ࡱ> $&#%` .bjbjNN 44,,2 C/DDDD   4xxx84,4R)Hddd$$$((((((($*hp,(] $"$$$(DDdu )((($jDVd( (($((( ( P.'x]%Z(5(T")0R)( -& -( - ( $$($$$$$(('^$$$R)$$$$444Dx444x444DDDDDD Find the amplitude, the period, and the phase shift.  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  Now we will do the reverse of graphing functions such as those in the previous lesson. Given a graph, we will find the equation. First, shown a curve (such as the one below), we could write either a sine function or a cosine function. We will assume we are writing a sine function. Secondly, we much decide the value of a. Could a be positive or negative? It could be either depending on where the phase shift is. So we will decide that a is positive. We also will assume that b is positive and that c is the least positive value possible. (There could be several phase shifts. If there is one, we assume it is the one just left of the y-axis. Remember, if both b and c are positive, the phase shift will be negative.) 1) The graph of the equation is shown in the figure. (a) Find the amplitude, period, and phase shift. (b) Write the equation in the form y = a sin (bx + c) for a > 0, b > 0, and the least positive real number c.  EMBED Excel.Sheet.8  Note: Only 1 value is marked on the x-axis of the graph. You can see that 4 marks equals . Amplitude is the distance from the average. In the graph on the previous page it would be 3. Phase shift is the first zero (x-intercept) before a maximum left of the y-axis. Phase shift of the previous graph would be  . To find the period, begin at   (the average) and determine when one cycle of  to maximum, back to average, to minimum, back to average is completed. This is at . From   to  gives a period of 2. Amplitude:  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  2) Find an equation of the form  EMBED Equation.DSMT4 , where  EMBED Equation.DSMT4 is the least positive value possible for the graph shown at the top of page 3. amplitude: period: EQUATION: phase shift:  EMBED Excel.Sheet.8  3) amplitude: period: phase shift: EQUATION:  EMBED Excel.Sheet.8  4) Amplitude: Period: Phase Shift: EQUATION:  EMBED Excel.Sheet.8  Scientists sometimes use the formula  EMBED Equation.3  to simulate temperature variations during the day, with time t in hours, temperature  EMBED Equation.DSMT4  in (C, and t = 0 corresponding to midnight, Assume that  EMBED Equation.DSMT4 is decreasing at midnight. a) Determine the values of a, b, c and d that fit the information. Note: The graph of this curve will only be to the right of the y-axis. Therefore the value of c will be negative, since the phase shift will be to the right. b) Sketch the graph of f for 0 d" t d" 24 1) The temperature varies between 10(C and 30(C, and the average temperature of 20(C first occurs at 9 AM         Since the average is at 20, the graph has been shifted up 20. d = 20 The difference be67JKLMNObcdeij}~ Y Z > ? D E w x " ( * 6 ĺ{{{{{{{t{{ h,h h6jhEHU$jB; hCJUVmHnHuj hEHU$jf8 hCJUVmHnHuj.hEHU$jcf8 hCJUVmHnHujhEHU$j?f8 hCJUVmHnHujhUh-56fghiw x    "$vx  @]gd`--.6 8 @ B N P \ ^  R T $&>@nprtxzsj0-hL_|hEHUj%»M hCJUVj)hL_|hEHUjM hCJUVj%hL_|hEHUjM hCJUV h5 h,hjhUjNi8 hUVjhUjhUmHnHuh h6-xu "#$;V @]gd  @]gd2345=>UVWX   ;<RSTUŸ쟗쌄yqj]hUjFn8 hUVjLhUjk8 hUVj`7hUjVj8 hUVjhUmHnHuj@4h.;hEHUjûM hCJUVj01h.;hEHUj~ûM hCJUVh h,hjhU$VZmno  " (.2>   @@gd   @@gd   @gd  @]gd 78OPQRVW^_PQpq"$tvµ׮ס׏׏׈z׮׮׮rmrzz h5hDUh5jhUmHnHu h.;h h6jph.;hEHUjŻM hCJUV jhjmh.;hEHUjŻM hCJUVhDUh6hjhUjqhhEHU$jL8 hCJUVmHnHu* &(,.02<>F,b,c,j,k,t,u,,,,,,,,,,,,,- -<-=-`-a-c-d-f-g-i-j-l------- jphhVjhVU jh hJhjvhJhEHUjAʻM hCJUVjAshJhEHUjɻM hCJUVjhUU h6jhUmHnHuh5>HJLi,j,,,,G-]-^-_-`-b-c-e-f-h-i-k-l-----   @gdtween the maximum of 30 and the average or the minimum of 10 and the average is 10. amplitude = a = 10 Period =  EMBED Equation.DSMT4  Phase shift is where the curve is rising at the average:  EMBED Equation.DSMT4  2) The high temperature of 28(C occurs at 2 PM and the average temperature of 20(C occurs 6 hours later.     MA 15400 Lesson 8 Section 6.5 Trigonometric Graphs (  EMBED Equation.DSMT4  ( Period = 24 hours, hash marks would be every 6 hours. Average is at 9 AM, 6 hours earlier (3 AM) would be minimum. Remember, temperature is falling at midnight. 6 hours later (15 or 3 PM) is a maximum. MAX AVG. MIN 21 15 3 9  EMBED Equation.DSMT4  -------....................gd------.........ɼ۸hVj2~hfjhEHUjʻM hUV jphhjhUjzhL_|hEHUj»M hUV21h:p/ =!"#$% .Dd B  S A? 2815u|I!tD`!l815u|I!DY ?3pxcdd``Vb 2 L0C$ c,NFMc`cjl@?H @fM\p~!'r4W"]jv İ@ac?tӘ b W߂9 Cw0?ӌ- \5ne?& ܁u}Wrlj $}oIT(D^f4 QCpn&\ \u @&2*Ń_fкkPtA.INi fD~}n;ـ:]mgSk](TkL03x_lsSUIm#wH־\Pt FcM~(Wʉ]l[%Q!`0vw%2}/⫒Ey{6:q蟠)Nqpb΋(Y8 cI=v9LFHQN&f™Ȓne\uR "z#f>Lo00>$1{o'dvTPwt/ŒEMI'U2K rl>JV+_o*֏1 0MRC,. ~Tڀ?Sf!u Уƪdp!)'+e rڵF8ǩdt^əB+mRxQc`I $z.1昬SE]7גm2Mjˮ퐀>+YBmW~ 9f#s,7KhKt\zϓ$-]$eQ,bfM^mQ.Yv&;R6O4E_+eeF3)0J,t!ohŃ>ӭtִ+ZD6y84_XAlXVT6ݜ˦E[ 3_Dd |@B  S A? 2\T Pj,5*r`!\T Pj,5*hS #xcdd`` @c0 0Y,P1=F (`d?3%$ lʛ27 27)?A} CXk"]jv İ@ac?tӘ b Ë+i TFJnhHp>7BLej 4nM ŭ&@3E8jB0|>I$'@Sm=ԽHqkTW5jMՄ4<_tX>u<^sC /ŃỒ@woS xTAF~v[$TqN@B=p y-HhV~E{J,oƉH}=@ pBcϬ _EI 4p ,l8nyltg-;pD#4FOzΚߚf|O*TVL?st$u glۚ~yk@of%::R1ŗ,dg)a>hEVZlA떫q΃}MH0pT̳ 8ʪxۣ| +ДUe4cUFReQ%M:qT fBVCʁ.h0@U<4 ={y1[Y,:rev:It?սq̟JR̚;Ώp:~iE^0%oD) IJFF tAQDДD>Γzn8THx-WCrTi] !v}eiϜ~:jȜxw-wh.~Aoy' I<GJYc_=j)y[JT0zFCd7BLej 4nM&ŭF@SE85wz:,;fbT F3zx}TAD~vm.44 =qrضq&vV"#]زDjJpy @3pby3c'Y2y{oKfsB b.hA^B-zv9u06\['Y Ђ[݁@(|lS̷ J)sʳDT"^sKdKr6L^Ә:?BawmDjOsF m3XRmc4w' 2ߢTp[mmBf 6GX?ebM4Y<`\S#1FIX>?Hĥ}`v}kd> ^A/[VE 48]Ul$?@ABCDEFGIJKLNOPQRSTVUWXZY[]|v_`abcdefghijklmnopqrstuwxyz{}~Root Entryu F@Z''@WData WordDocumentt44ObjectPoolw `'@Z'_941516351F`'`'Ole CompObjRObjInfo  !"#$%&'()*+,-./0123456789:;<>?@BCDEHKLMNORUVWXYZ[\_bcdefghijmpqrsvyz{|FMicrosoft Equation 3.0DNQE Equation.3L y=3cos12x-p4()FMicrosoft Equation 3.0DNQE Equation Native h_941516387 F`'`'Ole CompObj REquation.34 y=4sin2x+p()FMicrosoft Equation 3.0DNQE Equation.3ObjInfo Equation Native  P_941516422F`'`'Ole  CompObj RObjInfoEquation Native \_999326018F`'`'@ y=2sinpx+p2()FMicrosoft Equation 3.0DNQE Equation.3* y=-5cos(px)Ole CompObjRObjInfoEquation Native F_941517134 A F`'`'Ole CompObjTObjInfo FMicrosoft Excel Chart8FIBExcel.Sheet.8 ,,   UI.I".;";"8;";"B;";"K;";"U; B2B_"P2"Pc"P"P"P"P)"PZ"PWorkbook1H-PRNTPICTSummaryInformation(=DocumentSummaryInformation8A< !Ba= = 8X1Geneva1Geneva1Geneva1Geneva1Geneva1Geneva1Geneva1Geneva1Geneva"$"#,##0_);\("$"#,##0\)!"$"#,##0_);[Red]\("$"#,##0\)""$"#,##0.00_);\("$"#,##0.00\)'""$"#,##0.00_);[Red]\("$"#,##0.00\)7*2_("$"* #,##0_);_("$"* \(#,##0\);_("$"* "-"_);_(@_).))_(* #,##0_);_(* \(#,##0\);_(* "-"_);_(@_)?,:_("$"* #,##0.00_);_("$"* \(#,##0.00\);_("$"* "-"??_);_(@_)6+1_(* #,##0.00_);_(* \(#,##0.00\);_(* "-"??_);_(@_)                + ) , *     Chart2Sheet1v+Sheet2_,Sheet3iaZR3  @@  xy  1 0 0>l 1 0` 1 U%ugP 0x[,p 0x$ 1/U%W 1 1  1 1  1 1 U 3>l 1 1 0 1 U%p/U%XU` 1 3 1 1@ 2ŝ 1x 3 30 2P 1PG\ugug 1 2 1 1Z 4 1 1l 1 30U 2 30t 3Z 2PU% 28 2U 2PZ 4( 2>| 4 3>lR>l 2U@ 2>|ZD/U% U ugug 3t 2 2 2>l 3ug 3XU% 3D/U%6@Ut t| 3XD/U% U t"t| 3X 4@ 3x 3t 4UUt 3ug 4` 3U% 3KKH 4` 4F@ 4`״t؇5tNX>lZ  !"4?? 3h ,h , 3d !!3QQ ;"Q ;"Q3_  MM ]  d4E4D $% M3O&Q4$% M3O& Q4FAQ 3OQ3*>4a!)S!)@T!?#M43*#M43d" 3_  M MM ] MM<4444!e-DT!)Fۏ'u%dw4k$!3|"\G!^8U)zj̾:F-DT! u !3| ^8U)zj -DT!  !3|-DT!-DT!-DT!?-DT!?!3|@-DT! @^8U)zj@!3|@u@-DT!@̾:F@^8U)zj@\G!@!3|"@dw4k$@u%@Fۏ'@ -DT!)@evӼlvlv L9y<lv@@lv@ L9y lv  lv  lv@@lv@ L9y<lvlv L9yʼlv@@lv@v<lvlv L9yڼlv@@lv@ GË &G !  dMbP?_*+%Mz,,  c yg(,,(d'`"d??U }  }  #&&D&'''D  ލ < &l h('h(MH(M((D_pxX(X(Dd(D ( x y~ -DT!) DA&vӼDAA%D?Fۏ' DA&lvDAA% D?u% DA&DAA% D?dw4k$ DA&lvDAA%D?!3|" DA& L9y<DAA%D?\G! DA&lv@DAA%D?^8U)zj DA&@ DAA%  D? ̾:F  D A& lv@ D AA%  D ? -DT!  D A&  L9y D AA%  D ? u  D A& lv D AA%  D ? !3|  D A&  D AA%  D ? ^8U)zj  D A& lvD AA%D ?-DT!  DA&DAA%D?!3| DA&lv@DAA%D?-DT! DA&@DAA%пD?-DT! DA&lv@DAA%D? DA& L9y<DAA%?D?-DT!? DA&lvDAA%?D?-DT!? DA&DAA%?D?!3|@ DA&lvDAA%?D?-DT! @ DA& L9yʼDAA%?D?^8U)zj@ DA&lv@DAA%?D?!3|@ DA&@DAA%?D?u@ DA&lv@DAA%@D?-DT!@ DA&v<DAA%@D?̾:F@ DA&lvDAA%@D?^8U)zj@ DA&DAA%@D?\G!@ DA&lvDAA%@D?!3|"@ DA& L9yڼDAA% @D?dw4k$@ DA&lv@ DAA%  @ D? u%@  D A& @!D AADl&[vvvvvvvvvvvvvvvvvvvvvvvvvvvvv!&"&D%!@!D ?!Fۏ'@! D!A&!lv@"D!AA%"@"D!?"-DT!)@" D"A&"GË<D"AAv( <  p  6NMM?n ;;]  !"??3h ,h ,3d !!3QQ ;"Q ;"Q3_  MM ]  d4E4D $% M3O&Q4$% M3O&Q4FAQ 3OQv3*>4a!)S!)@T!?#M43*#M43d" 3_  M MM ] MM<4444!eee >@ !  dMbP?_*+%"??U >@ !  dMbP?_*+%"??U >@ "P"P"P "PQ"P"P"P"P"PH"Pz"P"P"P"P@"Pq"P"P"P"P7"Ph"P"P"P"P."P_ U2.`"@0"###$###"#!### # ###################################################################### # #####"#$#$###"#"###$###"#!### # ###################################################################### # #####"#$#$###"#"###$###"#!### # ###################################################################### # ###!#"###$###"#"###$#$#"##### # ###################################################################### # ###!#"###$###" , Geneva &.(=-4(-3(G-2(-1(Q 0( 1(Z 2( 3(d 4 Oh+'08@Th ' Math Dept  Math Dept Microsoft Excel@p ՜.+,0  PXt | 'Purdue Universitysh Sheet1Sheet2Sheet3Chart2  WorksheetsCharts FMathType 5.0 Equation MathTy_13041504194"F`'`'Ole FCompObj!#GiObjInfo$Ipe EFEquation.DSMT49q;$DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  amplitude = a==3a==3Equation Native JW_1304150484'F`'`'Ole PCompObj&(Qi FMathType 5.0 Equation MathType EFEquation.DSMT49q DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  periodObjInfo)SEquation Native T<_1304150565%/,F`'`'Ole ] =  2pb==2p               2pb== 2p1                b==1 FMathType 5.0 Equation MathType EFEquation.DSMT49qCompObj+-^iObjInfo.`Equation Native az_1304150910j1F`'`'^4DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  phase shift = "- cb=="-p                    "- c1=="-p                        c==p FMathType 5.0 Equation MathType EFEquation.DSMT49q<DSMT5WinAllBasicCodePagesOle kCompObj02liObjInfo3nEquation Native oTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  y==asin(bx++c) FMathType 5.0 Equation MathType EFEquation.DSMT49q_1304150935*V6F`'`'Ole tCompObj57uiObjInfo8wEquation Native x-_941517398; F`'`'Ole }CompObj:=~T DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  a>>0, b>>0, and c FMicrosoft Excel Chart8FIBExcel.Sheet.8ObjInfoWorkbook<?^P.PRNTPICT SummaryInformation(>@  ,,   UI.I".;";";"B;";";"U; B2B_"P2"Pc"P"P"P"P)"PZ"P"P"P"P "PQ"P"P"P"P"PH"Pz"P"P"P"P@"Pq"P"P"P"P7"Ph"P"P"P"P."P_ !Ba= = 8X1Geneva1Geneva1Geneva1Geneva1Geneva1Geneva1Geneva1Geneva1Geneva"$"#,##0_);\("$"#,##0\)!"$"#,##0_);[Red]\("$"#,##0\)""$"#,##0.00_);\("$"#,##0.00\)'""$"#,##0.00_);[Red]\("$"#,##0.00\)7*2_("$"* #,##0_);_("$"* \(#,##0\);_("$"* "-"_);_(@_).))_(* #,##0_);_(* \(#,##0\);_(* "-"_);_(@_)?,:_("$"* #,##0.00_);_("$"* \(#,##0.00\);_("$"* "-"??_);_(@_)6+1_(* #,##0.00_);_(* \(#,##0.00\);_(* "-"??_);_(@_)                + ) , *     Chart3Sheet1~,Sheet2g-Sheet3iaZR3  @@  xy  1 0 0>l 1 0` 1 U%ugP 0x[,p 0x$ 1/U%W 1 1  1 1  1 1 U 3>l 1 1 0 1 U%p/U%XU` 1 3 1 1@ 2ŝ 1x 3 30 2P 1PG\ugug 1 2 1 1Z 4 1 1l 1 30U 2 30t 3Z 2PU% 28 2U 2PZ 4( 2>| 4 3>lR>l 2U@ 2>|ZD/U% U ugug 3t 2 2 2>l 3ug 3XU% 3D/U%6@Ut t| 3XD/U% U t"t| 3X 4@ 3x 3t 4UUt 3ug 4` 3U% 3KKH 4` 4F@ 4`״t؇5tNX>lZ  !"4?? 3h ,h , 3d !!3QQ ;"Q ;"Q3_  MM ]  d4E4D $% M3O&Q4$% M3O& Q4FAQ 3OQ3*>4a!)S!)@T!?#M43*@?#M43d" 3_  M MM ] MM<4444!e-DT!)Fۏ'u%dw4k$!3|"\G!^8U)zj̾:F-DT! u !3| ^8U)zj -DT!  !3|-DT!-DT!-DT!?-DT!?!3|@-DT! @^8U)zj@!3|@u@-DT!@̾:F@^8U)zj@\G!@!3|"@dw4k$@u%@Fۏ'@ -DT!)@e@"t,[X L9y<@\\3&<@ L9yʼ  \3&< @ \3&@\3&<\3&@ L9y<\3&Ѽ@ sٿ< L9yڼ@IOG\3& @e> & !  dMbP?_*+%Mz,,  c yg(,,(d'`"d??U }  }  #&&D&'''D  ލ < &l h('h(MH(M((D_pxX(X(Dd(D ( x y~ -DT!)? DA.@DAA%D?Fۏ' DA."t,[XDAA% D?u% DA.DAA% D?dw4k$ DA. L9y<DAA%D?!3|" DA.@DAA%D?\G! DA.\DAA%D?^8U)zj DA. DAA%  D? ̾:F D A. \3&< D AA%  D ? -DT! D A. @ D AA%  D ? u D A.  L9yʼ D AA%  D ? !3| D A.  D AA%  D ? ^8U)zj D A. \3&<D AA%D ?-DT!  DA.@DAA%D?!3| DA.\3&DAA%D?-DT! DA.DAA%пD?-DT! DA.DAA%D? DA.@DAA%?D?-DT!? DA.\3&<DAA%?D?-DT!? DA.DAA%?D?!3|@ DA.\3&DAA%?D?-DT! @ DA.@DAA%?D?^8U)zj@ DA. L9y<DAA%?D?!3|@ DA.DAA%?D?u@ DA.\3&ѼDAA%@D?-DT!@ DA.@DAA%@D?̾:F@ DA. sٿ<DAA%@D?^8U)zj@ DA.DAA%@D?\G!@ DA. L9yڼDAA%@D?!3|"@ DA.@DAA% @D?dw4k$@ DA.IOG DAA%  @ D? u%@! D A. !D AADl&c~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!&"&D%!@!D ?!Fۏ'@" D!A.!\3&"D!AA%"@"D!?"-DT!)@ D"A."@D"AA$~( <  p  6NMM?n ;;]  !"??3h ,h ,3d !!3QQ ;"Q ;"Q3_  MM ]  d4E4D $% M3O&Q4$% M3O&Q4FAQ 3OQv3*>4a!)S!)@T!?#M43*@?#M43d" 3_  M MM ] MM<4444!eee >@" !  dMbP?_*+%"??U >@ !  dMbP?_*+%"??U >@  U2.` 0@a#####7###### # ######################################################### # ######6#########7###### # ######################################################### # ######6#########7###### # ######################################################### # ######6#########7###### # ######################################################### # ######7#########6###### # ######################################################### # ######7#########6###### # ######################################################### # ######7#########6###### # ######################################################### # ######6#########7###### # ############################!] , Geneva &.(=-3(-2(-1(Q 0( 1( 2(d 3 Oh+'08@Th ' Math Dept  Math Dept Microsoft Excel@p ՜.+,0  PXt | 'Purdue Universitysh DocumentSummaryInformation8<_9415177079QC F`'P.'Ole CompObjBET Sheet1Sheet2Sheet3Chart3  WorksheetsCharts FMicrosoft Excel Chart8FIBExcel.Sheet.8 ,,   UI.I".;";"ObjInfoWorkbookDG.PRNTPICTSummaryInformation(FH !Ba= = 8X1Geneva1Geneva1Geneva1Geneva1Geneva1Geneva1Geneva1Geneva1Geneva"$"#,##0_);\("$"#,##0\)!"$"#,##0_);[Red]\("$"#,##0\)""$"#,##0.00_);\("$"#,##0.00\)'""$"#,##0.00_);[Red]\("$"#,##0.00\)7*2_("$"* #,##0_);_("$"* \(#,##0\);_("$"* "-"_);_(@_).))_(* #,##0_);_(* \(#,##0\);_(* "-"_);_(@_)?,:_("$"* #,##0.00_);_("$"* \(#,##0.00\);_("$"* "-"??_);_(@_)6+1_(* #,##0.00_);_(* \(#,##0.00\);_(* "-"??_);_(@_)                + ) , *     Chart4Sheet1<,Sheet2%-Sheet3iaZR3  @@  xy  1 0 0>l 1 0` 1 U%ugP 0x[,p 0x$ 1/U%W 1 1  1 1  1 1 U 3>l 1 1 0 1 U%p/U%XU` 1 3 1 1@ 2ŝ 1x 3 30 2P 1PG\ugug 1 2 1 1Z 4 1 1l 1 30U 2 30t 3Z 2PU% 28 2U 2PZ 4( 2>| 4 3>lR>l 2U@ 2>|ZD/U% U ugug 3t 2 2 2>l 3ug 3XU% 3D/U%6@Ut t| 3XD/U% U t"t| 3X 4@ 3x 3t 4UUt 3ug 4` 3U% 3KKH 4` 4F@ 4`״tؗ5tNX>lZ  !"4?? 3h ,h , 3d !!3QQ ;"Q ;"Q3_  MM ]  d4E4D $% M3O&Q4$% M3O& Q4FA 3OQ3*@??#M43*@?#M43d" 3_  M MM ] MM<4444!e       п???????@@@@@ @ @@ @e\3&<;f@@;f@\3&;f;f ;f@ @ ;f@ \3&< ;f;f\3&Ѽ;f@@;f@ L9y<;f;f\3&;f@@;f@ sٿ<;f;f L9ye> &L !  dMbP?_*+%Mz,,  c yg(,,(d'`"d??U }  }  #&&D&'''D  ލ < &l h('h(MH(M((D_pxX(X(Dd(D ( x y~ D0\3&<ADAA%D?D0;f@ADAA% D? D0@ADAA% D? D0;f@ADAA%D?D0\3&ADAA%D?D0;fADAA% D? D0 ADAA%  D?  D 0 ;f AD AA%  D ?  D 0  AD AA%  D ?  D 0 ;f@ AD AA%  D ?  D 0 @ AD AA% D ? D 0 ;f@AD AA%D ?D0\3&<ADAA%D?D0;fADAA%D?D0ADAA%пD?пD0;fADAA%D?D0\3&ѼADAA%?D??D0;f@ADAA%?D??D0@ADAA%?D??D0;f@ADAA%?D??D0 L9y<ADAA%?D??D0;fADAA%?D??D0ADAA%?D??D0;fADAA%@D?@D0\3&ADAA%@D?@D0;f@ADAA%@D?@D0@ADAA%@D?@D0;f@ADAA%@D?@D0 sٿ<ADAA% @ D? @ D0;f ADAA%  @!D?  @!D 0 !AD AADl&a|||||||||||||||||||||||||||||!&"&D%!@"D ?!@"D!0!;f"AD!AA%"@"D!?"@D"0" L9yAD"AA |( <  p  6NMM?n ;;]  !"??3h ,h ,3d !!3QQ ;"Q ;"Q3_  MM ]  d4E4D $% M3O&Q4$% M3O&Q4FAq 3OQv3*@??#M43*@?#M43d" 3_  M MM ] MM<4444!eee >@" !  dMbP?_*+%"??U >@ !  dMbP?_*+%"??U >@ 8;";"B;";"K;";"U; BLBE"LL"L"L"L1"L~"L"L"Lc"L"L"LI"L"L"L."Lz"L"L"L`"L"L"LE"PL"P"P~"P"P"PI"P"Pz"P"P"PE UL.F"?############################### # # # ##########.#/#0#/#####/#0#/#-########## # # # ############################################################### # # # ##########-#/#0#/#####/#0#/#.########## # # # ############################################################### # # # ##########-#/#0#/#####/#0#/#.########## # # # ############################################################### # # # ##########-#/#0#/#####/#0#/#.########## # # # ############################### , Geneva &.(=-4(-3(G-2(-1(Q 0( 1(Z 2( 3(d 4(9-5)-4)-3)-2)-1)0)1)2)3)4)5 Oh+'08@Th ' Math Dept  Math Dept Microsoft Excel@p ՜.+,0  PXt | DocumentSummaryInformation8<_941518406K FP.'P.'Ole CompObjJMT'Purdue Universitysh Sheet1Sheet2Sheet3Chart4  WorksheetsCharts FMicrosoft Excel Chart8FIBExcel.Sheet.8f ,,ObjInfoWorkbookLO2:PRNTPICTfSummaryInformation(NP !Ba= = 8X1Geneva1Geneva1Geneva1Geneva1Geneva1Geneva1Geneva1Geneva1Geneva"$"#,##0_);\("$"#,##0\)!"$"#,##0_);[Red]\("$"#,##0\)""$"#,##0.00_);\("$"#,##0.00\)'""$"#,##0.00_);[Red]\("$"#,##0.00\)7*2_("$"* #,##0_);_("$"* \(#,##0\);_("$"* "-"_);_(@_).))_(* #,##0_);_(* \(#,##0\);_(* "-"_);_(@_)?,:_("$"* #,##0.00_);_("$"* \(#,##0.00\);_("$"* "-"??_);_(@_)6+1_(* #,##0.00_);_(* \(#,##0.00\);_(* "-"??_);_(@_)                + ) , *     Chart5Sheet1`8Sheet2I9Sheet3iaZR3  @@  xy  1 0 0>l 1 0` 1 U%ugP 0x[,p 0x$ 1/U%W 1 1  1 1  1 1 U 3>l 1 1 0 1 U%p/U%XU` 1 3 1 1@ 2ŝ 1x 3 30 2P 1PG\ugug 1 2 1 1Z 4 1 1l 1 30U 2 30t 3Z 2PU% 28 2U 2PZ 4( 2>| 4 3>lR>l 2U@ 2>|ZD/U% U ugug 3t 2 2 2>l 3ug 3XU% 3D/U%6@Ut t| 3XD/U% U t"t| 3X 4@ 3x 3t 4UUt 3ug 4` 3U% 3KKH 4` 4F@ 4`״t؇5tNX>lZ  !"4?? 3h ,h , 3d 113QQ ;2Q ;2Q3_  MM ]  d4E4D $% M3O&Q4$% M3O& Q4FA 3OQ3*@??#M43*@?#M43d" 3_  M MM ] MM<44441e       п???????@@@@ @! @" @#@$@%@&@'@(@)@*@+@,@-@.@/@0@e?Ή\? L9y\lv9B.Pv. Ov. 9B. lv  ։\܉\??lv@9B.@Pv.@@Pv.@9B.@lv@?\? L9y<Ή\lv~9B.Pv. !Pv."9B.#lv$%\& L9yʼ'ʉ\?(?)lv@*~9B.@+Nv.@,@-Pv.@.9B.@/lv@0?e> 6 !  dMbP?_*+%Mz,,  c yg(,,(d'`"d??U }  }  3&&D&'''D  ލ < &l h('h(MH(M((D_pxX(X(Dd(D ( x y~ D4?ADAA%D?D4Ή\?ADAA%D?D4 L9yADAA%D?D4\ADAA%D?D4ADAA%D?D4lvADAA% D? D49B. ADAA%   D?   D 4 Pv. AD AA%  D ?  D 4  AD AA%  D ?  D 4 Ov. AD AA%  D ?  D 4 9B. AD AA%  D ?  D 4 lvAD AA%D ?D4ADAA%D?D4։\ADAA%D?D4ADAA%D?D4܉\?ADAA%D?D4?ADAA%D?D4lv@ADAA%D?D49B.@ADAA%пD?пD4Pv.@ADAA%D?D4@ADAA%?D??D4Pv.@ADAA%?D??D49B.@ADAA%?D??D4lv@ADAA%?D??D4?ADAA%?D??D4\?ADAA%?D??D4 L9y<ADAA%?D??D4Ή\ADAA%@D?@D4ADAA%@D?@D4lv ADAA% @ D? @ D 4 ~9B.!AD AAD l&e!&"&D#$&%'&'''(D)*ލ+<,&l-.h(/'0h(12M%!@!D ?!@!D!4!Pv.AD!AA%"@"D!?"@"D"4"#AD"AA%# @#D"?# @#D#4#Pv.$AD#AA%$ @$D#?$ @$D$4$9B.%AD$AA%%@%D$?%@%D%4%lv&AD%AA%&@&D%?&@&D&4&'AD&AA%'@'D&?'@'D'4'\(AD'AA%(@(D'?(@(D(4( L9yʼ)AD(AA%)@)D(?)@)D)4)ʉ\?*AD)AA%*@*D)?*@*D*4*?+AD*AA%+@+D*?+@+D+4+lv@,AD+AA%,@,D+?,@,D,4,~9B.@-AD,AA%-@-D,?-@-D-4-Nv.@.AD-AA%.@.D-?.@.D.4.@/AD.AA%/@/D.?/@/D/4/Pv.@0AD/AA%0@0D/?0@0D0409B.@1AD0AA%1@1D0?1@1D141lv@AD1AA%2@2D1?2@2D242?"AD2AA(h T( <  p  6NMM?n ;;]  !"??3h ,h ,3d 113QQ ;2Q ;2Q3_  MM ]  d4E4D $% M3O&Q4$% M3O&Q4FAq 3OQv3*@??#M43*@?#M43d" 3_  M MM ] MM<44441eee >@111 !  dMbP?_*+%"??U >@ !  dMbP?_*+%"??U >@     !"#&)*+,-0345678;>?@ABEHIJKLNOPQRSTVWXYZ\   UI.I".;";"8;";"B;";"K;";"U; BLBE"LL"L"L"L1"L~"L"L"Lc"L"L"LI"L"L"L."Lz"L"L"L`"L"L"LE"PL"P"P~"P"P"PI"P"Pz"P"P"PE UL.F"J,# # # # #0#0#/#.# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # ##### # ## # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #.# # #0#0#/#.# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # ##### # ## # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #  , Geneva &.(=-4(-3(G-2(-1(Q 0( 1(Z 2( 3(d 4(9-5)-4)-3)-2)-1)0)1)2)3)4)5 Oh+'08@Th ' Math Dept  Math Dept Microsoft Excel@p ՜.+,0  PXt | 'Purdue Universitysh Sheet1Sheet2Sheet3Chart5  WorksheetsChartsFMicrosoft Equation 3.0DNQE DocumentSummaryInformation8 <_947866753ISFP.'P.'Ole CompObjRTREquation.3< f(t)=asin(bt+c)+d FMathType 5.0 Equation MathType EFEquation.DSMT49qObjInfoUEquation Native X_1304151529[eXFP.'P.'Ole CompObjWYiObjInfoZEquation Native _1304151512]FP.'P.'$DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  f(t) FMathType 5.0 Equation MathType EFEquation.DSMT49qOle CompObj\^iObjInfo_Equation Native  $DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  f(t) FMathType 5.0 Equation MathType EFEquation.DSMT49q_1304152536bFP.'P.'Ole $CompObjac%iObjInfod'Equation Native (__1304152641`ogFP.'P.'Ole .CompObjfh/iC<DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  24== 2pb!24b==2p!b== p12 FMathType 5.0 Equation MathType EFEquation.DSMT49q4DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  9=="- c p12!9=="- 12cp!9p=="-12cObjInfoi1Equation Native 2_1304150687lFP.'P.'Ole 9!c=="- 3p4 FMathType 5.0 Equation MathType EFEquation.DSMT49qD$DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_ECompObjkm:iObjInfon<Equation Native =`_1304152745qFP.'P.'_A  y==asin(bx++c)y==3sin(x++p) FMathType 5.0 Equation MathType EFEquation.DSMT49q]$DSMT5WinAllBasicCodePagesOle CCompObjprDiObjInfosFEquation Native GyTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  f(t)==10sin p12t"- 3p4()++20Oh+'0   4@ ` l x      !"#$%&'(& HrqH.,yͶbuw3Q 'G\ZƹXKңk(q%UyhtS;WA-{EĴE޽Q+;yf߰w{e=d#VCSC6Q F8$!suȩp8ZvI Thu$ s<=m;N#Lul<ûjH/ǥ1UhȘ뫣%x}oߣ[kߙ`F|g>e}D0/du]G.T0.mNr.lKDd B  S A? 2\H`c}sS"聵N8`!0H`c}sS"聵NG xcdd``nbd``baV fx,F^equ02Ȓcjl@?H @fM\7_c@`KZ P.P5;VdebX4&C $37gbm#7V&bύSMt<lvMbX5OHIS"BWM!"@VMhib(H:`\NCԣ3qeB2bZG x}Tn@iKnQЈ&qw Q8=VBN:k뤉B*E x^+O#DGdfo~ֻ_ e9ހʁ|ORC0`}Ʊkj9#%"2BW, VU#啌D ^7M)˒8dEbvl-E-ș4*5c_hҊO\a,vVhm5 [4D}'lr27KA=ǧV^'vpL(B=AF[3wi8"jrsύ"cGnF^=gnf8$~7VFCt}y@rszq2Iut3=7"cR Ig1˞)8hS1d[8Zo^+'n1 0"űZ#%HUDhCCHEqJ%%r)s3Lлe6;qf1v|{*Y|QaP!JfS V֘*D1޷]֨/5˸2QѼ".±%+-2BJF0#?;>b%9;e>NnUJ8zJ; _ᓣycX7j߼*j7G6_͑ 0 kXDd |0  # A2ɔfߛvY!/E;s`!kɔfߛvY!/E;#N5v xڍhVy9ךU-jִRmjj[(Z6EV) R77š*u:B3B:AQMH+,ʜn@F[%um2{ 2*dcOnag^F$^̹ͤ']~r,#߉nmI/Uaà=Ǜ&owfɛ%u9;[ݸF}5MI5#o.y]>oP^y;wTQy]7U=&1ymw@y=zx=F|IV _Jj:Ѧ'UVC[yT Zpy$UUCC}S}S[;yϻ=CM}C__3Ңi&U5בdGfMFek\ap7 nV|cua=q:ߝ:ߝݺݺ{t9sܫ睤睤LQ]~TiFg3cCc>>9>zǍ~{'|˧}g>o4ј<6f17kj2ɘÍn4O; ƶs͘׍ȉ7xȓ<>la#߷r}] 48r)7 .1t9_ov&UË7 nv|da>zu\ק麗u˺++~D2 ccSY*?TWy}gGyO먲=}TNIRe_XO8Oz3=037uT|M lϼ5;rz''{rb'Ola#<oxå~ks=anxkAlӮbkq:_סuy>|?==t. *Okiϩ?.?.GKKeW۫>>y|rr9ayeWovjuWr&5< Im w&rgB TȱɁȻyw ewU@ 0T/aQy2'y:\z6gZ =O}*y*Un uM̢:_פnu7669696y7y7.[T-6oSuީ=Z}Z}fGE}Ԣ~kU2KYJi紫jFhF:HM> K}ؿb'}vן}~XwоYоY cȢ+,د\k"EroPeHCFG0:‘1fl7c#\Ҹj#pn|s#<7"ܬ>6U7]Mug3ut"'DOS].#cF,T΋^ qnк/׺/WTЃ~hu^Kpxm/G8r_y-2#E8%-opx{û"0^7Z5voG8NDEE2#1,:ɢCpp">pgÝ\<gW$gUH8TB"$‘O"'¥z#foR%Dxx%7#|UwM]e999_~x9;"yGeTN]F'9 ENs\^5P9\9^|*.r>s8<5Ss8<=szfN̙9327 r8 Ër8(Ks84[ s_=6t}b?PѲSf/L&_Mee٭WƫWƫ)W7?a]ֺClDÊs |X BN5xOHTQ{z/]d3pBG#lBܸ l ʠ¥ܴۖ"Ast +sa|/'1A3oO%uD=Ns#VN!Wb%Qx4Cܔ#3dfH>"7/ȳxPF#G)n *%Y A>!g5et%32>BKrIi=999MW6 y|F!+JM4Ɉl]5/J;*W):>jv{=-ꗿ>=o\}xnp=ܠ$s־578~{uOxͿqޤt>=!'x=.fJ>E6ٰE=G2E\X1}EwrDd Db  c $A? ?3"`?2kqӶٵ0ay%`!kqӶٵ0ay @^xڥTAlbz`Q%"G09 s{fOKȃA$M,E@,R 66vW G Qfw~of|@ِ;.pbqGL{^Epc^UDI2"zSh*ֹW7u3$#} 6༰3K#f,;pe6 ?ҞKS>e|.l͈VWzQ׶~wٶNx1țS͚Vu5&y1&j:>Ŷo*KL`ɾkc Yb16 '+8šM2\ Q75/)8RSq8,Z\[*^+ʗ!7L;FU/jw6bci̛mt[I+uˌSc c]Qveg->VAID}3|Fwl[lu},ԏiSX'vnh`<ɛ0bU?#hԶ/=;m j>(PptAHڧ5B7mxC~gN%\2p=*sҒ5cU .=kqc&Jy3zz}~PGӵԬ^Φf:h sƩgN૖vFSN͵p)d6/ƃPVX ˏn4Fa(ȣ(XBHrM lڬ 6?QpqB_({L{$ ޾ġ<Ԁ[c୧^`-.Ho~{(ۃje* Ǜogs7^hIDd +b   c $A ? ?3"`?2J "?%,+?&t-`! "?%,+?  PMxUOQ_[*&FA`ⅤI 4B ,5-mh{QTB kzLl&\wۏ&B|̛7y1p"qLZ&삩k㖟J{JW\~5rq&gZLKy vQ J@;9%ԁ҆)Nq I&<ܰ.AW!_1#2VPƵe2U!$%{;)XKڑ))T:YTJ^#!B#W좁`i I'`q~-jw l(Y9*qI^GzN v/6-`y;Kׁ{zJus,o9*esm7cRۜ5U䙶fe^4x`~l^!%ܗYa><=38NYd#Sc[:̐ZH/ i}A JfEApRZ["#cq%B<]HtBo'?/_B? zLC a171&QDLcX8 {$KC! |ŵkU)/lSeA2f!Xtn!ʠjvŧDz,1.;v? 7{/ 83M|8 M\   xڕRkAf6ill BխRmx&LeIV $4'[/P<xcCO==]&B{pv{̼7߼O`> @b<$R 9).{19K S:1dg#A;IJ1^qb-|d4+KbK#PF"Q5D=3y"}(ZY2iͪwؕKY`U# k$n2[ۜ:az(NO0S(HtnL4h;A/q76 l!W 1ִUSdZU/>:0“yZ#i=k׼6劦mH²=.[y?u˗|ۿVB =f`Κ?P;iXNֱ}T!iPF2Ԡt!CRHI^%R&:vY5YU+T/'=;j1=@D>>\);]= U xBX]dh*_бgDd |0  # A 2>*}*|7`!>*}*|?N5xڍpUչAуѴ@PJ h"Fk)P?qFXjAx2Ph'bXT4 IE4S4 B^v^v:_{swn$$ǵ=W1u%vU'+v\& 9|h[[[%%m4$Ƕ u]uB2)67um@[f5(VL&I}@,6ڄ+J|SӜvfP[Km-R;E~-7ym2VP[AjPkDBM^Cm %ԖPFmj |mʨQVMZZnԮv/{URvAjAM^Lm0fS[GmZjZR+L2SMM;OvNH6Iz$)-ar'at4L.չAÔf4LҠaʴE˂)̢aʴY4L3K)qON Sməc+qg#ůyN$K~W# ' ' Oy ] wy|'y_ A[%])j8h.?݃vZz S]w0eZ4L߸*,$-P~H"A `Z = bx&~HA(Aߎ-^Eߣ=Z z6xd£0y|SbMK, =Ab=AI~O?['L߸M)~O{ߕX~v;$wЯk}E_g6s29<L~%rsԓ wH~7wD~7w B~$OZ?wwU*z:(wG;+zo(/P)z*xA+k,/V@c]4_R𻛂\rw6L~ݥ\w߽W4__繯/**}}O3'ݕݕ ~_U ~Q{?g86L7+}߷*}i1_)=N ~OT ~[?S3E ~P{߳q*ztG+voqTߥO#)Ga\y@c_4ߋ ~/V{1I?ao1up# ~+]cxK5KyX~?Nӯ _IW2'O2'O2OSS:ss9ޠw ~W*]SSoކF*UoQwB&w(/~|yU^ec#٣أططf/}}={<#W￐_Ǣ}~/w=Wrwu㺿|y,~%x4<Wj׏3ofNN0''橅;ܝd>[V s|y~%^/W^BEwUs \556L?79V_X~~m_//9s+i'󴓹2n~f0{ K~גߵ?oqE~$ooG#w]G~#w=@~7?wD~7^ }>==;=˾=^nc/ŢŢբՂււ+Y𫃍w ~wh< ~Yp\ .koɯ;ηw ~w63"W>ʧK,/9ENlynim>9c~gB ~ZAg?anjoW;&jK,}oH ~Q3ʂc-=ւ,=o0y~>LGY4nѷ-z^âgZLI-'GNx&ϕ96s,u,=ς,|7-,ax6ߥHECCbi1s[br ~3K^n^eU?k]т-]a ~nޡ[[,łU?5 ~ov ~d{;{;qe}|ffaa/^~:u7ȃ7Ƀ7ɕG#'rOA Ch~>JW}}KcS=T50w w#gMwL~7s9I~߭ 8;q7/5uws};9C?;;߁.pwCusn=ˡG{9e}{C/uϡ9O> xP.5{pE.r .r7>!ɯ뮆x&!.Cx׺X~_|ukF_o7b_̜Ȝ< g3w#Qhx:{;{kx+syƼo}g.gp?}==}}rrss=u=u}.]ُ h#{}{}{{w={#'WK4[O]ߟ'ۓ)rJ~r\9 h~4Ii,5_&_&..i 9"'S)/ER7"]R8K,ES=?ž(H/ R쟞)Ow};~b?IoطRo|ڴ@,Wr}:纣$ i}-wU:=I1ys>dOOܷo+>[K& g_7Օ-$" 2yAgA̤HABC`)Fn#5o- N5x͖MhA|d6iZQA-)ZAsjoRh{OzCMYW$U$$Mb7;IZS膗ߛɰǛwq\:ͮUT0Zu\Z|WQHԬq==q8ȸ0OX?O ПSgz'OEy1.7H>!쿶?7F΁`B^ h9o'Ps"ŐnŽ3n^O?Zd|2Oß !=>u_b!E:Ӈ鿶?H`{~XS=EUs㏷,H;ֈF42{oּnFlziGyO;a1ryI.ۜ/$=Dd |0   # A  2E*7^<"IB] M`!UE*7^<"IBB+N5 xڍZ lU>}ߏ0 NeZZPDM\EZ ? -Cb@aUh (D%8Gb*:X:"렻=Ok%I=O{~snot ]?Oe~ nkkWc\_I _J[[[nApU9¥Sq=<]*V=2հ^U`*b%v ]lQ vrbAwct'?bC|c뉭'vQbB`*[Dl?z lcUĪm#X+Vb8!ܿ;d 5>#bQbKl/lcM&Vb爝#=yF)Qy)}>)iW)U⾤)A7{KeL NT@a?=*rc"9c"Hy U$<*aPE20˨"PEvH x UfAW2d[c"Yc"Y\1T<\1T*b_+C<2;kĿ&}/%'}ʹ:^TL H&dPER1Tq7DB+"ޯ+C8o7 &9#qn GoBFF>Oe]Kx^IWRSS?S)!tVEUzB5!t[߄<*By;>1TG=*PERn[|<1T̑%C̺HdPEY1TZf]1TFpT7z U$ CI>1T5X"٩/x U$KCc"V_HB1T\b;j$}Mdo$H=F>=F-&Kϥqy\G?M?M]SO@VSk5:vyQ?<*~ڌ5*~N*xN*x{Y< o=]?EOUW~uHk-_k1Oq I'R橓ࠝy ӂ\sVk 9A9O4_y ] _yE1(g}h<.8\*RM.U𤻂'||U.W+R UZ߯U袿BN:W,_ -TPR'D/Ӥyj8iD>Dm'ﶓ;.}uMEEMM=R}<դSM<լSXsWq:SyEZ |_!|穣y8oa}qC3 `s=H2yv<;L>-}>N|I|I^NRW_QW_QY,|z>GݟEChs!uvs\7Q~R'3w;S?;X8p#|q:೷;qK|uwSƹs;y!됋uO!gMrY*7~U_\ o.i{9%cy.s]<6>D, OOOw ɻRx)|_F] !=jCUil=|]YP N5xKTQϻȨcIQB.M ɭ arFM6Ѥe$@ B=70Z3sϹsy#AspMTO.Fb|;3rQ^ZD.Tp黔v6|;Lf( 0XRiEY̙A5!1B9, nmд(Ǖ!W ]\ה -!d^F%ϒuy ׅXn"0}js=@GʻUʧV`k&7+!3 =۟.,0S` fR`Xfk`ւ|vօy=*qγ4焒|n^I*k񚼶Z2Z[vH{ݮؿ{=^q|︇KԢn߫b=84zL_QB=,zGsp8Hpoϫ?;s (?Pzp/<`z-S_z$*T'Gyڏz~OoNʐM_ysک7  f)$rͮ HF%zEȼQ7FK nU>NN:k~\i-u<峍1fZÕ1\E{ـz1z8x7맊?/mw Dd |0   # A  2! 7 q 4r ^`! 7 q 4rN5xڍ U =)Q2jc-]"+)MTJ貤$IM2,&+Vh P$Yt۴ v!]6Ip9Ϸ?~~gƚq9є?;^@_%̝aOH(}ƻ3մ5%Xۼ]K\t&jo;K.nrscXySn -0Ϙox1rggTr(rC )75QɭRnr+w5Q*׫V*wXQUyrO(r)ᚨQ(GIJzWnr;!嚕)9jTUFUGEQU+}UuUմVUWU*UUu.UՠTuoUViW9=bQu{C@I޷K2J]9ṔLՙ%ѮQ',͙% og#ٛ9P29PV~(tg@ ꂒ\gdk(b75s$wS2JrѠ$kݜ́<.( ́(fכ9PVK/Wk>2qaa}:|^:lQ^;Unu߯kjj=Z!ǰ0)GuKo"/'K5a4ϧ ~8Uéot >d d,}__|Jk2]9PF́R#mHEP%ɾ9P%鶟etM@IN?d[@I2@Ig31sF%L(́376ow6_972'OzؼYɺ+T]תksuzQ|QWu6G7}sۇ~ї;sG2Ae~8Ao o &y5)NSy__ɉŞXɓ;D~˜,"~u{IDg$OfGdv$w*i~$Grla$FH%\\\{#9{o$WGxu$kܮEH?/Fy%2/D\?#gwdDZ<"ss027!oH7:7uu]w]'kR:/-ujS Q:*Ӭz)眂_XP ZՂ>)ނ~\-sRSH{g%4lW#MeKi/Zm͚ܶWXNJbP]1nDw\լZf/\Yi. 3;z5\ru֌^UzxϳjrNZjϫkɭvt-5q-ks-kIwZjiZjr]KMB]KM^ЫW]U{c((C4:B+1;N5xmOHTQ{՘qY-qf̿D%9Pf"0r2E.ZrFMƂ(d{K {{ǫH8~*E|OigT!O_k\eNEϨJHXFWNo[R iEYrlEøc8, coUW.* ѧrUKºrA'D[X/G#\pUz#\brg?K%*c.DOf&O9J9s:eB.=lFdZ_mѿ}뾰?ӘsJr<\.O,2-%D͕_ږꚼ>zVs>"d}ُ\Nuϼ΁Gll"׬ʙDq=D'kkޛꞭ[& fP8FLԅ7p /ӅIF'WGg`4 A-ߣ.|xߧ|?w.4:|tWY. V(Gmz{㮗$J|m+^Dd pB  S A?  2(}ʧ1;*Aoh`!(}ʧ1;*AoBlRxڕK@K&j1uiA"J炫:9kBqs::U/A \p<"FfH_9Q$OͨryTadž$"&0zY@::qs\Z*=7"q\A@2zs tہcт ̧)t}HBvHr=s6aNt:ӤF|c1Äz"NR2`񴙹Rwz԰&ή@! wt|YSjCJ^JՅdI2 7bSS#8R89Ua%R;8 9[0h=*b4V_ypЃ;Yi4‚z] pvîeςkgz;s˔㑉EeA<3ţ$)vũ,p* ^)Jsς]{&lQ]Z)arqny<;ڪf4F"7r{5ƐxS.a/7UDd @b  c $A? ?3"`?2HV4GJܘfn`!HV4GJܘf xڕRJP=sc}BR A T7[qZCHJѝ#?@h\ ֹi*+'̹Μ\xaD!"tLް)UL#wڌY}táW 9=.4O X$hLQ&}wpC Hl9^bVHݾyԻ_{GٮFA¢ (=Kf}f8]"s5nvt:}4W~Gi!}B8s6F08b2+kꆥSUui~`'<@OZ嫫1?+"TAPmx}UDD9Q9W@ ש*{)7^O#M_]\!Dd @b  c $A? ?3"`?2HV4GJܘfp`!HV4GJܘf xڕRJP=sc}BR A T7[qZCHJѝ#?@h\ ֹi*+'̹Μ\xaD!"tLް)UL#wڌY}táW 9=.4O X$hLQ&}wpC Hl9^bVHݾyԻ_{GٮFA¢ (=Kf}f8]"s5nvt:}4W~Gi!}B8s6F08b2+kꆥSUui~`'<@OZ嫫1?+"TAPmx}UDD9Q9W@ ש*{)7^O#M_]\!Dd lb  c $A? ?3"`?2̩ވ6Ls`!̩ވ6LAxڥTo@~wg'ip@DJP5* H&eHH*B "凕L !11H7$`ad  j틛 `)MN $BG#]"=,vJ ačag|ԳLjb TEF@ӌK1-Bqi rͣ>|E-Uf;nv7J҃uAMxF N5ƾCt);b(c ;fnlNG!1  1Ѭ| ZdbY~vg'W`YIz̎M[0|,'OHjh1C¾P`6 6mldL@btHVjvny,TmPV2U4fO*KNK~vI/QZY/;)E;g_eJX^&5r+)!& g0OVVl xjY3);o.VDd b  c $A? ?3"`?26'f}4?:w`! 'f}4?:_,xڭUMhA~3566hZ4!%Ti\WM$ RM)GGrx7zQ0ILhݙ߼yM^8XHp|HRB,VeHS䬅 QMiCi~hqeX7"M@!Klu-]/koip4IL{ƸCiX.]bo I{) %sKPsHve<0L]b;+hV \/EXxv ځΒydni,4aQf2)_ fL/'mM|;Ƞ|̨]ǚWLrDR$`e!I7l/U=XB8rpH2P˪N${Ja>Jw.׫}Ι6 > y޳ ICYde)r2}fJNnk]nf#Js:-$6Yct:шOGR[^8)%zB7J/>YE"x&'&P*fyͶag$ C=ç!t7M1x l̛l!ny`7wkl^j~0]0 Wgײ ̰ ?OlDd @b  c $A? ?3"`?2a8w4 {`!a8w4 @pXxڥTkAfv71k ?h*(mV,^@IRIT&]5_d#ٜ*RDxBɹH;)B'j ܫ|-7?#G_؆cC_1R6.ܸ-0\!':UA&Uv3GqLr#ZF)#;7ʯ}fP.+R[9ˇ(ҔҩjHhdݺ5ou`d"0VSيvstKMeo:W:Kw5u+%Ӂru1 >PFh,exܗ3ԗ3c`$sFc*㞦033FôDq? 6g}1̌cÊ'1' * ^D8w_ЊFC)^K (hM( nP" 8#0bƛhTY /h-Ȧ5*U@K0SQN/'X  1Table -SummaryInformation(vMDocumentSummaryInformation8U\CompObj[q4Find the amplitude, the period, and the phase shift charlotb Normal.dot charlotb1Microsoft Office Word@G@H@R: ՜.+,0, hp  Purdue University, ' 4Find the amplitude, the period, and the phase shift Title  FMicrosoft Office Word Document MSWordDocWord.Document.89q@@@ NormalCJ_HaJmH sH tH DA@D Default Paragraph FontRiR  Table Normal4 l4a (k(No List2B`2  Body TextaJ4@4 Header  !4 @4 Footer  ! # .   # .1    456fghiwxMdfCu "#$;VZmno D Z ] ` b f i k q v w x ; < b  / 0 1 2 4 5 7 8 : ; = > ] s t u w x ghlmrswx{|000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000X00_X00X00_X00X00_X00X00_X00@0@0X00_X00 0@00H00h0H00h0H00h0H00h0H00h0H00h0H00h0H00h0H00h0H00h0H00h0 BBBBBE6 -. xV>-. .6JLNbdi}g~24=UW ;RT7 O Q F ^ ` ::::::::::::::::::)+1::8@, (  T  C  T  C  Z  S o NB  S DNB  S DHB  C D \  3 "` HB   C D\   3  "`  J2   # "` B     HB   C D\  3  "`  \  3 "`  HB  C DHB  C D\  3 "` J2  # "` J2  # "`HB  C D\  3  "`  N  3    HB  C DJ2  # "` \  3 "` B S  ?f Z [ ] ^ ` b c d f g i k l m n o q r s t <  q t)C$t w t 0&Mtf &tDtBltHtOt 4 t -taHat$ctiwtHt  ttxxt xt t (, t7" tH(t 47et%t2 2 4 4 5 5 7 8 : ; = > t u Y]UY}$)) . K Q ( 1 2 2 4 4 5 5 7 8 : ; = > t u  mq333333333333333333333Uf 1 2 2 4 4 5 5 7 8 : ; = > \ ^ r t u hkmqsvxz|~2 2 4 4 5 5 7 8 : ; = > t u VV D x ; @2X @ $@X@UnknownGz Times New Roman5Symbol3& z Arial"1h&&: : !4, , 2qHX ?23Find the amplitude, the period, and the phase shiftcharlotbcharlotb