00020001010008main.ACT0005020012eActivity Save.EAC010000002161 unitcircle.EAC main.ACT!+.2 :E ^% '[*,The Ud Ce and Trigonometric Functions 3\; AuthorSWProfessor Dr. Wei-Chi YangQ +Department of Maths/Stat{ Radfordversity h , VA 24142_U.S.A.ene-K l: wyang@r[.eduwww./~* Sou/ack  Professor Jonathan Lewin "!Kennesaw State University (USA) I email: l=s@mindspring.com& URL: http://www.ms-movies)v[ Object 0We would like to mo!the und tandings of 8 graphs y=sin(t), cos &02t) and* by using an it circle.=ōfX4Note. When the angle t is drawn in standard position& d terminates <line OPH n MTmeaning of cos(t)@sin reyxUy"ordXf point P. [V _ Construc\rOpˊap+Έ 5Qgq `S9vP rH7 V#I@DvQr ^A 'L'C uxy qH! u H# A@6y`F" '* C #CB%AZYZ#Pqp%$ @ ٌ̆YTm "!*)(6Ql 1aߣ)(4`AxG fy dr1r8t"d#$! $G470"8e5< E4a `QcT pt < ` yyR$ 5bBhY fTxPt`Ia$c&X$ 04FX&<f H91Vd)TfV  `Y$(H$Y<w TxYl#$S0'<@HT ` pt H `Qc%x E4a Y"8ea! $G4st"d$dr1rfydT`A6XhPYU Y@ 2 k `tE6$}  # @6 ` 8!AOC8  @  Y  ".Ƙ. #͘oوG  E;͈H"oŠb יr%hFTB y`F !H  +W2gf@'@';n9"U2B6'6u!6x& "GPY[ Kt: Phh Ȑgqp%$YJ Ę`0\9 C1RR Coord of P5@  "2 @A6 LW  SH Fr7a4 16YU!%ȘX"\hSVUX pZbYn*ӈ%1Z   s(Ep#fi #|Fg4 qp%"  [#!Step 1. Construct a unit circle. (/(2( vector on the6_Q73. When measuring0KselB ONLYBP whose head is^UX4. SCpoint/ AND> Edit->Add Animation->Goc\K^5. Tap[and angle, we ge6table fs?QDStep 6. Tap the point and select (x,y) coordinates, we get tables of9x5 y 2 for each^. $W}7. Copy data from~imationcn dragang x-+P oGeometry Strip y=cos(t).[8. Ifqyqj y=sinq>Step 9. Edit the animation by changing t from 0 to 2. **Notice2a7is meanswe rotat'e circlconte ockwise twP6.[A RAnd collecgEOP, xd oordinates of P again. copy#paste inጚ e-Activity. A Drag^dropfow rixOa 'List=or'. OPrd Data:umn1=OP;2=x-valu3=yN`\^a$ N PFinaFormX$NGraph2D| 3 LISTSYS4< Modify ЈP<STATCALC d< \x S9equence,xSheetO|iolveEqwr(UptupFLG1(<Lis{DPicViewWind(_osvevExy^ PH2h<4(h9 (  iT̒ؒ  ,8 DPZ\!,h "@t #T $h %| & !'(  )~Ȇ*Ԇ+-.x / 0(1 2̆ 3؆ 4䆌5 E F H I Jh"KLMN\І O*@)Q(R'S&T%] ^_`abĆdeLfІ g,Ҏ@ؒT͑h Α|n ב    kنf,jچ8ۆvKD< FinancialFormat  E system]^_` a bR @R @x% a seq_histb NewFolde (lj/  *<$GPD<h(A   3xP(x) b2*4L4s` P)$$p Pv0 `aS& 17E 9av `9QF 0 (10qy`#YuY$ !& H $H $0<HT`mlqf)rBdS&idcET"8Ș$X -Y(Ďx̆؆ I ,8DP\htȆD1ԙYaS` i#i S8F8P$ ##%v0)<G8pf8F Vi#$!SaP0@8<XFa8v0vT8F(Ul20&xP  #lHakGTȎ8Vu `I#i g88A86v( $0<HT`lxĂ؆I ,8DP\htԆ`  HSdA D'c@ hGFpx!tc$eAYT`HLY2DSu`/EP/ pTY us< C`/ HQH HYV` Sf0(i%arCSl E`% b $A What do you think e plot of list2(x) and *3(y) will be?[Hinit: (sin(t))2  +(cos:=1. F PQ Exercise 1. c @If we tak4 to (1)/2, which means+halfЎ[egles Vfrom 1,oo 2 togetherzL ouDisscatter`?@tKR: The list4 is half of toriginal angles,d*2 was# x-value on2'unit 2circle, so we are getting^graphk y=cos(2t). : DE Exercise 2. W@IfOtakto be (1)/2, which means+َ[eߒVfrom 1plot&(x) 3 (y) toherzat d outMis  scatterR?Hint?R: The list4 is half of toriginal angles,d*3 was# y-value on2%unit 1circle, so we are getting\graphi y=sin(2t).[: BeAct02000eunitcircle.EAC010000002161 unitcircle.EAC main.ACT!+.2 :E ^% '[*,The Ud Ce and Trigonometric Functions 3\; AuthorSWProfessor Dr. Wei-Chi YangQ +Department of Maths/Stat{ Radfordversity h , VA 24142_U.S.A.ene-K l: wyang@r[.eduwww./~* Sou/ack  Professor Jonathan Lewin "!Kennesaw State University (USA) I email: l=s@mindspring.com& URL: http://www.ms-movies)v[ Object 0We would like to mo!the und tandings of 8 graphs y=sin(t), cos &02t) and* by using an it circle.=ōfX4Note. When the angle t is drawn in standard position& d terminates <line OPH n MTmeaning of cos(t)@sin reyxUy"ordXf point P. [V _ Construc\rOpˊap+Έ 5Qgq `S9vP rH7 V#I@DvQr ^A 'L'C uxy qH! u H# A@6y`F" '* C #CB%AZYZ#Pqp%$ @ ٌ̆YTm "!*)(6Ql 1aߣ)(4`AxG fy dr1r8t"d#$! $G470"8e5< E4a `QcT pt < ` yyR$ 5bBhY fTxPt`Ia$c&X$ 04FX&<f H91Vd)TfV  `Y$(H$Y<w TxYl#$S0'<@HT ` pt H `Qc%x E4a Y"8ea! $G4st"d$dr1rfydT`A6XhPYU Y@ 2 k `tE6$}  # @6 ` 8!AOC8  @  Y  ".Ƙ. #͘oوG  E;͈H"oŠb יr%hFTB y`F !H  +W2gf@'@';n9"U2B6'6u!6x& "GPY[ Kt: Phh Ȑgqp%$YJ Ę`0\9 C1RR Coord of P5@  "2 @A6 LW  SH Fr7a4 16YU!%ȘX"\hSVUX pZbYn*ӈ%1Z   s(Ep#fi #|Fg4 qp%"  [#!Step 1. Construct a unit circle. (/(2( vector on the6_Q73. When measuring0KselB ONLYBP whose head is^UX4. SCpoint/ AND> Edit->Add Animation->Goc\K^5. Tap[and angle, we ge6table fs?QDStep 6. Tap the point and select (x,y) coordinates, we get tables of9x5 y 2 for each^. $W}7. Copy data from~imationcn dragang x-+P oGeometry Strip y=cos(t).[8. Ifqyqj y=sinq>Step 9. Edit the animation by changing t from 0 to 2. **Notice2a7is meanswe rotat'e circlconte ockwise twP6.[A RAnd collecgEOP, xd oordinates of P again. copy#paste inጚ e-Activity. A Drag^dropfow rixOa 'List=or'. OPrd Data:umn1=OP;2=x-valu3=yN`\^a$ N PFinaFormX$NGraph2D| 3 LISTSYS4< Modify ЈP<STATCALC d< \x S9equence,xSheetO|iolveEqwr(UptupFLG1(<Lis{DPicViewWind(_osvevExy^ PH2h<4(h9 (  iT̒ؒ  ,8 DPZ\!,h "@t #T $h %| & !'(  )~Ȇ*Ԇ+-.x / 0(1 2̆ 3؆ 4䆌5 E F H I Jh"KLMN\І O*@)Q(R'S&T%] ^_`abĆdeLfІ g,Ҏ@ؒT͑h Α|n ב    kنf,jچ8ۆvKD< FinancialFormat  E system]^_` a bR @R @x% a seq_histb NewFolde (lj/  *<$GPD<h(A   3xP(x) b2*4L4s` P)$$p Pv0 `aS& 17E 9av `9QF 0 (10qy`#YuY$ !& H $H $0<HT`mlqf)rBdS&idcET"8Ș$X -Y(Ďx̆؆ I ,8DP\htȆD1ԙYaS` i#i S8F8P$ ##%v0)<G8pf8F Vi#$!SaP0@8<XFa8v0vT8F(Ul20&xP  #lHakGTȎ8Vu `I#i g88A86v( $0<HT`lxĂ؆I ,8DP\htԆ`  HSdA D'c@ hGFpx!tc$eAYT`HLY2DSu`/EP/ pTY us< C`/ HQH HYV` Sf0(i%arCSl E`% b $A What do you think e plot of list2(x) and *3(y) will be?[Hinit: (sin(t))2  +(cos:=1. F PQ Exercise 1. c @If we tak4 to (1)/2, which means+halfЎ[egles Vfrom 1,oo 2 togetherzL ouDisscatter`?@tKR: The list4 is half of toriginal angles,d*2 was# x-value on2'unit 2circle, so we are getting^graphk y=cos(2t). : DE Exercise 2. W@IfOtakto be (1)/2, which means+َ[eߒVfrom 1plot&(x) 3 (y) toherzat d outMis  scatterR?Hint?R: The list4 is half of toriginal angles,d*3 was# y-value on2%unit 1circle, so we are getting\graphi y=sin(2t).[: BeAct020010unitcircle_2.EAC010000001ae6 unitcircle_2.EAC main.ACT #-04 <G ^% '[*,The Uf Cg and Trigonometric Functions 3\; AuthorSWtProfessor Wei-Chi YangL 'e-l: wyang@radford.edu*!URL: http://www.#/5Ra[t Souack"Professor Jonathan Lewin "!Kennesaw State University (USA) I email: l=s@mindspring.com& URL: http://www.ms-movies)v[ Object 0We would like to mo!the und tandings of 8 graphs y=sin(t), cos &y=2 and*2+.&O XNote. Whenangle t is drawn in ard poHionTter4ate<line OPnXthe meaning of cos(t) and sin re defined to be 3x#y0 ordinates?Npoint P respectively. [ " Constru!on\5Opentapn+ΈOSY b5Qgq `0Ys@ rH7  r DvQ^A 'L'C uxy qH" u(-(.2  b`? HSdA E`%pD'c@ rCSP hGFp(i%a$x!tc0 Sf0<eHYVYT`H_Yg 2DSu`$HQH 0EY CY pY usl $ "!F1 2FpDBb0$Sewn fd8@<wQ (XRP Delw!Gl2xl C%UAAf slWwls$6l1hl8l82SblTC`pTh%leuWlv 4RQg!DC&xlT4 1eAA@ GvHrcVP$yc6/0 pg`< w H(10pT(  `A\ fy dr1rt"dP ! $G00"8e< E4 `Q pt{ H yyR` 5bB fTt`Iac&X4FX&Tf 91VdfV Y$Y<YTYlYYYY yyRY  pt`Q`$E4 "8e<! $G0Ht"dHdr1r`fyT`A<H!((as "!F1 2FpDBb Sewn fd8@<wQ (XRP Dellw!G2xl C%UAAf slWwls$6l1hl8l82SblTC`jpTh%euW@ v P$4R/0Q`<g! H2FpTC&x0`T4 l1eAAlGvHrlcVlyc6l pgl wl(10l((  b HSdA E`% D'c rCS hG (i%a$x!tcH Sf eYVXYT`HcYY2DSuYHQH@YEY CY pY usY  p@Cp$EP0HQH <2DSu`HOSTT`H Vlex Sf0 x!tc (i%a hGF rCS D'c$E`%$ HSdAH b H!Lj H#A6#y`C HQ  O #B BZ9' #^P qp%%   @    /m" C!*)(Tc;u2 1a)(`Ax fy dr1r8t"d#$! $G470"8e5< E4a `QcT pt < ` yyR$x 5bBhYfTxPt`Iac&X$ 4FX&f 91Vd)fV `Y$(H$Y<w TxYl#$t`IaSYfTx'  5bBh@ yyR$ 0 pt < `Qc%H E4a$T"8ea`! $G4slt"d$xdr1rHfydT`A6Xh@   `E6$P  #UBg_: !Oz ވY"@    #@)6 '<4W` -EG;ĘYH"o Š ה `r%hFTB y`C F\!H\/ W2gf1 ݈ˉ(9Ȏ2,'6u!6xg"GPY Kt: 5  @D6Kqp%%VYy`C J @J`0}9 1u!6x& RRP Coord of P!5"H P  #\H Yr7aBM1e$%@  "%*Ę#<"hSVUG I VAVAk pbPn 6. e1~ j  (Q!&i #F@ 6<qp%"l["!Step 1. Construct a unit circle. (/(2( vector on the6_Q(Step 3. When measuring the Kselect ONLYvor whose head is on.circle. UX4. SCPpoint/ AND> Edit->Add Animation->Goec\^K^5. Tap[and angle, we get a table fsQR6R(x,y) coordinatesZXf6xy 2|each . W&Step 7. Copy data from animation table d then drag "g x-coordinate of +P into:# Geometry Strip, we get y=cos(t).[4W8. If$pypi y=sinpxXRepeat process by u/circ whose center is (0,0) radius2 އ3 "graphy=2Vy=2 00\L_2Έ' FGu`` tA2T# YDv Ir   A kL'xC uxy qq( O@6,3)CEC &R*D@ +VH J!X!SPU, #UB!X!SP `-! %Q@,6+ X O+.G@ GY,*"/*H!*@0  1B Cɠ–2Y"34 5!G@6  63@ 1475_4.0-, 88H!+9  `r%hFTB !X!SPF:z\;H IgA < "U+  N=`:529Q"p>?Y gPY@'H  0P6++ UT`K 7S;An@ GY?>.0-,"B*@4CDD"`r%hFT] FE\!H\r 9W2gfF5Ř-9GHeH#>H>2IwHDHJ !H  4 W2gf@K3@'EI76;5La2.MH kFX6gP YUT` @GNUO"X@hy ACQH"IB 6X %5iWx CR%ș7SQOT @ MU" "@168UT`C YgP  ?F1-V``WH!d0U5296X<H "Y@VZ85H[Ȑ4 \\H!%p.$i U]~%˘ֈX^,n[F9g0f VAVA WVU-]^[\1RSOQPJB )19IQ@M54DH9;?<+0,)((eZ[   Exercise 1. / Sketch the graphs of y=3*sin(t): _andcos by u*gAf techniques described inm is eActivity.ˢ2#-Sketch the graphs of y=(1/2)*sin(t)  and"cos" by u-gH0 techniques: described insis eActivity.[7f geAct020014unitcircle_draft.EAC0100000035fa unitcircle_draft.EAC main.ACT$'148 @K ^% '[*,The Uj Ck and Trigonometric Functions 3\; AuthorSWProfessor Dr. Wei-Chi YangQ +Department of Maths/Stat{ Radfordversity h , VA 24142_U.S.A.ene-K l: wyang@r[.eduwww./~* Sou/ackProfessor Jonathan Lewin "!Kennesaw State University (USA) I email: l=s@mindspring.com& URL: http://www.ms-movies)v[ Object 0We would like to mo!the und tandings of 8 graphs y=sin(t) and cos ( by using aX it circle.'P XNote. 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TQT6T(x,y) coordinates\Zs ofxy Y2~each 1|7. Copy data fromяHn: 9 8. Paste ^ o eActivity%AcStep 9. Drag and drop the following matrix into a 'List Editor'. 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