, evalf(theta,3)], align=\{ABOVE, CENTER\});\n J := textplot([ - .2, acos, evalf( acos, 3)],align=\{ABOVE, LEFT\});\ndisplay([A,B,E,F, G,C,H,J ]);\nend proc:" }}}{PARA 0 "" 0 "" {TEXT -1 2 "\n\n" }{TEXT 262 23 " Example 2.1" }{TEXT -1 24 " : Compute arccos(0.3). \n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "arccosplot(.3);\narcco s(.3);" }}}{PARA 0 "" 0 "" {TEXT -1 121 "\nNoticethe difference betwee n what happens when we compute arcsine of a negative number and the ar ccosine of a negative.\n" }}{PARA 0 "" 0 "" {TEXT 264 24 " \+ Example 2.2 " }{TEXT -1 25 ": Compute arccos( -0.6).\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "arccosplot(-.6);\narccos(-.6);" }}} {PARA 0 "" 0 "" {TEXT -1 1 "\n" }}{PARA 0 "" 0 "" {TEXT 263 23 " \+ Example 2.3" }{TEXT -1 23 ": Compute arccos(0.8).\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "arccosplot(.8);\narccos(.8);" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 35 " 3. Visualizing the Inverse Tangent" }}{PARA 0 "" 0 "" {TEXT -1 1 "\n " }{TEXT 271 118 "[ Execute the code resource section. Although there \+ will be no output immediately, these definitions are used below.]\n" } {TEXT -1 1 "\n" }{TEXT 261 2 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1011 "restart: with(plots):\narctanplot := proc( a)\n local A,B, C,E,F,G, H,J, theta, c1, c2, c3, L,R,m;\n theta := arctan(a); \+ L:= -Pi/2 + .01; R:= Pi/2 - .01; m := 12;\n c1 := COLOR(RGB, .75, 95, .75 );\n c2 := COLOR(RGB, .4, .9, .4);\n c3 := COLOR(RGB, .2 , .5, .2);\n A := plot(tan(x), x = -Pi..Pi, y = -m..m, color = c3, \n tickmarks = [1,1], discont = true);\n B := plot(ta n(x), x = L..R, y = -m..m, color = c2, thickness = 4);\n C := poly gonplot( [[L,-m],[R,-m],[R,m],[L,m],[L,-m]], \n color = c1, style = patchnogrid );\n E := plot( [[L,-m],[R,-m],[R,m],[L,m] ,[L,-m]], \n color = green, linestyle = 3);\n F := \+ plottools[arrow]( [0,a], [theta, a], .4, .6, .15, \n color = c 3);\n G := plottools[arrow]( [theta,a], [theta, 0],.08,.15,.15, \n \+ color = c3);\n H := textplot([theta, -.8, evalf(theta,3)],a lign=\{ABOVE, CENTER\});\n J := textplot([ -.2, a, evalf(a, 3)] ,align=\{ABOVE, LEFT\});\ndisplay([F,G,A,B,C,E,H,J ]);\n\nend proc:" } }}{PARA 0 "" 0 "" {TEXT 268 26 " \n\n\n Example 3.1" }{TEXT -1 26 " : Compute arctan(4.5).\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "arctanplot(4.5);\narctan(4.5);" }}}{PARA 0 "" 0 "" {TEXT -1 2 "\n\n" }{TEXT 260 23 " Example 3.2" }{TEXT -1 24 " : Compute arctan( 10).\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "arctanplot(10);\narctan( 10);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 1 "\n" }{TEXT 259 23 " Example 3 .3" }{TEXT -1 24 " : Simplify arctan(-6).\n" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 27 "arctanplot(-6);\narctan(-6);" }}}{EXCHG }{EXCHG } {PARA 0 "" 0 "" {TEXT -1 2 "\n " }}}{PARA 0 "" 0 "" {TEXT 258 40 " \n \+ \251 2002 Waterloo Maple Inc" }}}{MARK "0 1" 37 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }