ª¬½¯ˆš¶ÿïÿïÿnþÿÿ±¯÷NP8Pack*?À8 @EACTMØEACT1MÄÔf.À‚Øô  ‚8‚Tpˆ ¨¬‚ÈØÌÐä(@X0x|¨ÀØ,”,˜,°,Ä-Ì-Ð-è-ü. ..,IØIÜIìKXK\MÀ======TP13 =======~Dans cette e™activityonon propose de faire remarquer que les onouvelles fonctions æ f~dæ finies dans l'æ non™x™cæ , C et S, ont desprpropriæ tæ s semblablesaux fonctions cos et\ sin...ion1)Gæ næ ration alæ atoireÿÿZ.Fonction Á@RUNMATRandom«Íï‰Ø\Pack`@ˆ9Ä@RUN*?ÿë(  ’€a3Gu)0ÿÿ@RUNMAT´RUN2D1 Ô(Th”Á •‘€(”`\4\L\Hx†20Á™10,1)`@ˆ9Ä@RUNmain˜VWIN„Š`0n 0¼Z ‘WIN`¼ZŠë(1…0qy` †(1…0qy` ’"XE.Listes de valeurs@SSHEETAlea«Íï‰@Pack*?ÿè(  “`2cuWW0@SSHEET°@SNAME< Ô ALEAHXÔ SHEET Ô ALEApp ÿø`€@``@` “`@`p `@```0`P p`p`€(8HXhxˆ˜¨¸ÈØèø(8" XP=†20Á™10,1)e>=†20Á™10,1)e>=†20Á™10,1)e>=†20Á™10,1)e>=†20Á™10,1)e>=†20Á™10,1)e>=†20Á™10,1)e>=†20Á™10,1)e>=†20Á™10,1)e>=†20Á™10,1)e>=†20Á™10,1)e>=†20Á™10,1)e>=†20Á™10,1)e>=†20Á™10,1)e>=†20Á™10,1)e>=†20Á™10,1)e>=†20Á™10,1)e>=†20Á™10,1)e>=†20Á™10,1)e>=†20Á™10,1)e>" C(XP)A" S(XP)Lis2)Fonctions C et SOn peut alors dæ finirl les deux fonctions:L\@SSHEETAlea2«Íï‰ ¼@Pack*?ÿè(  ”BXb€5CG0@SSHEET ´@SNAMEP Ô ALEA\Ô ALEA2l 8Ô SHEET ¤Ô ALEA2Àpppp ÔÔÿø`€` €€ ``p`P`€ ``p`P€`ÿø1IyRY262‰ 9hrI@31q"…I"qV6$V4BT’Y2qX)ˆw49Ix8da%!"4€ Qx)!e“s!—9–Q…$BPf…U8"&  ##@14†A4•G4haˆ%)ƒw3fY†ƒwrFY262‰ f…U8"&ÿø1Ix‚W‰U`Q 8…„0`9hrCaˆE31q!’wrA"q1W7y4A ‚y`2qX)p6(`Ii…‡Q`!"49"tc‘`!e‚ftR9–Q…@'€`3VGG$` Rvf€14†@—‡bI@bc`fU`) 0hXE3fY†pƒSQ 8…„0`3VGG$ÿø2˜ W˜pAs x"—G  UTQY”2p6cBDbw‰$B‡“I'580ƒ’uu8 a„W“fuy! ”qrE!# tgqC„d suTtSuA™078# “2‡ƒi€€ v gFVUd2ir‚2‚hQHys$‡( eSCpx473sS‘U™!!QQ‡5 “2‡ƒi€€(8HXhxˆ˜¨¸ÈØèø(8" XP =†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1) ,<L\l|Œ ´ÈÜð,@Th" C(XP)Ã=(¥A2‰¥(™A2))¹2=(¥A3‰¥(™A3))¹2=(¥A4‰¥(™A4))¹2=(¥A5‰¥(™A5))¹2=(¥A6‰¥(™A6))¹2=(¥A7‰¥(™A7))¹2=(¥A8‰¥(™A8))¹2=(¥A9‰¥(™A9))¹2=(¥A10‰¥(™A10))¹2=(¥A11‰¥(™A11))¹2=(¥A12‰¥(™A12))¹2=(¥A13‰¥(™A13))¹2=(¥A14‰¥(™A14))¹2=(¥A15‰¥(™A15))¹2=(¥A16‰¥(™A16))¹2=(¥A17‰¥(™A17))¹2=(¥A18‰¥(™A18))¹2=(¥A19‰¥(™A19))¹2=(¥A20‰¥(™A20))¹2=(¥A21‰¥(™A21))¹2 ,<L\l|Œ ´ÈÜð,@Th" S(XP)ÿø=(¥A2™¥(™A2))¹2=(¥A3™¥(™A3))¹2=(¥A4™¥(™A4))¹2=(¥A5™¥(™A5))¹2=(¥A6™¥(™A6))¹2=(¥A7™¥(™A7))¹2=(¥A8™¥(™A8))¹2=(¥A9™¥(™A9))¹2=(¥A10™¥(™A10))¹22=(¥A11™¥(™A11))¹22=(¥A12™¥(™A12))¹22=(¥A13™¥(™A13))¹22=(¥A14™¥(™A14))¹22=(¥A15™¥(™A15))¹22=(¥A16™¥(™A16))¹22=(¥A17™¥(™A17))¹22=(¥A18™¥(™A18))¹22=(¥A19™¥(™A19))¹22=(¥A20™¥(™A20))¹22=(¥A21™¥(™A21))¹22 (08@HPX`hpx€ˆ˜ " ¥XP=¥A21™¥=¥A31™¥=¥A41™¥=¥A51™¥=¥A61™¥=¥A71™¥=¥A81™¥=¥A91™¥=¥A10™¥=¥A11™¥=¥A12™¥=¥A13™¥=¥A14™¥=¥A15™¥=¥A16™¥=¥A17™¥=¥A18™¥=¥A19™¥=¥A20™¥=¥A21™¥main˜VWIN„Š`0n 0¼Z ‘WIN`¼ZŠë(1…0qy` †(1…0qy` ’"XE@GRAPHcourbes«Íï‰,hPack`\o Än ~vE9R@\o Än ~*?À( @SSHEETD@SNAME( Ô SHEET4Ô SHEET@GRAPH$GMEM1Ô`0n 0¼Z ‘WIN`axE™7VP\‰’)–‡‚S\(1…0qy` †(1…0qy` ’"XE€€(¥X‰¥‡X)¹2(¥X™¥‡X)¹2@RUNMAT,RUN2D1Ô mainà1<È2LÈVWIN\„Š€(¥X‰¥‡X)¹2€(¥X™¥‡X)¹2`\\ „’4’4’\`axE™7VP\‰’)–‡‚S\(1…0qy` †(1…0qy` ‘3)Rel fondamentaleìPour cela, on æ valuedp d'abord les carræ s,enensuite on observe...n@SSHEETCarræ «ÍDPack*?ÿê(  —`Dˆc”yx0@SSHEET<@SNAME< Ô CARREHäÔ SHEET,Ô CARRE pppppp Ôô444ÿø`€ “``€`0 `0` `0 p `@@`p `€Y• ÿøY262‰ 8‡’x`S8QA(† E„)GIu31q"…I— #&c4”…dW˜‘f5tvD–8‡’x`— #&c8‡’x`1At"#W "†dbT9˜FS“˜FS“$ 5(—#&iqWUI31q"…Iv%–R88‡’x`ÿø`Q 8…„036&U6P “R“DqA` •aF“5`31q!’wrA`iƒ‚Cr’b4”…dGˆR&`57‡xvb„`36&U6P`iƒ‚Cr’b36&U6P1Asv•0"Eˆ9–VU`CPQSCPQS`$ "—x &iqPC`31q!’wrAY•! SI7P36&U6Pÿø3i•@ƒ&Q8!TBb• '2`‘!0udhf ˆq)ˆƒp†ˆE3rDˆ)5ƒ!„'A7@%8!TBb•ˆE38!TBb•a!’q3!P–t…s@bcd „0Vbcd „0VQeTHQ‘“•q)ˆƒp†'@1tb8!TBb•ÿø3i•@ƒ&Q8!DBb‘ ‰'2`‘!) udhf ‰q)xƒp…ˆE3rDˆ)5ƒ!ƒ'A7@%8!DBb‘ˆE38!DBb‘a!‘™q3!I–t…s9bcd „0Ubcd „0UQeTHQ““q)xƒp… ’qT@v%8!DBb‘ÿø@ ™™™™™™™ ™™™™™™™ ™™™™™™@ ™™™™™™™@ @(8HXhxˆ˜¨¸ÈØèø(8" XP=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1)=†20Á™10,1) ,<L\l|Œ ´ÈÜð,@Th" C(XP)Ã=(¥A2‰¥(™A2))¹2=(¥A3‰¥(™A3))¹2=(¥A4‰¥(™A4))¹2=(¥A5‰¥(™A5))¹2=(¥A6‰¥(™A6))¹2=(¥A7‰¥(™A7))¹2=(¥A8‰¥(™A8))¹2=(¥A9‰¥(™A9))¹2=(¥A10‰¥(™A10))¹2=(¥A11‰¥(™A11))¹2=(¥A12‰¥(™A12))¹2=(¥A13‰¥(™A13))¹2=(¥A14‰¥(™A14))¹2=(¥A15‰¥(™A15))¹2=(¥A16‰¥(™A16))¹2=(¥A17‰¥(™A17))¹2=(¥A18‰¥(™A18))¹2=(¥A19‰¥(™A19))¹2=(¥A20‰¥(™A20))¹2=(¥A21‰¥(™A21))¹2  4H\p„˜¬ÀÔèü$8L`tˆ" S(XP)A=(¥(A2)™¥(™A2))¹2=(¥(A3)™¥(™A3))¹2]=(¥(A4)™¥(™A4))¹2]=(¥(A5)™¥(™A5))¹2]=(¥(A6)™¥(™A6))¹2]=(¥(A7)™¥(™A7))¹2]=(¥(A8)™¥(™A8))¹2]=(¥(A9)™¥(™A9))¹2]=(¥(A10)™¥(™A10))¹2=(¥(A11)™¥(™A11))¹2=(¥(A12)™¥(™A12))¹2=(¥(A13)™¥(™A13))¹2=(¥(A14)™¥(™A14))¹2=(¥(A15)™¥(™A15))¹2=(¥(A16)™¥(™A16))¹2=(¥(A17)™¥(™A17))¹2=(¥(A18)™¥(™A18))¹2=(¥(A19)™¥(™A19))¹2=(¥(A20)™¥(™A20))¹2=(¥(A21)™¥(™A21))¹2 $,4<DLXdp|ˆ” ¬¸ÄÐ"CåÂ(XP)6=(B2)¨2=(B3)¨2=(B4)¨2=(B5)¨2=(B6)¨2=(B7)¨2=(B8)¨2=(B9)¨2=(B10)¨2(™?=(B11)¨2(™?=(B12)¨2(™?=(B13)¨2(™?=(B14)¨2(™?=(B15)¨2(™?=(B16)¨2(™?=(B17)¨2(™?=(B18)¨2(™?=(B19)¨2(™?=(B20)¨2(™?=(B21)¨2(™? $,4<DLXdp|ˆ” ¬¸ÄÐ"SåÂ(XP)A=(C2)¨2=(C3)¨2=(C4)¨2=(C5)¨2=(C6)¨2=(C7)¨2=(C8)¨2=(C9)¨2=(C10)¨2(™?=(C11)¨2(™?=(C12)¨2(™?=(C13)¨2(™?=(C14)¨2(™?=(C15)¨2(™?=(C16)¨2(™?=(C17)¨2(™?=(C18)¨2(™?=(C19)¨2(™?=(C20)¨2(™?=(C21)¨2(™? $,4<DLXdp|ˆ” ¬¸ÄÐ"Cå™SåÂÃ=D2™E2=D3™E3=D4™E4=D5™E5=D6™E6=D7™E7=D8™E8=D9™E9=D10™E10z\=D11™E11z\=D12™E12z\=D13™E13z\=D14™E14z\=D15™E15z\=D16™E16z\=D17™E17z\=D18™E18z\=D19™E19z\=D20™E20z\=D21™E21z\nsuLa relation apparaættalors d'elle mæ me:@EACT Relation«Íï‰è8Pack*?À( @RUNMATTEXT1|Ô 4@T‚XxIl s'agit de la elarelation :dPour tout x ræ el,\ourh C¨åÂ(x)™S¨åÂ(x)=1ÿÿl slor4)Formules d'additionþÿIl faut cette fois deux variableXi Xi et Yi. On obtient alors :@SSHEETAddition C et S«Í@Pack*?ÿè(  •)WcR'0@SSHEET(@SNAME< Ô ADDHÐÔ SHEETÔ ADD€ppøøøøøøøøøøøø00ÿøTy'˜&`Y”B”`˜1r˜xe•W6(ht–gp`r•H4 ’PApD`"ut%$™™ “XvWˆ`Y˜1–v€`5&)`‚cB ’u8&)@trwdsr‘Sp`”•Y…R` '9r •CS@ÿøds&EF`˜D7 r ‘68(`#$P!pY“‚R˜—@'x–gGX(‡H…`v •h”``Y“™2`’ ™vb–)@Y•i‰``’$“S”wd3DU’X`hqwvY‘We@r”Cs ‘wE`àErbWUqS˜yep–"‰W„‰tq‡e"—%F”2pu(FˆXBA—T€rd‘2DB˜‰$4VI73ài( hci ‘)huU“Ahv†™’x‰@a ˜1’™fA28y — ƒa3g9V"’Yg#VXCb`9W‘à$E‘Ied`54u˜F `V@d8“Vrvi™s"0v‡ WV!ƒI€c`ppC†! ’S$„"c@s™6”y`fE'C†àPVcf` †$yP ‘6€IhV`V"duXPY“‘’v—$dF7"%HU—d'93g…Y’†`3vQ“ˆ`" –Tp Uà"(g!’…YS GH!$…“†FFt4'–@ˆQCViH˜y HwRy$˜d@'1‰$t6!‰ˆCg%'2ubx˜bàah@ˆ”•SHacP3sau5w"%5…s94#g8y(Cq–%c4y•80x‡Dr"W4ˆ4Sƒ‡„ pp‰Eˆfàac1!$&2‘E—Y”‡X‡#P`‘‰2‡`bT9˜ 3€‚™4‚`w˜F– ˜Rs “%``ˆ&e`Q ™d G30™dà"(g!’…YS GH $…“†FFw4'–@ˆRCViH˜ HwRy$˜d@'1‘$t6!‰Cg%'3ubx˜bà!‡qFrR`…I#2w%` Q5G’ ˜“ewsEp%(('r7F CI e”PY•``G €5€9ƒH „…–ˆi‰…”ƒa‚3à@v8ƒR`3)’P‘%`YraU&IVˆy@gR•#TBh’'"'“!p`„x18 ˜D3hgGyx50Cd6@‡7ftBà68B8Ah`R0•…™ •A—…s`R!c2•’`”ˆx@C!Q!ƒrr‚(ri`9˜(7–6p`0”DFufPW‡w‘à!‡qFrR`…I#2w$` Q5G’ ˜“ewsEp0(('r7G CI e”RY•``G €@€9ƒH „…–ˆi”ƒa‚3 (08@HPX`hpx€ˆ˜ " XP =6Á™3Í=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3 (08@HPX`hpx€ˆ˜ " YP=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3=6Á™3   4H\p„˜¬À" C(XP))=(¥(A2)‰¥(™A2))¹2Á,=(¥(A3)‰¥(™A3))¹2Á,=(¥(A4)‰¥(™A4))¹2Á,=(¥(A5)‰¥(™A5))¹2Á,=(¥(A6)‰¥(™A6))¹2Á,=(¥(A7)‰¥(™A7))¹2Á,=(¥(A8)‰¥(™A8))¹2Á,=(¥(A9)‰¥(™A9))¹2Á,=(¥(A10)‰¥(™A10))¹2=(¥(A11)‰¥(™A11))¹2   4H\p„˜¬À" C(YP)Ã=(¥(B2)‰¥(™B2))¹22=(¥(B3)‰¥(™B3))¹22=(¥(B4)‰¥(™B4))¹22=(¥(B5)‰¥(™B5))¹22=(¥(B6)‰¥(™B6))¹22=(¥(B7)‰¥(™B7))¹22=(¥(B8)‰¥(™B8))¹22=(¥(B9)‰¥(™B9))¹22=(¥(B10)‰¥(™B10))¹2=(¥(B11)‰¥(™B11))¹2   4H\p„˜¬À" S(XP)Ã=(¥(A2)™¥(™A2))¹22=(¥(A3)™¥(™A3))¹22=(¥(A4)™¥(™A4))¹22=(¥(A5)™¥(™A5))¹22=(¥(A6)™¥(™A6))¹22=(¥(A7)™¥(™A7))¹22=(¥(A8)™¥(™A8))¹22=(¥(A9)™¥(™A9))¹22=(¥(A10)™¥(™A10))¹2=(¥(A11)™¥(™A11))¹2   4H\p„˜¬À" S(YP)Ã=(¥(B2)™¥(™B2))¹22=(¥(B3)™¥(™B3))¹22=(¥(B4)™¥(™B4))¹22=(¥(B5)™¥(™B5))¹22=(¥(B6)™¥(™B6))¹22=(¥(B7)™¥(™B7))¹22=(¥(B8)™¥(™B8))¹22=(¥(B9)™¥(™B9))¹22=(¥(B10)™¥(™B10))¹2=(¥(B11)™¥(™B11))¹2  8Ph€˜°Èä"C(X‰Y)=(¥(A2‰B2)‰¥‡(A2‰B2))¹2=(¥(A3‰B3)‰¥‡(A3‰B3))¹2=(¥(A4‰B4)‰¥‡(A4‰B4))¹2=(¥(A5‰B5)‰¥‡(A5‰B5))¹2=(¥(A6‰B6)‰¥‡(A6‰B6))¹2=(¥(A7‰B7)‰¥‡(A7‰B7))¹2=(¥(A8‰B8)‰¥‡(A8‰B8))¹2=(¥(A9‰B9)‰¥‡(A9‰B9))¹2=(¥(A10‰B10)‰¥‡(A10‰B10))¹2=(¥(A11‰B11)‰¥‡(A11‰B11))¹2  (08@HT"CX©CY=C2©D2‰=C3©D3‰=C4©D4‰=C5©D5‰=C6©D6‰=C7©D7‰=C8©D8‰=C9©D9‰=C10©D1011)=C11©D1111)  (08@HT"SX©SY=E2©F21=E3©F31=E4©F41=E5©F51=E6©F61=E7©F71=E8©F81=E9©F91=E10©F1011)=E11©F1111)  (08@HT" H‰I=H2‰I21=H3‰I31=H4‰I41=H5‰I51=H6‰I61=H7‰I71=H8‰I81=H9‰I91=H10‰I1011)=H11‰I1111)  8Ph€˜°Èä"S(X‰Y)=(¥(A2‰B2)™¥‡(A2‰B2))¹2=(¥(A3‰B3)™¥‡(A3‰B3))¹2=(¥(A4‰B4)™¥‡(A4‰B4))¹2=(¥(A5‰B5)™¥‡(A5‰B5))¹2=(¥(A6‰B6)™¥‡(A6‰B6))¹2=(¥(A7‰B7)™¥‡(A7‰B7))¹2=(¥(A8‰B8)™¥‡(A8‰B8))¹2=(¥(A9‰B9)™¥‡(A9‰B9))¹2=(¥(A10‰B10)™¥‡(A10‰B10))¹2=(¥(A11‰B11)™¥‡(A11‰B11))¹2  (08@HT"SX©CY=E2©D2‰=E3©D3‰=E4©D4‰=E5©D5‰=E6©D6‰=E7©D7‰=E8©D8‰=E9©D9‰=E10©D1011)=E11©D1111)  (08@HT"SY©CX=F2©C21=F3©C31=F4©C41=F5©C51=F6©C61=F7©C71=F8©C81=F9©C91=F10©C1011)=F11©C1111)  (08@HT" L‰M =L2‰M21=L3‰M31=L4‰M41=L5‰M51=L6‰M61=L7‰M71=L8‰M81=L9‰M91=L10‰M1011)=L11‰M1111)l fCe qui donne:@EACT Relations«Íï‰L8Pack*?À( @RUNMATôTEXT1àÔ ,D\t‚Œ‚˜‚´‚ÀÜOn obtient alors les …relations suivantes:\Pour tout couple de \ræ els x et y, on a :…$C(x‰y)C~ =C(x)C(y)‰S(x)S(y)))$S(x‰y)~ =S(x)C(y)‰S(y)S(x)L =@EACT Cachette«Íï‰DPPackR6C\\4\L\*?À( @RUNMATÔRUN2D1(@ÔTEXT1hlÔ ,8d„°¼è4$¢1T0€cH$\\4\L\B(»¥1‰¥‡12T0€cH%\\4\L\B$¡1R6C€\\4\L\B(»¥1™¥‡12R6C\\4\L\B,D\Allez voir dans le mode run, vous verrezou sont cachæ es ces\fonctions...us