Algebra and Trigonometry Review .pdf

1. Algebra and Trigonometry Review Material Department of Mathematics Vanderbilt University June 2, 2004 http://atlas.math.vanderbilt.edu/~pscrooke/calculus/calculus.html

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43. OW PRG JOKMQOE1LKY [ JOKMQOE1LK g1PR VGUHGG h 1I SLKKGV

44. OH £

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64. ¢RGQGNGH L HOOP 1QNOKNGI PRG ItDLHG HOOP OW L QGULP1NG QDEFGHT gG SLKK PR1I HOOP 0

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70. e me î ¤ eÌ q h_e q a h qh_ qh b _ r q_ r a h«b qa qhm_ ú î qô K qú î r …1QSG PRG JOKMQOE1LK 1I SDF1ST 1P RLI LP EOIP PRHGG HOOPIY ¢G RLNG WODQV PRHGG HOOPI ƒe ] _T q_T LQV qú î „T IO gG RLNG WODQV PRG HOOPI OW PRG JOKMQOE1LKY _Y W MOD SLQ QV OQG HOOP OW L JOKMQOE1LK ƒJGHRLJI FM LJJKM1QU PRG ZLP1OQLK ZOOP jRGOHGE LI gG V1V 1Q PRG KLIP G‘LEJKG„T PRGHG LHG PgO EGPROVI OW LPPGEJP1QU PO QV PRG HGEL1Q1QU HOOPIY ÂQG OW PRGIG EGPROVI 1I SLKKGV Œ Y $ª Š 1QV LKK HOOPI OW eë q e î q eÌ q hae q _aY jRG ZLP1OQLK ZOOP jRGOHGE PGKKI DI PRLP LKK HLP1OQLK HOOPI EDIP FG OW PRG WOHE ÎG H T gRGHG I LQV J LHG JOI1P1NG 1QPGUGHIT I 1I L V1N1IOH OW “ô ] q_aT LQV J 1I L V1N1IOH OW “ç ] hY ËGQSG PRG SLQV1VLPGI WOH HLP1OQLK HOOPI LHG Îh`Î_`Îm`Îa`Îb`Îc`Îh_`Î_an …1QSG ƒa„ë q ƒa„ î q ƒa„Ì q haƒa„ q _a ] rT e ] a 1I L HOOP LQV IO e q a 1I L WLSPOHY àIG JOKMQOE1LK KOQU V1N1I1OQ PO V1N1VG PRG JOKMQOE1LK FM e q ak _h

71. e î ¤meÌ ¤«e ¤b e q a eë qe î qeÌ qhae q_a qƒeë qae î „ me î qeÌ qhae q_a qƒme î qh_eÌ„ «eÌ qhae q_a qƒ«eÌ q_re„ be q_a qƒbe q_a„ r ƒ…1QSG gG |QGg e q a gLI L WLSPOH OW ODH JOKMQOE1LKTgG G‘JGSPGV PO UGP r LI ODH QLK HGEL1QVGHY„ jRDI eëqe î qeÌqhaeq_a ] ƒeqa„ƒe î ¤meÌ¤«e¤b„Y jO WLSPOH e î ¤meÌ¤«e¤bT gG LJJKM PRG ZLP1OQLK ZOOP jRGOHGE LQV UGP SLQV1VLPG HLP1OQLK HOOPI Îh`Î_`Îm`ÎbY …1QSG ƒq_„ î ¤ mƒq_„Ì ¤ «ƒq_„ ¤ b ] rT e ] q_ 1I L HOOP LQV IO e q ƒq_„ ] e ¤ _ 1I L WLSPOHY àIG JOKMQOE1LK KOQU V1N1I1OQ LUL1Qk eÌ ¤e ¤m e ¤ _ e î ¤meÌ ¤«e ¤b qƒe î ¤_eÌ„ eÌ ¤«e ¤b qƒeÌ ¤_e„ me ¤b qƒme„ ¤b„ r ƒ[I FGWOHGT gG G‘JGSPGV PO UGP r LI ODH QLK HGEL1QVGH I1QSG gG |QGg PRLP e ¤ _ gLI L WLSPOH OW e î ¤ meÌ ¤ «e ¤ bY„ __

72. ËGQSG eë q e î q eÌ q hae q _a ] ƒe q a„ƒe ¤ _„ƒeÌ ¤ e ¤ m„Y jO QV PRG HOOPI OW eÌ ¤ e ¤ mT DIG PRG tDLVHLP1S WOHEDKLk e ] qhÎ ? hÌ q aƒh„ƒm„ _ƒh„ ] qhÎ }qhh _ jRGIG LHG 1ELU1QLHM HOOPIT LQV IO PRG HGLK HOOPI OW PRG OH1U1QLK JOKMQOE1LK LHG e ] a LQV e ] q_Y mY 21NGQ OQG HOOP OW L JOKMQOE1LKTPRG OPRGH EGPROV WOH QV1QU PRG HGEL1Q1QU HOOPI 1I L JHOSGII SLKKGV + Œ Y ¢R1KG JOKMQOE1LK KOQU V1N1I1OQ KGPI MOD V1N1VG LQM JOKMQOE1LK1QPO LQM OPRGH JOKMQOE1LKTIMQPRGP1S V1N1I1OQ 1I OQKM JOII1FKG 1WPRG V1N1IOH1I L JOKMQOE1LKOW PRG WOHE eq Y ƒGGJ 1Q E1QV PRLP SODKV FG QGULP1NGTIO e¤_ ] eqƒq_„ 1I IDSR L JOKMQOE1LKY„ jO DIG IMQPRGP1S V1N1I1OQ PO V1N1VG e q 1QPO “çeç ¤“çøúeçøú¤ nnn¤“úe¤“ôT FGU1Q g1PR PRG WOKKOg1QU V1LUHLEk “ç “çøú ÀÀÀ “ú “ô W L JOgGH OW e 1I E1II1QU WHOE PRG JOKMQOE1LKTEL|G IDHG PO JKLSG L r 1Q POJ HOg OW PRG SOHHGIJOQV1QU SOKDEQ 1Q PRG V1LUHLEY Š OH G‘LEJKGT PO V1N1VG e ¤ _ 1QPO eë q eÌ ¤ hT FGU1Q g1PR q_ h r qh r h CG‘PT gH1PG “ç 1Q PRG FOPPOE HOg OW PRG SOKDEQ g1PR “ç 1Q PRG POJ HOgY jRGQT WOH GLSR SOKDEQ WHOE KGWP PO H1URPT ƒL„ EDKP1JKM PRG NLKDG 1Q PRG FOPPOE HOg OW PRG JHGN1ODI SOKDEQ FM T ƒF„ gH1PG PR1I NLKDG 1Q PRG E1VVKG HOgT _m

73. ƒS„ LVV PR1I NLKDG PO PRG NLKDG 1Q PRG POJ HOgT LQV ƒV„ gH1PG PRG HGIDKP OW PR1I LVV1P1OQ 1Q PRG FOPPOE HOgY ‚NGQPDLKKM MOD g1KK UGP L QDEFGH 1Q PRG KOgGH H1URPRLQV SOHQGH OW PRG V1LUHLEY W PR1I QDEFGH 1I QOP rT PRGQ e q 1I QOP L WLSPOH OW PRG JOKMQOE1LK LQV IO 1I QOP L HOOPY W PR1I QDEFGH 1I rTPRGQ eq 1I L WLSPOH OW PRG JOKMQOE1LKT 1I L HOOP OW PRG JOKMQOE1LKT LQV PRG QDEFGHI 1Q PRG FOPPOE HOg PO PRG KGWP OW PRG NGHP1SLK K1QG PGKK MOD PRG SOGF S1GQPI OW PRG OPRGH WLSPOHT PRG JOKMQOE1LK “çeç ¤ nnn¤ “ô e q Y #ª Š 1QV LKK HOOPI OW e î q aeÌ q _e ¤ mY jRG ZLP1OQLK ZOOP jRGOHGE U1NGI DI SLQV1VLPG HLP1OQLK HOOPI Îh LQV ÎmY àIG IMQPRGP1S V1N1I1OQ PO IGG 1W h 1I L HOOPk h h qa q_ m h qm q« h qm q« q_ …1QSG q_ y] rT e ] h 1I QOP L HOOPY jHM e ] qhk qh h qa q_ m qh « qm h q« m r …1QSG r LJJGLHI 1Q PRG KOgGH H1URPRLQV SOHQGHT e ] qh 1I L HOOP LQV e î q aeÌ q _e ¤ m ] ƒe ¤ h„ƒeÌ q «e ¤ m„n COPG ROg PRG QDEFGHI 1Q PRG FOPPOE HOg OW PRG V1LUHLE ƒhT q«T LQV m„ U1NG DI PRG SOGF S1GQPI OW PRG OPRGH WLSPOHY jO QV PRG HOOPI OW eÌ q «e ¤ mT DIG PRG tDLVHLP1S WOHEDKLk e ] qƒq«„Î ? ƒq«„Ì q aƒh„ƒm„ _ƒh„ ] «Î }hm _ ËGQSG PRG HOOPI OW PRG OH1U1QLK JOKMQOE1LK LHG e ] qhT « ¤ }hm _ T LQV « q }hm _ Y _a

74. ¸¹@Aµ´B@B ßGPGHE1QG PRG VGUHGG OW PRG WOKKOg1QU JOKMQOE1LKIY hY eÌ q h _Y h qe mY ha aY “e î ¤ ”eÌ ¤ ¿e ¤

75. …1EJK1WM PRG WOKKOg1QU G‘JHGII1OQI FM EDKP1JKM1QU LQV SOKKGSP1QU K1|G JOgGHI OW eY «Y _eƒe î q h„ bY ƒaeë ¤ _eÌ q „eÌ Y ƒ«e q h„ƒe ¤ b„ cY ƒeÌ q h„ƒeÌ ¤ h„ iY ƒe ¤ _„Ì hrY ƒe q h„Ì hhY ƒ_eÌ q h„ƒhq e q meÌ„ h_Y ƒqeÌ ¤ _e q m„ƒhae î ¤ h„ hmY ƒ“e ¤ ”„ƒ¿e ¤

76. „ haY ƒ“e ¤ ”„ î h«Y eƒe ¤ h„ƒe ¤ _„ hbY ƒe q _„ƒe ¤ m„Ì Š LSPOH SOEJKGPGKM PRG WOKKOg1QU JOKMQOE1LKIY hY eÌ ¤ e hcY meë ¤ ie î hiY _e î ¤ aeÌ ¤ _e _rY qeÌ ¤ be q i _hY hbeÌ q _« __Y aieÌ q cheë _mY c q e î _aY _e î ¤ h _«Y eÌ ¤ h_e ¤ _ _bY _eÌ ¤ ce ¤ b _Y eÌ q _e q c _cY eÌ ¤ ae q _h _iY e î ¤ eÌ qe q h mrY hbeë q hbe î ¤ _e q _ mhY eë ¤ _e î q e q _ m_Y eë q ceÌ ¤ hb _«

77. Š 1QV LKK HGLK HOOPI OW PRG WOKKOg1QU JOKMQOE1LKIY mmY eÌ ¤ hre q hh maY eÌ q ae ¤ a m«Y eÌ q i mbY eÌ ¤ _«e ¤ hrr mY eÌ q e q h mcY e î ¤ _eÌ ¤ _e miY qeÌ ¤ ae ¤ h arY _eÌ q e ¤ _ ahY eÌ ¤ ae ¤ i a_Y meÌ ¤ e ¤ _ àIG PRG LVNLQSGV HOOP¡ QV1QU PGSRQ1tDGI V1ISDIIGV 1Q PR1I IGSP1OQ PO QV LKK HGLK HOOPI OW PRG WOKKOg1QU JOKMQOE1LKIY amY e î q beÌ ¤ e q b aaY e î ¤ eÌ q _ae ¤ mb a«Y _eë q ie î q _eÌ ¤ mie q hc abY eë q ae î ¤ beÌ q ae ¤ h aY _eë ¤ h«e î ¤ _«eÌ q ce ¤ hb acY aeï q hbeë ¤ he î q hieÌ ¤ hme q m aiY eë q eÌ ¤ h_ «rY eë q e î q _e q a «hY eë q hmeÌ q h_e «_Y meë q me î q be q h_ _b

78. 9:' 567åæ 67æå jRG I1EJKGIP WOHE OW LQ LKUGFHL1S WHLSP1OQ 1I L

79. L gR1SR 1I L tDOP1GQP OW PgO JOKMQOE1LKIY ‚‘LEJKGI OW HLP1OQLK G‘JHGII1OQI LHG _ «“” ` me ¤ a î e ` LQV e ¤ « c n M »N@BÄ C@AB [ WHLSP1OQ 1I IL1V PO FG 1Q .

80. 1W LKK SOEEOQ WLSPOHI OW PRG QDEGHLPOH LQV VGQOE1QLPOH RLNG FGGQ SLQSGKGVY ª ZGVDSG PRG WOKKOg1QU WHLSP1OQI PO KOgGIP PGHEIk ƒL„ eë q _e î eÌ q _e ] e î ƒe q _„ eƒe q _„ ] eÌ ƒF„ _eÌ ¤ e q m a q «e ¤ eÌ ] ƒe q h„ƒ_e ¤ m„ ƒh qe„ƒa q e„ ] ƒe q h„ƒ_e ¤ m„ qƒe q h„ƒa q e„ ] _e ¤ m qƒa q e„ ] _e ¤ m e q a [ ¢[ZCC2 [‹Âàj õ[Cõ‚éC2 k me ¤ e y] m ¤ ¢G SLQQOP SLQSGK PRG eêI FGSLDIG e 1I QOP L WLSPOH OW œœ; PGHE 1Q PRG QDEGHLPOH LQV œœ; PGHE 1Q PRG VGQOE1QLPOHY jRG WHLSP1OQ me ¤ e 1I LKHGLVM 1Q KOgGIP PGHEIY =·Ä´º·) ´¼ ¶¼ù O ´A ´ù´¼ ¢RGQ EDKP1JKM1QU WHLSP1OQI gG DIG PRG WOKKOg1QU HDKGk P Q À R S ] P R Q S PRLP 1IT gG EDKP1JKM QDEGHLPOHI POUGPRGH LQV VGQOE1QLPOHI POUGPRGHY _

81. ª ¾DKP1JKM LQV HGVDSG PO KOgGIP PGHEIk ƒL„ e ¤ _ e ¤ h À e e ¤ h ] eƒe ¤ _„ ƒe ¤ h„Ì ƒF„ e T À T Ì eÌ Ì ] e T Ì T eÌ Ì ] T e ƒS„ _e q c e ¤ _ À eÌ ¤ ae ¤ a eÌ q hb ] _ƒe q a„ e ¤ _ À ƒe ¤ _„Ì ƒe ¤ a„ƒe q a„ ] _ƒe q a„ƒe ¤ _„Ì ƒe ¤ _„ƒe ¤ a„ƒe q a„ ] _ƒe ¤ _„ e ¤ a ƒV„ “ ì”¿ “Ìí ] “ h À ”¿ “Ì ] “”¿ “Ì ] ”¿ “ Q OHVGH PO V1N1VG WHLSP1OQIT gG DIG PRG WOKKOg1QU HDKGk ìP Q í ìR S í ] P Q À S R PRLP 1ITgG EDKP1JKM PRG QDEGHLPOHFM PRG HGS1JHOSLKOWPRG G‘JHGII1OQ 1Q PRG VGQOE1QLPOHY ª ß1N1VG LQV HGVDSG PO KOgGIP PGHEIk ƒL„ e e ¤ eÌ ƒe ¤ „ î ] e e ¤ À ƒe ¤ „ î eÌ ] e ƒe ¤ „ î eÌ ƒe ¤ „ ] ƒe ¤ „Ì e ƒF„ e q e T e T À ] e q e T e T ] e q e T À T e ] eƒ q „ T À T e ] eT ƒ q „ eT ] q _c

82. Ãùù´¼ ¶¼ù U=?ÄA¶µÄ´¼ ¢RGQ LVV1QU OH IDFPHLSP1QU WHLSP1OQIT PRGHG LHG PgO SLIGI PO SOQI1VGHY * ª ßGQOE1QLPOHI LHG PRG ILEG ¢RGQ LVV1QU OH IDFPHLSP1QU WHLSP1OQI g1PR PRG ILEG VGQOE1QLPOHIT gG DIG PRG WOK¡ KOg1QU HDKGIk P Q ¤ R Q ] P ¤ R Q OH P Q q R Q ] P q R Q PRLP 1IT gG LVV OH IDFPHLSP PRG QDEGHLPOHI LQV |GGJ PRG SOEEOQ VGQOE1QLPOHY $ª [VV OH IDFPHLSP LQV HGVDSG PO KOgGIP PGHEIk ƒL„ “ ” ¤ _ q “ ¤ ” ” ¤ _ ] “ q ƒ“ ¤ ”„ ” ¤ _ ] “ q “ q ” ” ¤ _ ] q” ” ¤ _ ƒF„ aeÌ q «e eÌ q Ì ¤ _e q Ì eÌ q Ì ] aeÌ q me q Ì eÌ q Ì ] ƒae ¤ „ƒe q „ ƒe ¤ „ƒe q „ ] ae ¤ e ¤ * ª ßGQOE1QLPOHI LHG V1GHGQP ¢RGQ LVV1QU OH IDFPHLSP1QU WHLSP1OQI g1PR V1GHGQP VGQOE1QLPOHIT gG HIP QV L SOEEOQ VGQOE1QLPOHY jRGHG LHG ELQM SOEEOQ VGQOE1QLPOHI gG SLQ DIGT FDP PRG ¨FGIP© OQG 1I DIDLKKM PRG éGLIP õOEEOQ ßGQOE1QLPOH ƒéõß„Y jO QV PRG éõß OW PRG U1NGQ WHLSP1OQIT HIP WLSPOH PRG VGQOE1QLPOHIY jRGQ DIG GLSR WLSPOH PRG UHGLPGIP QDEFGH OW P1EGI 1P OSSDHI 1Q LQM OQG OW PRG VGQOE1QLPOHIY #ª Q OHVGH PO SLKSDKLPG “ ƒ“ q ”„Ì ¤ “ “ q ”` gG DIG LI L SOEEOQ VGQOE1QLPOH ƒ“ q ”„Ì I1QSG ƒ“ q ”„ 1I PRG ›ž ; WLSPOH OSSDHH1QU 1Q PRG VGQOE1QLPOHIT LQV PRG UHGLPGIP QDEFGH OW P1EGI 1P OSSDHI 1Q LQM OQG OW PRG VGQOE1QLPOHI 1I PgOY ¢G SOEJDPGk “ ƒ“ q ”„Ì ¤ “ “ q ” ] “ ƒ“ q ”„Ì ¤ “ƒ“ q ”„ ƒ“ q ”„Ì ] “ ƒ“ q ”„Ì ¤ “Ì q “” ƒ“ q ”„Ì ] “ ¤ “Ì q “” ƒ“ q ”„Ì Y COP1SG gRLP RLJJGQI g1PR PRG LFONG G‘LEJKG 1W gG RLV DIGV LI ODH SOEEOQ VGQOE¡ 1QLPOH PRG JHOVDSP OW PRG 1QV1N1VDLK VGQOE1QLPOHI 1QIPGLV OW PRG éõßk _i

83. “ ƒ“ q ”„Ì ¤ “ “ q ” ] “ƒ“ q ”„ ƒ“ q ”„ î ¤ “ƒ“ q ”„Ì ƒ“ q ”„ î ] “ƒ“ q ”„¤ “ƒ“ q ”„Ì ƒ“ q ”„ î ] ƒ“ q ”„Žƒ“ ¤ “ƒ“ q ”„ ƒ“ q ”„ î ] “ ¤ “ƒ“ q ”„ ƒ“ q ”„Ì ] “ ¤ “Ì q “” ƒ“ q ”„Ì n ¢G UGP PRG ILEG LQIgGHT FDP 1P PL|GI EOHG gOH|V (ª [VV OH IDFPHLSP LQV HGVDSG PO KOgGIP PGHEIk ƒL„ e e q _ q _ eÌ q a ] e e q _ q _ ƒe q _„ƒe ¤ _„ ] eƒe ¤ _„ ƒe q _„ƒe ¤ _„ q _ ƒe q _„ƒe ¤ _„ ] eƒe ¤ _„ q _ ƒe q _„ƒe ¤ _„ ] eÌ ¤ _e q _ ƒe q _„ƒe ¤ _„ ƒF„ e Ì ¤ e Ì q e ] e ÌÌ ¤ e ÌÌ q e ÌÌ ] e ¤ e qe ÌÌ ƒS„ “ ¤ h m“ ¤” q _ «” ] «”ƒ“ ¤ h„ h«“” ¤m“ƒ” q _„ h«“” ] «”ƒ“ ¤ h„¤ m“ƒ” q _„ h«“” ] «“”¤ «” ¤ m“” q b“ h«“” ] qb“ ¤ c“” ¤ «” h«“” [ ¢[ZCC2 [‹Âàj Š Z[õjÂC…k e ¤ _ y] e ¤ e _ W gG LVV PRG WHLSP1OQI OQ PRG H1URP RLQV I1VGT gG IGG PRLP gG UGP e ¤ _e _ T ž›Ÿ e ¤ _Y WÄD@A Ã·@?A¶´µ +A¶µÄ´»¼B jRG PGSRQ1tDGI DIGV PO I1EJK1WM HLP1OQLKG‘JHGII1OQI ELM LKIO FG DIGV PO I1EJK1WM LKUG¡ FHL1S WHLSP1OQI 1Q gR1SR PRG QDEGHLPOH LQVXOH VGQOE1QLPOH PRGEIGKNGI SOQPL1Q WHLSP1OQLK mr

84. G‘JHGII1OQIY jRGIG PMJGI OW WHLSP1OQI LHG SLKKGV •

85. Y jgO G‘LEJKGI OW SOEJKG‘ WHLSP1OQI LHG ae e qeøÌ LQV h }“ ¤ a _ ” q }” n ¢G DIG PRG WOKKOg1QU UD1VGK1QGI PO I1EJK1WM SOEJKG‘ WHLSP1OQIY U´º·´Y µ¶Ä´»¼ =´ù@·´¼@B ñ»A Z»º·@¹ +A¶µÄ´»¼B 0 + ª hY …1EJK1WM PRG QDEGHLPOH LQV PRG VGQOE1QLPOH IGJLHLPGKM PO OFPL1Q L I1QUKG WHLS¡ P1OQLK G‘JHGII1OQ 1Q GLSRY _Y jHGLP PRG HGIDKP LI L V1N1I1OQ JHOFKGEY mY …1EJK1WM LI DIDLKY 0 + ª hY Š 1QV PRG éõß OW LKK VGQOE1QLPOHI LJJGLH1QU 1Q PRG GQP1HG WHLSP1OQY _Y ¾DKP1JKM PRG GQP1HG WHLSP1OQ FM hT DI1QU w w gRGHG w 1I PRG éõß WODQV 1Q IPGJ hY mY …1EJK1WM LI DIDLKY %ª 3GHWOHE PRG U1NGQ OJGHLP1OQI LQV I1EJK1WMk ƒL„ h¤ h e h q h eÌ àI1QU ¾GPROV hk h¤ h e h q h eÌ ] e e ¤ h e eÌ eÌ q h eÌ ] e ¤ h e eÌ q h eÌ ] e ¤ h e À eÌ eÌ q h ] ƒe ¤ h„eÌ eƒe ¤ h„ƒe q h„ ] e e q h mh

86. àI1QU ¾GPROV _k jRG G‘JHGII1OQ h¤ h e h q h eÌ RLI VGQOE1QLPOHI e LQV eÌÁ PRG éõß 1I eÌY …O h¤ h e h q h eÌ ] h¤ h e h q h eÌ ÀeÌ eÌ ] ìh¤ h eíeÌ ìhq h eÌíeÌ ] eÌ ¤ e eÌ q h ] eƒe ¤ h„ ƒe ¤ h„ƒe q h„ ] e e q h ƒF„ ƒeÌ ¤ h„[ q _eÌƒeÌ ¤ h„ø[ h q eÌ àI1QU ¾GPROV hk ƒeÌ ¤ h„[ q _eÌƒeÌ ¤ h„ø[ h qeÌ ] ƒeÌ ¤ h„[ q _eÌ ƒeÌ ¤ h„[ h q eÌ ] eÌ ¤ h ƒeÌ ¤ h„[ q _eÌ ƒeÌ ¤ h„[ h q eÌ ] eÌ ¤ hq _eÌ ƒeÌ ¤ h„[ h q eÌ ] h q eÌ ƒeÌ ¤ h„[ h q eÌ ] h q eÌ ƒeÌ ¤ h„[ À h h q eÌ ] h ƒeÌ ¤ h„[ àI1QU ¾GPROV _k Š 1HIP gH1PG ƒeÌ ¤ h„[ q _eÌƒeÌ ¤ h„ø[ hq eÌ ] ƒeÌ ¤ h„[ q _eÌ ƒeÌ ¤ h„[ h q eÌ Y m_

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128. [ tDLVHLP1S G‘JHGII1OQ gRGHG “ y] h HGtD1HGI LQ LVV1P1OQLK IPGJ 1Q SOEJKGP1QU PRG ItDLHGY $ª õOEJKGPG PRG ItDLHG 1Q PRG G‘JHGII1OQ aeÌ q ace ¤ «Y hY 2HODJ PRG PGHEI SOQPL1Q1QU eÌ LQV eY aeÌ q ace ¤ « ] ƒaeÌ q ace„¤ « _Y Š LSPOH ODP PRG SOGF S1GQP “ OW eÌ WHOE PRG PGHEI 1Q PRG JLHGQPRGIGIY aeÌ q ace ¤ « ] aƒeÌ q h_e„¤ « mY jL|G PRG SOGF S1GQP OW eT V1N1VG 1P FM _T LQV ItDLHG PRG HGIDKPY ìqh_ _ í Ì ] mb aY [VV PRG QDEFGH WHOE …PGJ m 1QI1VG PRG JLHGQPRGIGI LQV 7…Ÿ 8Ÿ “ Ÿ: œ Ÿ5 œ ž7: …œ ›7Ÿšœ Ÿ5 œ = œžŸ5 œœY aeÌ q ace ¤ « ] aƒeÌ q h_e ¤ mb„¤ « qaƒmb„ «Y ¢H1PG PRG G‘JHGII1OQ 1QI1VG PRG JLHGQPRGIGI LI L ItDLHG LQV I1EJK1WM PRG QDEGH1SLK G‘JHGII1OQ ODPI1VG PRG JLHGQPRGIGIY aeÌ q ace ¤ « ] aƒe q b„Ì q hmi #ª õOEJKGPG PRG ItDLHG WOH h¤ h«v q hrvÌY h¤ h«v q hrvÌ ] qhrvÌ ¤ h«v ¤ h ] ƒqhrvÌ ¤ h«v„¤ h ] qhr ìvÌ q m _ví ¤ h ] qhr ìvÌ q m _v ¤ i hbí ¤ h q ƒqhr„ ì i hbí ] qhr ìv q m aí Ì ¤ «m c «a

129. (ª õOEJKGPG PRG ItDLHG WOH PRG G‘JHGII1OQ hae q eÌY hae qeÌ ] ƒqeÌ ¤ hae„ ] ƒqh„ƒeÌ q hae„ ] ƒqh„ƒeÌ q hae ¤ ai„ q ƒqh„ƒai„ ] ai q ƒe q „Ì ¸¹@Aµ´B@B õOEJKGPG PRG ItDLHG 1Q GLSR OW PRG WOKKOg1QU G‘JHGII1OQIk hY eÌ ¤ hre q _r _Y b Ì q _a mY úKú úö q úÌT q T Ì aY aeÌ ¤ _e q h_ «Y i q «Ì ¤ __ bY qbwÌ q hcw q hm õOEJKGPG PRG ItDLHG 1Q e LQV WOH GLSR OW PRG WOKKOg1QU GtDLP1OQIk Y ieÌ q hce ¤ a Ì ¤ a ] _ cY _ Ì q be ¤ a ¤ qeÌ ] r iY hbeÌ q i Ì ] mr« ¤ ir q bae hrY h_e q _ Ì q meÌ qa ¤ c ] r hhY q e ] h q _eÌ q _ Ì ««

130. ’6å' 46% C D@ “ ¼´Ä Z ´Aµ·@ jRG HIP |GM PO DQVGHIPLQV1QU PH1UOQOEGPHM 1I PO |QOg PRG DQ1P S1HSKGY jRG

131. 1I PRG S1HSKG SGQPGHGV LP ƒr`r„ g1PR HLV1DI hY (-1, 0) (1, 0) (0, 1) (0, -1) õOQI1VGH LQ LQUKG ” 1Q PRG DQ1P S1HSKGY jRG LQUKG 1I JOI1P1NG 1W 1P 1I EGLIDHGV SODQ¡ PGHSKOS|g1IG WHOE PRG JOI1P1NG e¡L‘1I LQV QGULP1NG 1W 1P 1I EGLIDHGV SKOS|g1IGY -135 135 jRG LFONG LQUKGI LHG EGLIDHGV DI1QU

132. Y [Q LQUKG ” ELM LKIO FG EGLIDHGV DI1QU

133. Y jRG HLV1LQ EGLIDHGEGQP SOHHGIJOQVI PO L V1IPLQSG LHODQV PRG S1HSDE¡ WGHGQSGT • T OW PRG DQ1P S1HSKG ƒ• ] _€„Y éGP DI EGLIDHG LQ LHS OQ PRG DQ1P S1HSKG IPLHP1QU LP ƒh`r„ OW KGQUPR ë LQV GQV1QU LP L JO1QP P Y W gG VHLg L HLM WHOE PRG OH1U1Q PRHODUR JO1QP P T gG RLNG WOHEGV LQ LQUKG ” T gRGHG ” ] ë HLV1LQIY radians P (1,0) θ 4 π «b

134. jRG WOKKOg1QU PgO LQUKGI LHG PRG ILEGY 4 π radians 45 OR jO SOQNGHP HLV1LQI PO VGUHGGI LQV N1SG NGHILT DIG PRG WOKKOg1QU GtDLP1OQY € HLV1LQI ] hcr– ª õOQNGHP mr– PO HLV1LQIY € HLV1LQI ] hcr– € hcr HLV1LQI ] h– mr À € hcr HLV1LQI ] mr Àh– € b HLV1LQI ] mr– ª õOQNGHP ï HLV1LQI PO VGUHGGIY € HLV1LQI ] hcr– c « À€ HLV1LQI ] c « Àhcr– c€ « HLV1LQI ] _cc– «

135. CA´»¼»@ÄA´µ +=¼µÄ´»¼B õOQI1VGH PRG JO1QP P ] ƒe` „ gRGHG PRG LQUKG OW EGLIDHG ” 1QPGHIGSPI PRG DQ1P S1HSKGY ¢G DIG PRG SOOHV1QLPGI e LQV OW PR1I JO1QP PO VG QG I1‘

136. • OW ” Y θ (x, y) (1, 0) (-1, 0) (0, 1) (0, -1) P ¢G VG QG PRG OW ” PO FG PRG e¡SOOHV1QLPG OW PR1I JO1QP LQV PRG OW ” PO FG PRG ¡SOOHV1QLPG OW PR1I JO1QPY ¢G DIG PRG LFFHGN1LP1OQI ¨SOI© WOH SOI1QG LQV ¨I1Q© WOH I1QGY jRDIT SOI” ] e LQV I1Q” ] n COP1SG PRLP PRG e LQV SOOHV1QLPGI OW LKK JO1QPI OQ PRG DQ1P S1HSKG K1G IOEGgRGHG FGPgGGQ qh LQV hY jRDI qh SOI” h LQV q h I1Q” h QO ELPPGH gRLP ” 1IY ¢G SLQ DIG UGOEGPHM PO VGPGHE1QG I1Q ë LQV SOI ëY …1QSG ë HLV1LQI GtDLKI a«– T SOQI1VGH L a«–¡a«–¡ir– PH1LQUKG g1PR L RMJOPGQDIG OW KGQUPR hY …DSR L PH1LQUKG EDIP RLNG KGUI GLSR OW KGQUPR ú @ÌY 45 45 2 1 1 2 1 «c

137. ‹M EON1QU PR1I PH1LQUKG 1QPO PRG DQ1P S1HSKG LQV HGEGEFGH1QU PRLP a«– GtDLKI ë HLV1LQIT gG QV PRLP PRG SOHHGIJOQV1QU JO1QP OQ PRG DQ1P S1HSKG RLI ƒe` „¡SOOHV1QLPGI ú @Ì` ú @Ì Y 1 2 1 2 , ( ) 1 2 x = 1 1 2 y = π 4 jRDI I1Q € a ] ] h }_ LQV SOI € a ] e ] h }_n ¢G SLQ QV I1Q î TSOI î TI1Q öTLQV SOI ö 1Q L I1E1KLHWLIR1OQ FM QOP1QU PRLP î HLV1LQI GtDLKI br– LQV ö HLV1LQI GtDLKI mr– Y [ mr–¡br–¡ir– PH1LQUKG g1PR L RMJOPGQDIG OW KGQUPR h U1NGI DI PRG 1QWOHELP1OQ gG QGGVY 30 60 3 2 2 1 1 «i

138. π 6 3 2 x = 2 1 y = 3 2 1 2 1 ( , ) 1 2 x = 3 2 y = 1 2 3 2 1 ( , ) π 3 jRDI I1Q € b ] h _ LQV SOI € b ] }m _ LQV I1Q € m ] }m _ LQV SOI € m ] h _n Q SLKSDKDIT gG EGLIDHG LQUKGI 1Q š žT LQV gG OWPGQ DIG PRG PH1U NLKDGI gG XDIP WODQVT IO 1P g1KK FG RGKJWDK PO EGEOH1pG PRG ¨GQRLQSGV© DQ1P S1HSKG OQ PRG QG‘P JLUGY br

139. π 6 π 4 π 3 π 3 2 π 2 3 2 , ( 1 2 ) 1 2 , 3 2 ) ( ( 2 1 , 0) 0 , 1 ( ) -1 , 0 ( ) 0 , -1 ( ) π 2 π 0, , ) ( 1 1 2 Š ODHOPRGH PH1UOQOEGPH1SWDQSP1OQI LHG VG QGV DI1QU I1QG LQV SOI1QGY jRGM LHG PRG 0 ƒ¨IGS©„T ƒ¨SIS©„T ƒ¨PLQ©„TLQV ƒ¨SOP©„ PH1UOQOEGPH1S WDQSP1OQIT VG QGV LI WOKKOgIY IGS” ] h SOI” SIS” ] h I1Q” PLQ” ] I1Q” SOI” SOP” ] h PLQ” ] SOI” I1Q” …1QSG SOI” LQV I1Q” LHG r WOH IOEG NLKDGI OW ” T PRG PH1U WDQSP1OQI IGS” T SIS” T PLQ” T LQV SOP” LHG DQVG QGV WOH IOEG NLKDGI OW ” Y Š OH EOHG 1QWOHELP1OQT IGG PRG UHLJRI OW PRG PH1U WDQSP1OQI LP PRG GQV OW PR1I IGSP1OQY bh

140. ª Š 1QV SOP öY SOP € b ] SOI ö I1Q ö ] @ î ÌúÌ ] }m jRG DQ1P S1HSKG RLI WODH tDLVHLQPIY III IV x y II I x0 (0,0) y0 x0 y0 x0 y0 x0 y0 COPG PRLP L JO1QP 1Q —DLV g1KKRLNG L QGULP1NG e¡NLKDG LQV L JOI1P1NG ¡NLKDGY jRDIT SOI1QG 1I QGULP1NG LQV I1QG 1I JOI1P1NG 1Q —DLV Y jO HGEGEFGH gR1SR PH1U WDQSP1OQI LHG JOI1P1NG 1Q gR1SR tDLVHLQPIT DIG PRG ILM1QUT ¨[KK …PDVGQPI jL|G õLKSDKDIY© Sin csc Tan positive cot positive Cos sec θ positive All positive θ θ θ θ θ $ª Š 1QV SOI ë î Y ¢G g1KK HIP QV 1Q gR1SR tDLVHLQP ë î K1GIY b_

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142. CA´»¼»@ÄA´µ ˜ù@¼Ä´Ä´@B jRG WOKKOg1QU PH1UOQOEGPH1S 1VGQP1P1GI g1KK FG DIGWDK 1Q SLKSDKDIY SOIÌ” ¤ I1QÌ” ] h PLQÌ” ¤ h ] IGSÌ” SOPÌ” ¤ h ] SISÌ” I1Qƒ“ ¤ ”„ ] I1Q“SOI” ¤ SOI“I1Q” I1Qƒ“ q ”„ ] I1Q“SOI” q SOI“I1Q” SOIƒ“ ¤ ”„ ] SOI“SOI” q I1Q“I1Q” SOIƒ“ q ”„ ] SOI“SOI” ¤ I1Q“I1Q” I1Q_” ] _I1Q” SOI” SOI_” ] SOIÌ” q I1QÌ” ] _SOIÌ” q h ] h q _I1QÌ” SOIÌ” ] h¤ SOI_” _ I1QÌ” ] h q SOI_” _ SOIƒq”„ ] SOI” I1Qƒq”„ ] qI1Q” P 1I ž›Ÿ QGSGIILHM PO EGEOH1pG LKK OW PRG LFONG 1VGQP1P1GIV ‹M |QOg1QU ROg LQ 1VGQP1PM 1I VGH1NGVT OQG SLQ HGVDSG PRG LEODQP OW EGEOH1pLP1OQ QGSGIILHMY ba

143. jRG GtDLP1OQ OW PRG DQ1P S1HSKG 1I eÌ ¤ Ì ] hY jRG 3MPRLUOHGLQ PRGOHGE LKIO U1NGI DI PRG GtDLP1OQ eÌ ¤ Ì ] hY jR1I GtDLP1OQ U1NGI DI SOIÌ” ¤ I1QÌ” ] hn ß1N1V1QU PR1I GtDLP1OQ FM SOIÌ” T gG OFPL1Q SOIÌ” SOIÌ” ¤ I1QÌ” SOIÌ” ] h SOIÌ” OH h¤ PLQÌ” ] IGSÌ” n ß1N1V1QU SOIÌ” ¤ I1QÌ” ] h FM I1QÌ” gG OFPL1Q SOIÌ” I1QÌ” ¤ I1QÌ” I1QÌ” ] h I1QÌ” OH SOPÌ” ¤ h ] SISÌ” n àI1QU I1Qƒ“ ¤ ”„ ] I1Q“SOI” ¤ SOI“I1Q” LQV SOIƒ“ ¤ ”„ ] SOI“SOI” q I1Q“I1Q” g1PR “ ] ” ] ” T gG OFPL1Q PRG WOHEDKLI I1Q_” ] _I1Q” SOI” LQV SOI_” ] SOIÌ” q I1QÌ” n [KIO SOI_” ] SOIÌ” q I1QÌ” ] SOIÌ” q ƒh q SOIÌ”„ ] _SOIÌ” q h LQV SOI_” ] SOIÌ” q I1QÌ” ] ƒh q I1QÌ”„ q I1QÌ” ] h q _I1QÌ” DI1QU PRG 1VGQP1PM SOIÌ” ¤I1QÌ” ] hY ¢G SLQ PRGQ IOKNG WOH SOIÌ” 1Q SOI_” ] _SOIÌ” qh PO UGP SOIÌ” ] h¤ SOI_” _ n b«

144. …OKN1QU WOH I1QÌ” 1Q SOI_” ] h q _I1QÌ” U1NGI DI I1QÌ” ] h q SOI_” _ n + ´¼ù´¼ ÄD@ Å¶·=@B »ñ CA´»¼»@ÄA´µ +=¼µÄ´»¼B 21NGQ PRG NLKDGI WOH OQG PH1U WDQSP1OQT gG SLQ QV PRG NLKDGI WOH PRG OPRGH NG PH1U WDQSP1OQIY jRGHG LHG PgO gLMI PO VO PR1IY 0 + ª àIG 1VGQP1P1GIY #ª ™š 0 + › 21NGQ ” 1I 1Q —DLV LQV SOP” ] _T QV PRG NLKDGI OW PRG HGEL1Q1QU PH1U WDQSP1OQIY Š 1HIPT SOPLQUGQP LQV PLQUGQP LHG HGS1JHOSLKIT IO PLQ” ] h SOP” ] h _n CG‘P DIG PRG 1VGQP1PM SOPÌ” ¤ h ] SISÌ” PO UGP SIS” k SOPÌ” ¤ h ] SISÌ” _Ì ¤ h ] SISÌ” SIS” ] Î}« SIS” ] q}« I1QSG ” 1I 1Q —DLV Y õOIGSLQP LQV I1QG LHG HGS1JHOSLKIT IO I1Q” ] h SIS” ] q h }«n àI1QU I1QÌ” ¤ SOIÌ” ] hT gG UGP SOIÌ” ¤ œ q h }« Ì ] h bb

145. SOIÌ” ] a « SOI” ] Î _ }« SOI” ] q _ }« I1QSG ” 1I 1Q —DLV Y õOI1QG LQV IGSLQP LHG HGS1JHOSLKIT IO IGS” ] h SOI” ] q}« _ n jR1I U1NGI DI LKK I1‘ PH1U WDQSP1OQ NLKDGIY 0 + ª àIG L H1URP PH1LQUKG g1PR r HLV1LQI ’ ” ’ Ì HLV1LQIY hypotenuse θ opposite adjacent jR1I U1NGI I1Q” ] OJJOI1PG RMJOPGQDIG SOI” ] LVXLSGQP RMJOPGQDIG PLQ” ] OJJOI1PG LVXLSGQP ÂQG SLQ HGEGEFGH PRGIG GtDLP1OQI DI1QU PRG LSHOQME ¨…ÂË õ[Ë jÂ[© gRGHG … ] I1QGT Â ] OJJOI1PGT Ë ] RMJOPGQDIGT õ ] SOI1QGT [ ] LVXLSGQPT LQV j ] PLQUGQPY ƒQ PRG JHGN1ODI PH1LQUKGTgG LIIDEGV ” gLI 1Q —DLV Y ËOgGNGHT FM DI1QU IMEEGPHMT gG SLQ LIIDEG ” 1I 1Q LQM tDLVHLQPY ‹DP FG SLHGWDK OW PRG …2C… OW PRG PH1U WDQSP1OQI gRGQ ” 1I 1Q —DLV T T OH ‹ V„ ¢G g1KK QOg gOH| ‚‘LEJKG « LUL1Q DI1QU ¾GPROV _Y b

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152. -10 -8 -6 -4 -2 2 4 6 8 10 ¡¢ £¤ ¥ ¢ ¤ ¥ ¤ ¥ ¢ £¤ ¥ ¡¢ ¦¤ ¥ §¢ ¨¤ ¥ ©¢ ] IGSe -10 -8 -6 -4 -2 2 4 6 8 10 ¡¢ £¤ ¥ ¢ ¤ ¥ ¤ ¥ ¢ £¤ ¥ ¡¢ ¦¤ ¥ §¢ ¨¤ ¥ ©¢ ] SISe ¸¹@Aµ´B@B õRLQUG PO HLV1LQ EGLIDHGk hY «r– _Y h_r– mY m«– aY qh_– õRLQUG PO VGUHGG EGLIDHGk «Y qï ö bY î ï úÌ Y cY qÌ î m

153. Š 1QV PRG WDQSP1OQ NLKDGIk iY I1Q ï î hrY PLQ ö hhY SIS úú ë h_Y SOI qÌ î ! hmY IGS úú ö haY I1Q q î Ì ! h«Y SOP ï ë hbY SOI ï ö [ WDQSP1OQ NLKDG LQV L tDLVHLQP LHG IJGS1 GVY Š 1QV PRG OPRGH NG WDQSP1OQ NLKDGIY hY I1Q” ] ú î T hcY IGS” ] ï î T hiY PLQ” ] «T _rY SOP” ] qaT ‹ _hY Š 1QV PRG I1‘ PH1UOQOEGPH1S WDQSP1OQ NLKDGI WOH PRG WOKKOg1QU ” k 17 θ 8 …OKNGT QV1QU LKK IOKDP1OQIk __Y PLQe ] }m _mY _SOIÌe ] h _aY _I1QÌe q «I1Qe ¤ _ ] r …OKNGT QV1QU LKK IOKDP1OQI 1Q Žr`_€Y _«Y IGSÌe q a ] r _bY _I1Q î e ] I1Qe _Y SOI_eI1Qe ¤ I1Qe ] r _cY IGSÌe ] aPLQÌe _iY SOI_e q I1Qe ] h a

154. 9ª 6 « 88¬ 234568 áâ6æå =?@AB ¶¼ù Ã?B»·=Ä@ Å¶·=@B hY IGP QOPLP1OQk Ðe xxx q h e ’ mÑÁ QDEFGH K1QGk ® ® ® ® ¯ ¯ ¯ ¯ ° ° ± ± 3 -3 -1 4 -2 0 -4 1 2 mY 1QPGHNLK QOPLP1OQk ƒqa`qh§ ƒr`m„Á IGP QOPLP1OQk Ðe xxx qa ’ e qh OH r ’ e ’ mÑ «Y e ] hT « Y e ] q_T qh ² ¸¹º»¼@¼ÄB ¶¼ù ð¶ù´µ¶·B hY eú î û î mY m_ «Y hbeë Y a iY _ hhY ai hmY h h«Y hr_a hY e _ hiY î c _hY eÌë Ìô _mY qaeûö øïû î _«Y ba”Ì¿ “úö _Y m€ q }heÁ i€Ì q he _iY q_ q e}m ¤ Á a q eÌƒm ¤ „ ] a q meÌ q eÌ ³ (»·) ¼»´¶·B ¶¼ù +¶µÄ»A´¼ hY _ mY r «Y _eë q _e Y «eÌ ¤ _ie q b iY eÌ ¤ ae ¤ a hhY qbeë q _e î ¤ «eÌ ¤ e q h hmY “¿eÌ ¤ ƒ“

155. ¤ ”¿„e ¤ ”

156. h«Y e î ¤ meÌ ¤ _e hY eƒe ¤ h„ hiY _eƒe ¤ h„Ì «

157. _hY ƒae q «„ƒae ¤ «„ _mY ƒ_ q e„ƒa ¤ _e ¤ eÌ„ _«Y ƒe ¤ m„ƒe ¤ i„ _Y ƒe qa„ƒe ¤ _„ _iY ƒe q h„ƒe ¤ h„Ì mhY ƒe ¤ _„ƒe q h„ƒeÌ ¤ e ¤ h„ mmY e ] qhhT h m«Y e ] Îm mY e ] ú´@ï Ì miY e ] _ Î }« ahY QO HGLK HOOPI amY e ] b a«Y e ] úÌT q_T m aY e ] qa aiY e ] Î_T Î}m «hY e ] qmT qhT rT a µ Ã·@?A¶´µ +A¶µÄ´»¼B hY e q h e q _ mY “ q m” ”Ì «Y qc Y m _e q h iY q « qa hhY _« ï _ce ¤ a hmY m ¤ « q _ h«Y ieÌ q hb Ì h_e hY a ƒe ¤ _„ƒe ¤ m„ hiY a î Ì q _eÌ ¤ e eÌ Ì _hY e ¤ e _mY h¤ e h qe _«Y e q h eÌƒe ¤ h„úûÌ _Y qh qe }e ¤ _ q ƒe ¤ _„ _iY q } mhY }e ¤ _ ¤ e ¤ _ e ¤ _ mmY }e q } e q b

158. ¶ ˜¼@E =¶·´Ä´@B hY ƒq_`¥„ mY Ì î `¥ ! «Y úÌ`¥ ! Y ƒq¥`qa„§ ƒr`¥„ iY ·q_`ë î¸ hhY ƒq¥`qa§ · îÌ`¥ ! hmY ƒqa`r„ h«Y ƒqh`r§ Ž`¥„ hY ƒq¥`r„§ ƒm`¥„ hiY ƒq¥`q_„§ ƒ«`¥„ _hY ·q«`qúï ¸ _mY ƒq¥`r§ Ž`¥„ ¹ +=¼µÄ´»¼B ¶¼ù M ´¼@B hY QOP L WDQSP1OQ FGSLDIG € ƒh„ SODKV FG qh OH h mY WDQSP1OQk }e 1I PRG OQKM QDEFGH PRLP gRGQ SDFGV GtDLKI e VOEL1Q ] ƒq¥`¥„ «Y QOP L WDQSP1OQk PRGHG LHG Ÿþ› SLKGQVLH MGLHI 1Q gR1SR MOD gGHG LQM U1NGQ LUG Y WDQSP1OQk PRGHG SLQ FG QO EOHG PRLQ OQG ÿœŸ JH1EG KGII PRLQ L U1NGQ QDEFGH VOEL1Q ] Ž_`¥„ iY ƒq¥`q_„§ ƒq_`_„§ ƒ_`¥„ hhY ƒh`_„§ ƒ_`m„§ ƒm`¥„ hmY WDQSP1OQ h«Y QOP L WDQSP1OQ hY € ƒqh„ ] qhT € ƒr„ ] rT € ƒm„ ] « hiY € ƒq_„ ] q_T € ƒr„ ] úÌT € ƒh„ 1I DQVG QGVT € ƒm„ ] h_ _hY ] qïöe ¤ m _mY ] qúÌƒe q a„¤ _ _«Y ] qe ¤ a _Y ] ú î ƒe q _„¤ _

159. _iY mhY -2 -1 1 2 -4 -3 -2 -1 1 2 3 4 5 6 7 8 -3 -2 -1 1 2 3 -6 -5 -4 -3 -2 -1 1 º Z »º·@Ä´¼ ÄD@ UE=¶A@ hY ƒe ¤ «„Ì q a« mY h_ q ƒT ¤ úë„Ì «Y úöö ï q «ƒ q úú ï „Ì Y iƒe q h„Ì ¤ aƒ ¤ úÌ„Ì ] m iY hbƒe ¤ _„Ì q iƒ ¤ «„Ì ] haa hhY _ƒe q úë„Ì ¤ _ƒ ¤ úë„Ì ] ïë » CA´»¼»@ÄA) hY ï ú mY Ìï úÌ «Y qh«r– Y h«n«– iY q@ î Ì hhY }_ hmY Ì @ î h«Y h hY SOI” ] qÌ@Ì î T PLQ” ] q ú Ì@ÌT IGS” ] q î Ì@ÌT SOP” ] q_}_T SIS” ] m hiY SOI” ] q ú @ÌöT I1Q” ] q ï @ÌöT IGS” ] q}_bT SIS” ] q@Ìö ï T SOP” ] úï c

160. _hY SOI” ] ú T I1Q” ] úï ú T PLQ” ] úï T IGS” ] ú T SIS” ] ú úïT SOP” ] úï _mY ¼ ë ¤ _w€` î ë ¤ _w€`ï ë ¤ _w€` ë ¤ _w€½ OH ¼ ë ¤ çÌ€½ _«Y ¼ î `Ì î `ë î `ï î ½ _Y ¼r`€`_€` Ì` î Ì ½ _iY ¼r`€`_€` ö ` úú ö ½ i

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