ZXTape! 0Created with Ramsoft MakeTZXTRIG 1  o  N0:0:0::236099\,502:0:0:0 q$="y"x -z$="  " K12 ,10 ;1;4;"PLEASE WAIT";0;0 "" .a=07:a,0;1;z$:a (H12 ,6;4;1;" LOADING PROGRAM ";:0 -*18,5;" " .13 ,0; / 0 2 "file" <*:15,0;"Leave tape running" F"" P*15,0;"Stop and rewind tape" R"clear (y/n) ?";q$ Tq$="y""address ? ";x ZJ17,0;"Type in file name in ";1;"UPPER CASE";0 n"Filename",a$ o015,0;"Recording " p517,0;" " x a$10 "logo"16384@,2304  '10 ,5;"Load main program" )12 ,5;"SAVE""file"" LINE 2" Z&  QnATRIG 1%logo @ ??80?߀????>?#|?~???|?|~?8???1???<???????<?0~|??~?~|?|~?>??#???8??????1???????~<?|??|~?|?|~?|?|~???9??>?? ?????8<0p??>?x?~file T7&7Z'V7 Kpcl=400:cls=150:str=100d:cll=165:nin=200 ha=07:b:"a"+a,b:a:24,36$,36$,24,0,0,0,0 280:0:0:0:0:7: F 500 d**** str **** n30:.3,10 xN1;21,31;8;9 ;"*":30:=""120x #21,31;8;" ": **** cls **** u=0:v=21 **** cll **** str Bf=vu-1:f,0;" ":f  **** nin **** 30:.3,30 z=0:z$="":fs=0 ,21,z;4;0;1;"N" 2 4a$=:a$=13 z=1fs=1250 a$=12 340T ta$=13 z0a=z$:.05|L,20:21,0;0;" ": &a$<46.ůa$>579230 "a$=47/230 ,$fs=1Ưa$=46.230 6z=31230 @a$=46.fs=1 JN4;0;21,z;a$:.05|L,20:z=z+1:380| Tz=0230 ^a$=12 z>021,z-1;1;4;0;"N":21,z;0;" ":.05|L,20:z$(z)=46.fs=0 h#z=z-1:z$=z$(z):230 | z$=z$+a$  230 **** pcl **** str =f=vu-1:f,15;0;" ":f  5:36$,132:191,0:0,-47/:-191,0:0,47/:6:6,5;"I N T R O D U C T I O N";8,15;"T O";10 ,5;"T R I G O N O M E T R Y" /15,11 ;3;"LESSON ONE":cls 6;7,1;"In this study pack we are goingto explore the basic ideas oftrigonometry by first looking athow the coordinates of the endP, of a line segment OP, changeas OP turns about O.":cls 5:2,15;" We start with a";3,15;"unit vector OP,";4,15;"which is a line";5,15;"whose length is";6,15;"1 unit." m4;9 ,7;"O";4;9 ,13 ;"P":7:58:,107k:491,0 zstr:6:9 ,15;"O is fixed, and";10 ,15;"we make OP turn";11 ,15;"about O." $9 ,13 ;" " L27:1:n=02*ͧ/30 V-58:,107k:502*n,502*n [(-n)<.01z# =1200 `-58:,107k:502*n,502*n jn t>0:4;9 ,7;"O";9 ,13 ;"P" ~ 1250 5:0:14,15;"As OP rotates,";15,15;"you can see it";16,15;"turning through";17,15;"an ANGLE.":1:7:1120` cls m4;9 ,7;"O";4;9 ,13 ;"P":7:58:,107k:491,0 j6:105i,107k:10 ,0:-3,3:115s,107k:-3,-3 8,15;"x"  7:3,15;" We can measure";4,15;"this angle if we";5,15;"first draw in a";6,15;"fixed line Ox." str w5:11 ,15;"We can measure";12 ,15;"the angle xOP as";13 ,15;"OP turns." #821,9 ;7;1;"Angle xOP = 0 " &9 ,13 ;" " (27:1:n=02*ͧ/30 2-58:,107k:502*n,502*n 4M0;1;7;21,21;n*(360h/(2*));"" 7 2 <-58:,107k:502*n,502*n F,58:+20*n,107k+20*n Pn Z 0 dm4;9 ,7;"O";4;9 ,13 ;"P":7:58:,107k:491,0 n06:105i,107k:10 ,0 x 10 : Q4:18,15;"Next we will draw";19,15;"axes.":cls U7:4,107k:112p,0:62>,502:0,114r >y=5791575:61=,y:2,0:y ?x=12 112p5:x,106j:0,2:x b3:9 ,0;"-1";9 ,14;"1";2,8;"1";14,8;"-1" \8,7;6;"O";2;0,7;"y";2;8,15;"x" 5:12 ,15;" Now we can see";13 ,15;"what happens to";14,15;"the coordinates";15,15;"(x,y) of P as OP";16,15;"turns." u=12 :v=21:pcl 4:12 ,15;" As angle xOP";13 ,15;"increases to 90,";14,15;"x decreases from";15,15;"1 to 0, while y";16,15;"increases from 0";17,15;"to 1." str H20,0;1;7;" Angle xOP= x=0.00 y=0.00 " 47:1:n=0.51\)*ͧ/60<  5000 3;2,8;"1" ,#0:0:v=19:pcl 67:12 ,15;" As angle xOP";13 ,15;"rises above 90,so";14,15;"x continues to";15,15;"decrease to -1,";16,15;"and now y";17,15;"decreases from 1";18,15;"to 0." @2str:7:1:n=.5*̧ͧ/60< J 5000 ^pcl h6:12 ,15;" When xOP is more";13 ,15;"than 180, x";14,15;"increases, but y";15,15;"continues from 0";16,15;"to -1." r3str:7:1:n=̧*1.5@ͧ/60< | 5000 &1;20,18;"0 "  3;9 ,0;"-1" pcl 5:12 ,15;" From 270, x";13 ,15;"continues to";14,15;"increase to 1,";15,15;"while y starts to";16,15;"go from -1 to 0." ;str:7:1:n=1.5@*2*ͧ/60<  5000 &1;20,26;"0 " @3;9 ,14;"1";3;14,8;"-1" pcl q4:13 ,15;" Do you want to";14,15;"see that again?";15,15;"(Y/N)" ="n"Ŧ="N"1900l ;="y"Ŧ="Y"u=0:v=21:180:1420 0 1810 l#u=12 :v=19:420 v5:12 ,15;" Let us explore";13 ,15;"the relationship";14,15;"between the angle";15,15;"xOP and the";16,15;"coordinates of P";17,15;"a little further." pcl 6:13 ,15;" If the angle is";14,15;"between 0 and";15,15;"90, then both x";16,15;"and y are posi-";17,15;"tive." pcl r7:14,15;" Enter an angle";15,15;"between 0 and";16,15;"90." ,nin:a<0a>90Zaɺa1960  5100 pcl v4:14,15;" Enter another";15,15;"angle between 0";16,15;"and 90." ,nin:a<0a>90Zaɺa2000 5100:pcl 6:12 ,15;" If the angle is";13 ,15;"between 90 and";14,15;"180, x is";15,15;"negative and y is";16,15;"still positive." xpcl:7:14,15;" Enter an angle";15,15;"between 90 and";16,15;"180." .nin:a<90Za>180aɺa2040 5100:pcl  w4:14,15;" Enter another";15,15;"angle between 90";16,15;"and 180." .nin:a<90Za>180aɺa2070  5100:pcl *5:12 ,15;" If the angle is";13 ,15;"between 180 and";14,15;"270, both x and";15,15;"y are negative." 4pcl Hs7:14,15;" Enter an angle";15,15;"between 180 and";16,15;"270." R/nin:a<180a>270aɺa21004 \5100:pcl f|6:14,15;" Enter another";15,15;"angle between";16,15;"180 and 270." p/nin:a<180a>270aɺa2160p z5100:pcl 4:12 ,15;" If the angle is";13 ,15;"between 270 and";14,15;"360, x is";15,15;"positive and y is";16,15;"negative." pcl s7:14,15;" Enter an angle";15,15;"between 270 and";16,15;"360." /nin:a<270a>360haɺa2230 5100:pcl |6:14,15;" Enter another";15,15;"angle between";16,15;"270 and 360." /nin:a<270a>360haɺa2260 5100:pcl 5:12 ,15;" Now you can do";13 ,15;"some work.Use the";14,15;"special worksheet";15,15;"1, which shows";16,15;"axes like those";17,15;"here.":pcl 6:12 ,15;" On it draw unit";13 ,15;"vectors OP for";14,15;"the angles XOP in";15,15;"the following";16,15;"exercise.":pcl `4:10 ,15;"You will be given";11 ,15;"an angle. Draw OP";12 ,15;"and read off the";13 ,15;"x and y coord-";14,15;"inates of P. Type";15,15;"in your x and y,";16,15;"and the computer";17,15;"will check your";18,15;"answers."  r=0 $cls:4;5,0;" When entering x and y values inthe following exercise, thecomputer will automatically puta ~-~ sign at the start of anegative answer, so you shouldonly type the number.":cls .U7:4,107k:112p,0:62>,502:0,114r 8>y=5791575:61=,y:2,0:y B?x=12 112p5:x,106j:0,2:x Lb3:9 ,0;"-1";9 ,14;"1";2,8;"1";14,8;"-1" V\8,7;6;"O";2;0,7;"y";2;8,15;"x" H1:7:20,0;" Angle xOP= x=0.00 y=0.00 " 1:7:sc=0 j=15 20,1;0;3;"Question ";j an=(*361i) k20,11 ;" ";20,11 ;an;"";20,18;" ";20,26;" " B20,18;("-"(an>90Zan<270));1;"?" nin:a>12590 (20,18;("-"(an>90Zan<270));(100d*(a+.005y# =))/100d:a2=a:an>90Zan<270a2=-a2-.005y# = 2C20,26;("-"(an>180an<360h));1;"?" <nin:a>12620< FO20,26;("-"(an>180an<360h));(a*100d)/100d K,an>180an<360ha=-a-.005y# = Md5:62>,107k:502*(2**an/360h),502*(2**an/360h) P(a2-(((an*/180))*100d)/100d)<.02{# =ƽ(a-(((an*/180))*100d)/100d)<.02{# =0;5;15,20;"CORRECT!":sc=sc+1:u=12 :v=19:pcl:j Z14,19;0;4;"INCORRECT!";16,15;"The answers are:";17,18;"x=";(((an*/180))*100d)/100d;18,18;"y=";(((an*/180))*100d)/100d d u=12 :v=19:pcl:j Z6:0:14,15;"You scored ";sc;" out";15,21;"of 5." sc<3r=04;17,15;"You need to try";18,15;"another exercise.":r=1:cls:2350. cls 6:5,0;" Now try exercise 1 in thebooklet. Be sure to check youranswers as this is an importantexercise, and you will need youranswers for lesson 2." cls:9000(# $0:0  -62>,107k:502*n,502*n an=n*(360h/(2*)):0:1:7:20,11 ;an;"";20,18;" ";20,18;(((an*/180))*100d)/100d;20,26;" ";20,26;(((an*/180))*100d)/100d 61:62>,107k:502*n,502*n n 0:0  a1=2**a/360h 85:62>,107k:502*a1,502*a1 1:7:20,11 ;" ";20,11 ;a;"";20,18;" ";20,18;(((a*/180))*100d)/100d;20,26;" ";20,26;(((a*/180))*100d)/100d ( 0: #(20,11 ;5;1;"LESSON ONE" #285,1;6;"That completes Lesson One." #<6;7,1;"If you would like to go over"'" Lesson One again, ";10 ,13 ;2;6;"PRESS R":'" otherwise:-";12 ,13 ;6;1;"PRESS S" #F=""9030F# #P="R"Ŧ="r"5 #Z="S"Ŧ="s"9100# #d 9030F# #"u=0:v=21:180 #5,0;5;" When you are ready to begin thenext lesson, type NEW followedby-"'';7;1;9 ,10 ;"LOAD ~TRIG2~" #23636T\,255: & 5 &"file"9899&: '"" cltdlibuvTRIG2 #&#(##<str=100d:cls=150:cll=165:nin=200 ha=07:b:"a"+a,b:a:24,36$,36$,24,0,0,0,0 20:0:7: F 500 d**** str **** n30:.3,10 xN1;21,31;8;9 ;"*":30:=""120x #21,31;8;" ": **** cls **** u=0:v=21 **** cll **** str Bf=vu-1:f,0;" ":f  **** nin **** 30:.3,30 z=0:z$="":fs=0 ,21,z;4;0;1;"N" 2 4a$=:a$=13 z=1fs=1250 a$=12 340T  oa$=13 z=0a=0:.05|L,20:21,0;" ": ka$=13 z0a=z$:.05|L,20:21,0;" ": &a$<46.ůa$>579230 "a$=47/230 ,$fs=1Ưa$=46.230 6z=31230 @a$=46.fs=1 JN4;0;21,z;a$:.05|L,20:z=z+1:380| Tz=0230 ^a$=12 z>021,z-1;1;4;0;"N":21,z;" ":.05|L,20:z$(z)=46.fs=0 h#z=z-1:z$=z$(z):230 | z$=z$+a$  230 5:36$,132:191,0:0,-47/:-191,0:0,47/:6:6,5;"I N T R O D U C T I O N";8,15;"T O";10 ,5;"T R I G O N O M E T R Y" *3;14,11 ;"LESSON TWO" cls U7:4,107k:112p,0:62>,502:0,114r >y=5791575:61=,y:2,0:y &?x=12 112p5:x,106j:0,2:x 0b3:9 ,0;"-1";9 ,14;"1";2,8;"1";14,8;"-1" :\8,7;6;"O";2;0,7;"y";2;8,15;"x" D5:1,15;" In exercise one,";2,15;"you drew unit";3,15;"vectors OP at 10";4,15;"intervals." Istr N n=0̧*2ͧ/18 X-62>,107k:502*n,502*n bn lstr v4:12 ,15;" From this you";13 ,15;"made up a table";14,15;"showing the angle";15,15;"xOP and the co-";16,15;"ordinates x and y";17,15;"of P." cls 3:43+,171:144,0:0,-168:-144,0:0,168:43+,147:144,0:91[,171:0,-168:139,171:0,-168 f6:1,6;"Angle";2,7;"xOP";1,13 ;"x";1,19;"y"  5 f=016010 *(f/10 )+4,10 -f;f;"" *yv=(f*/180):xv=(f*/180) *f>90Zf<270xv=xv-.005y# = *f<90Zf>270xv=xv+.005y# = f>180xv=xv-.005y# = f<180xv=xv+.005y# = <xv=(xv*100d)/100d:yv=(yv*100d)/100d f=90Zyv=1 0(f/10 )+4,12 +(xv0);xv 0(f/10 )+4,18+(yv0);yv f cls  3:43+,171:144,0:0,-168:-144,0:0,168:91[,171:0,-168:139,171:0,-168  5  f=170360h10  +(f/10 )-16,10 -f;f;"" *Xxv=((f*/180)*100d)/100d:yv=((f*/180)*100d)/100d 41(f/10 )-16,12 +(xv0);xv >1(f/10 )-16,18+(yv0);yv Hf Rcls 7:3,0;" Within the table of valuesthere is a pattern. As angle xOPincreases so x decreases from 1through 0 to -1 and then backagain. Meanwhile, y increasesfrom 0 to 1 then back through 0to -1 and back to 0 again." 4:11 ,0;" When in mathematics we see apattern between two sets ofnumbers, we like to make itclearer by drawing a graph." U5:16,0;" In this case a graph of x or yagainst the angle xOP." cls y3:5,0;" First we look at the way xchanges as the angle xOPincreases from 0 to 360." cls }6:0,122z:250,0:f=428+36$*66:f,121y:0,2:f f28,175:0,-106j:f=72H1725:27,f:2,0:f Pf=2828+36$*6546:f,120x:0,4:f K3:0,2;"1";13 ,1;"-1";7,2;"0" 17,4;" 90 180 270 360" v4:16,0;" We begin by drawing axes forthe angle xOP from 0 to 360,and for x from 1 to -1." u=16:cll u6:16,0;" Now we plot the points (anglexOP,x) using the table made upfrom the last lesson." cll ?3:17,0;"When angle xOP is 0, x is 1.00." &x1=28:y=172:5000 $cll .?3:17,0;"When angle xOP is 10,x is 0.98." 8Ix1=34":y=((10 */180)*502)+122z:5000 Bcll L?3:17,0;"When angle xOP is 20,x is 0.94." VIx1=40(:y=((20*/180)*502)+122z:5000 `cll jf5:16,0;" Now use your table and enterthe value of x for the angle xOPshown." tcll yE1;7;20,1;" Angle xOP = x = " ~x=30360h10 ,1;7;20,14;x;"" Bx>90Zx<2701;7;20,24;"-" nin:a>11180 a>0a=a+.005y# = a<0a=a-.005y# = ^1;7;20,24;("-"(x>90Zx<270));(a*100d)/100d x>90Zx<270a=-a U(a-(x*/180))<.01z# =16,20;3;"Correct!":1210 W.3,0:2;18,1;"Wrong. The correct value is-":10 xx=(x*/180) xx>0xx=xx+.005y# = xx<0xx=xx+.005y# = [1;20,24;" ";6;20,24;(xx*100d)/100d Sx1=x/10 *6+28:y=(x*/180)*502+122z:5000 6v=19:cll:20,24;1;" " x i4:16,0;" Now we join the points with asmooth curve.":u=16:v=21:cll b7:x=0360h:x/10 *6+28,(x*/180)*502+122z:x str R3:14,14;"Graph of x against";15,14;"angle xOP." u=16:v=21:cll 5:17,0;" Turn to exercise 2 in yourworkbook and using your table,draw a graph of y against anglexOP on worksheet 2."  cll M7:17,0;" Press ENTER to see the graph ofy against xOP." cls (}6:0,122z:250,0:f=428+36$*66:f,121y:0,2:f 2f28,175:0,-106j:f=72H1725:27,f:2,0:f 579230 "a$=47/230 ,$fs=1Ưa$=46.230 6z=19230 @a$=46.fs=1 JN4;0;21,z;a$:.05|L,20:z=z+1:380| Tz=0230 ^a$=12 z>021,z-1;1;4;0;"N":21,z;" ":.05|L,20:z$(z)=46.fs=0 h#z=z-1:z$=z$(z):230 | z$=z$+a$  230 **** pcl **** str 7f=vu-1:f,0;" ":f  5:36$,132:191,0:0,-47/:-191,0:0,47/:6:6,5;"I N T R O D U C T I O N";8,15;"T O";10 ,5;"T R I G O N O M E T R Y" ,3:14,10 ;"LESSON THREE" cls  5000 c5:17,0;" In Lesson Two the computer drewthe graph of x against anglexOP." &u=16:v=21:cll 0m2:x=0360h2:28+x*216/360h,(x*/180)*502+122z:x :R6:17,0;" Then you drew the graph of yagainst angle xOP." Dcll Nm5:x=0360h2:28+x*216/360h,(x*/180)*502+122z:x Xj4:17,0;" They show a definite patternwhich you may have noticed fromthe tables." bcll l7:14,0;" If you only had the part of thegraph or table between 0 and90, you could draw the rest ofthe graph or make out the restof the table to 360 by copyingthe first part, but in differentpositions or with differentsigns." vu=14:cll ?3:17,0;"Let's look at that more closely." cls  5000 l2:x=090Z2:28+x*216/360h,(x*/180)*502+122z:x 6:15,0;" For the x curve, to draw thepart that goes from 90 to 180,you draw the same curve butstarting from (180,-1) and goingback to 90." u=15:cll o2:x=18090Z-2:28+x*216/360h,(x*/180)*502+122z:x h7:17,0;" The curve from 180 to 270 isthe same as the first part butnegative." cll o2:x=1802702:28+x*216/360h,(x*/180)*502+122z:x Z5:17,0;" And the last part we get bydrawing back from (360,1)." cll q2:x=360h270-1:28+x*216/360h,(x*.01745{Mj)*502+122z:x 4:16,0;" We can use this to help uswrite down the values of x whenangle xOP is greater than 90 byusing the table for 0 to 90."  cls  5200P  T4;17,0;" First a table for"'"angle xOP from 0 to"'"90." *83:1,22;"xOP";1,27;"x" 4 5 >x=090Z5 H'2+x/5,24-x;x;"" RE2+x/5,26;((x*/180)*100d)/100d \x fu=16:pcl p=6:17,0;" Then a sketch of the"'"curve."  5300 m2:f=0360h2:10 +f*140/360h,(f*/180)*30+135:f pcl D5:12 ,0;"First, angles between"'"90 and 180." u=10 :pcl 4:12 ,0;" When we drew the"'"graph for that part"'"of the x - axis, we"'"worked back from"'"180." pcl ʪ7:10 ,0;" That implies that we"'"should subtract the"'"angle whose x value"'"we want from 180,"'"and look up that"'"angle in the table." str t4:17,0;" Don't forget x is"'"negative, so put a"'"minus sign in front"'"of the value." u=10 :pcl base=90Z:6000p E5:13 ,0;" Now angles between"'"180 and 270." u=10 :pcl 6:13 ,0;" When we drew the"'"graph for that part"'"of the x - axis, we"'"worked from 180"'"forwards." pcl $4:10 ,0;" That implies that we"'"should subtract 180"'"from the angle whose"'"x value we want, and"'"look up that angle in"'"the table." .str 8t7:17,0;" But again x is"'"negative, so we put a"'"minus sign in front"'"of the value." Bpcl Lbase=180:6000p VE5:13 ,0;" Now angles between"'"270 and 360." `u=10 :pcl j6:13 ,0;" When we drew the"'"graph for that part"'"of the x - axis, we"'"worked back from"'"360." tpcl ~4:10 ,0;" That implies that we"'"should subtract the"'"angle whose x value"'"we want from 360,"'"and look up that"'"angle in the table." str z7:17,0;" But now x is posi-"'"tive, so there is no"'"need for a sign in"'"front of the value." pcl base=270:6000p ?3:12 ,0;" Now we look at the"'"y curve." cls  5000 dx=090Z:2:28+x*216/360h,(x*/180)*502+122z:x ث5:15,0;" For the y curve, to draw thepart that goes from 90 to 180,you draw the same curve butstarting from (180,0) and goingback to 90." u=15:cll ox=18090Z-1:2:28+x*216/360h,(x*/180)*502+122z:x i6:16,0;" The curve from 180 to 270 isthe same as the first part butnegative." cll  gx=180270:2:28+x*216/360h,(x*/180)*502+122z:x Y4:16,0;" And the last part we get bydrawing back from (360,0)." cll (px=360h270-1:2:28+x*216/360h,(x*/180)*502+122z:x 27:15,0;" We can use this to help uswrite down the values of y whenangle xOP is greater than 90 byusing the table for 0 to 90." <cls F 5200P PQ4;17,0;" First a table for"'"angle xOP from 0 to"'"90." Z83:1,22;"xOP";1,27;"y" d 5 ny=090Z5 x'2+y/5,24-y;y;"" N2+y/5,26;((y*/180)*100d+.4L)/100d y u=16:pcl =6:17,0;" Then a sketch of the"'"curve."  5300 m2:f=0360h2:10 +f*140/360h,(f*/180)*30+135:f pcl D5:12 ,0;"First, angles between"'"90 and 180." u=10 :pcl ܄4:12 ,0;" When we drew the"'"graph for that part"'"of the x - axis, we"'"worked back from"'"180." pcl 7:10 ,0;" That implies that we"'"should subtract the"'"angle whose y value"'"we want from 180,"'"and look up that"'"angle in the table." str @4:18,0;" Notice that y is"'"positive." u=10 :pcl base=90Z:6500d "E5:13 ,0;" Now angles between"'"180 and 270." ,u=10 :pcl 66:13 ,0;" When we drew the"'"graph for that part"'"of the x - axis, we"'"worked from 180"'"forwards." @pcl J4:10 ,0;" That implies that we"'"should subtract 180"'"from the angle whose"'"y value we want, and"'"look up that angle in"'"the table." Tstr ^@7:18,0;" Notice that y is now"'"negative." hpcl rbase=180:6500d |E5:13 ,0;" Now angles between"'"270 and 360." u=10 :pcl 6:13 ,0;" When we drew the"'"graph for that part"'"of the x - axis, we"'"worked back from"'"360." pcl 4:10 ,0;" That implies that we"'"should subtract the"'"angle whose y value"'"we want from 360,"'"and look up that"'"angle in the table." str 37:18,0;"y is still negative." pcl base=270:6500d "u=0:v=21:180  9000(#  }6:0,122z:250,0:f=428+36$*66:f,121y:0,2:f f28,175:0,-106j:f=72H1725:27,f:2,0:f Pf=2828+36$*6546:f,120x:0,4:f K3:0,2;"1";13 ,1;"-1";7,2;"0" 17,4;" 90 180 270 360"  P6:171,171:72H,0:0,-168:-72H,0:0,168:203,171:0,-168 Z W6:10 ,165:0,-60<:10 ,135:142,0 @f=10 15035#:f,133:0,4:f  pI5:13 ,0;" Let's try a short"'"exercise together." zu=13 :pcl  sc=0 j=15 @ang=(*89Y)+base:ang/5ɺ(ang/5)6040 *3:10 ,0;"Question ";j U6:12 ,0;" What is the value of"'"x if angle xOP is"'ang;"?" U4:16,0;" First, what angle do"'"we look up in the"'"table?" ,nin:a<0a>90Zaɺa6080 t2=base+90Z-ang base=180t2=ang-base 9t2=a7;20,5;"Correct!":6140 o2:.3,0:20,0;" No, you subtract ";ang'"from ";base+90Z;" giving ";t2;"." u=16:pcl <7:16,0;" So what is the value"'"of x?" F3;19,5;"x = "+("-"(ang>90Zang<270)) $nin:a>16180$ .xx=(t2*/180) 8Ha=((a+.005y# =)*100d)/100d:19,10 ;3;a BU(a-xx)<.01z# =4;21,5;"Correct!":sc=sc+1:6250j Vc.3,0:2:21,1;"No, x = ";((ang*/180)*100d)/100d ju=10 :pcl tj ~95:14,0;"You scored ";sc;" out of 5" u=10 :pcl: dI5:13 ,0;" Let's try a short"'"exercise together." nu=13 :pcl x sc=0 j=15 @ang=(*89Y)+base:ang/5ɺ(ang/5)6540 *3:10 ,0;"Question ";j U6:12 ,0;" What is the value of"'"y if angle xOP is"'ang;"?" U4:16,0;" First, what angle do"'"we look up in the"'"table?" ,nin:a<0a>90Zaɺa6580 t2=base+90Z-ang base=180t2=ang-base 9t2=a7;20,5;"Correct!":6640 o2:.3,0:20,0;" No, you subtract ";ang'"from ";base+90Z;" giving ";t2;"." u=16:pcl <7:16,0;" So what is the value"'"of y?" G3;19,5;"y = "+("-"(ang>180ang<360h)) nin:a>16680 "xx=(t2*/180) ,Ha=((a+.005y# =)*100d)/100d:19,10 ;3;a 6U(a-xx)<.01z# =4;21,5;"Correct!":sc=sc+1:6750^ Jc.3,0:2:21,1;"No, y = ";((ang*/180)*100d)/100d ^u=10 :pcl hj r95:14,0;"You scored ";sc;" out of 5" |u=10 :pcl: #' #(40,10 ;5;1;"LESSON THREE" #2:5,1;6;"That completes Lesson Three." #<6;7,1;"If you would like to go over"'" Lesson Three again, ";10 ,13 ;2;6;"PRESS R":'" otherwise:-";12 ,13 ;6;1;"PRESS S" #F=""9030F# #P="R"Ŧ="r"5 #Z="S"Ŧ="s"9100# #d 9030F# #"u=0:v=21:180 #5,0;5;" When you are ready to begin thenext lesson, type NEW followedby-"'';7;1;9 ,10 ;"LOAD ~TRIG4~" #23636T\,255: & 5 &"file"9899&: '"" ctdllibuv7