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350.46 318.24 Tm <6465676565732E> Tj 1.50 Tc /F3 8.0 Tf 1 0 0 1 316.80 309.06 Tm <4256> Tj 0.18 Tc /F3 12.0 Tf 1 0 0 1 85.86 282.06 Tm <54686520> Tj 1 0 0 1 106.92 282.06 Tm <766572746963616C20> Tj 1 0 0 1 146.16 281.88 Tm <7472616E736C6174696F6E20> Tj 1 0 0 1 199.98 281.52 Tm <6F6620> Tj 1 0 0 1 212.94 281.52 Tm <6120> Tj 1 0 0 1 221.40 281.88 Tm <677261706820> Tj 1 0 0 1 251.82 281.34 Tm <697320> Tj 1 0 0 1 262.80 281.34 Tm <74686520> Tj 1 0 0 1 280.80 281.34 Tm <616D6F756E7420> Tj 1 0 0 1 319.32 280.98 Tm <627920> Tj 1 0 0 1 334.26 281.16 Tm <776869636820> Tj 1 0 0 1 367.20 280.98 Tm <697420> Tj 1 0 0 1 377.10 280.98 Tm <697320> Tj 1 0 0 1 388.44 280.98 Tm <7368696674656420> Tj 1 0 0 1 423.90 280.80 Tm <757020> Tj 1 0 0 1 439.02 280.80 Tm <6F7220> Tj 1 0 0 1 452.16 280.80 Tm <646F776E2E20> Tj 1 0 0 1 484.56 280.80 Tm <546865> Tj 0.18 Tc 1 0 0 1 86.04 268.02 Tm <7374616E6461726420> Tj 1 0 0 1 129.24 267.84 Tm <73696E6520> Tj 1 0 0 1 151.92 268.02 Tm <616E6420> Tj 1 0 0 1 171.72 267.84 Tm <636F73696E6520> Tj 1 0 0 1 205.56 268.02 Tm <67726170687320> Tj 1 0 0 1 240.66 267.30 Tm <626F746820> Tj 1 0 0 1 265.14 267.30 Tm <6861766520> Tj 1 0 0 1 291.24 267.30 Tm <616E20> Tj 1 0 0 1 305.64 267.30 Tm <6176657261676520> Tj 1 0 0 1 345.60 267.30 Tm <76616C756520> Tj 1 0 0 1 375.12 267.12 Tm <6F6620> Tj 1 0 0 1 388.62 267.12 Tm <302C20> Tj 1 0 0 1 400.14 266.94 Tm <62757420> Tj 1 0 0 1 418.68 266.94 Tm <74686520> Tj 1 0 0 1 436.68 267.48 Tm <67726170687320> Tj 1 0 0 1 471.42 266.94 Tm <63616E20> Tj 1 0 0 1 490.50 266.76 Tm <6D6F7665> Tj 0.18 Tc 1 0 0 1 86.94 253.98 Tm <6177617920> Tj 1 0 0 1 113.58 253.98 Tm <66726F6D20> Tj 1 0 0 1 140.04 253.98 Tm <7468697320> Tj 1 0 0 1 160.20 254.34 Tm <706F736974696F6E2E20> Tj 1 0 0 1 205.20 253.80 Tm <54686520> Tj 1 0 0 1 226.98 253.62 Tm <616D6F756E7420> Tj 1 0 0 1 265.86 253.44 Tm <627920> Tj 1 0 0 1 280.98 253.44 Tm <776869636820> Tj 1 0 0 1 313.56 253.26 Tm <7468697320> Tj 1 0 0 1 333.72 253.26 Tm <76616C756520> Tj 1 0 0 1 363.24 253.08 Tm <697320> Tj 1 0 0 1 374.58 253.08 Tm <7368696674656420> Tj 1 0 0 1 410.40 253.08 Tm <697320> Tj 1 0 0 1 421.56 252.90 Tm <657175616C20> Tj 1 0 0 1 450.18 252.90 Tm <746F20> Tj 1 0 0 1 462.60 252.90 Tm <4420> Tj 1 0 0 1 474.30 252.90 Tm <696E20> Tj 1 0 0 1 486.36 252.72 Tm <746865> Tj 0.18 Tc 1 0 0 1 85.86 240.48 Tm <66756E6374696F6E277320> Tj 1 0 0 1 137.34 240.30 Tm <6571756174696F6E2E20> Tj 1 0 0 1 184.32 239.94 Tm <46726F6D20> Tj 1 0 0 1 213.66 239.94 Tm <6120> Tj 1 0 0 1 223.38 240.30 Tm <67726170682C20> Tj 1 0 0 1 255.42 239.76 Tm <697420> Tj 1 0 0 1 265.14 239.58 Tm <697320> Tj 1 0 0 1 276.48 239.58 Tm <666F756E6420> Tj 1 0 0 1 306.90 239.40 Tm <627920> Tj 1 0 0 1 322.02 239.58 Tm <74616B696E6720> Tj 1 0 0 1 356.22 239.40 Tm <74686520> Tj 1 0 0 1 373.14 239.40 Tm <6176657261676520> Tj 1 0 0 1 415.44 239.22 Tm <6F6620> Tj 1 0 0 1 428.22 239.22 Tm <74686520> Tj 1 0 0 1 445.86 239.04 Tm <6D696E696D756D20> Tj 1 0 0 1 495.54 239.04 Tm <616E64> Tj 0.18 Tc 1 0 0 1 85.32 226.62 Tm <6D6178696D756D20> Tj 1 0 0 1 137.16 226.44 Tm <76616C7565732E> Tj 0.18 Tc 1 0 0 1 85.50 198.72 Tm <54686520> Tj 1 0 0 1 106.20 199.08 Tm <706861736520> Tj 1 0 0 1 137.34 198.36 Tm <73686966742C20> Tj 1 0 0 1 164.52 198.36 Tm <302C20> Tj 1 0 0 1 176.22 198.36 Tm <697320> Tj 1 0 0 1 187.38 198.18 Tm <6F6674656E20> Tj 1 0 0 1 214.74 198.18 Tm <74686520> Tj 1 0 0 1 232.56 198.00 Tm <6D6F737420> Tj 1 0 0 1 259.38 198.00 Tm <74726F75626C65736F6D6520> Tj 1 0 0 1 321.66 197.82 Tm <746F20> Tj 1 0 0 1 334.44 197.64 Tm <66696E642E20> Tj 1 0 0 1 360.00 197.64 Tm <497420> Tj 1 0 0 1 370.26 197.82 Tm <697320> Tj 1 0 0 1 381.06 197.82 Tm <74686520> Tj 1 0 0 1 399.24 197.64 Tm <616D6F77727420> Tj 1 0 0 1 437.76 197.28 Tm <627920> Tj 1 0 0 1 452.88 197.46 Tm <776869636820> Tj 1 0 0 1 484.92 197.28 Tm <746865> Tj 0.18 Tc 1 0 0 1 85.14 184.86 Tm <77686F6C6520> Tj 1 0 0 1 117.00 185.04 Tm <677261706820> Tj 1 0 0 1 147.96 184.50 Tm <697320> Tj 1 0 0 1 159.12 184.50 Tm <7368696674656420> Tj 1 0 0 1 194.58 184.32 Tm <6C65667420> Tj 1 0 0 1 213.66 184.14 Tm <6F7220> Tj 1 0 0 1 226.26 184.14 Tm <726967687420> Tj 1 0 0 1 252.72 183.96 Tm <66726F6D20> Tj 1 0 0 1 279.00 184.14 Tm <69747320> Tj 1 0 0 1 293.76 183.78 Tm <7374616E6461726420> Tj 1 0 0 1 336.60 184.14 Tm <706F736974696F6E2E20> Tj 1 0 0 1 382.50 183.78 Tm <54686520> Tj 1 0 0 1 403.92 183.96 Tm <706861736520> Tj 1 0 0 1 434.70 183.42 Tm <736869667420> Tj 1 0 0 1 458.82 183.42 Tm <697320> Tj 1 0 0 1 469.98 183.42 Tm <666F756E6420> Tj 1 0 0 1 500.04 183.24 Tm <6279> Tj 0.18 Tc 1 0 0 1 85.14 170.64 Tm <7573696E6720> Tj 1 0 0 1 113.40 170.64 Tm <74686520> Tj 1 0 0 1 131.94 170.46 Tm <666F6C6C6F77696E6720> Tj 1 0 0 1 181.62 170.28 Tm <666F726D756C613A> Tj 1.50 Tc /F3 15.0 Tf 1 0 0 1 217.08 148.14 Tm <302D20> Tj 1 0 0 1 237.60 150.66 Tm <2D63> Tj 0.00 Tc /F3 12.0 Tf 1 0 0 1 248.04 138.42 Tm <42> Tj 0.18 Tc 1 0 0 1 85.50 129.06 Tm <2A4E6F74653A20> Tj 1 0 0 1 123.30 125.46 Tm <497420> Tj 1 0 0 1 133.74 125.28 Tm <697320> Tj 1 0 0 1 144.72 125.28 Tm <626573742C20> Tj 1 0 0 1 169.92 125.10 Tm <74686F75676820> Tj 1 0 0 1 206.46 124.92 Tm <6E6F7420> Tj 1 0 0 1 225.18 124.92 Tm <616C7761797320> Tj 1 0 0 1 261.54 124.74 Tm <72657175697265642C20> Tj 1 0 0 1 307.98 124.56 Tm <666F7220> Tj 1 0 0 1 324.54 124.56 Tm <74686520> Tj 1 0 0 1 342.18 124.92 Tm <706861736520> Tj 1 0 0 1 373.50 124.38 Tm <736869667420> Tj 1 0 0 1 397.98 124.38 Tm <616E6420> Tj 1 0 0 1 418.14 124.20 Tm <427820> Tj 1 0 0 1 435.06 124.20 Tm <746F20> Tj 1 0 0 1 447.48 124.20 Tm <6861766520> Tj 1 0 0 1 473.04 124.20 Tm <74686520> Tj 1 0 0 1 490.86 124.02 Tm <73616D65> Tj 0.36 Tc 1 0 0 1 85.14 111.60 Tm <756E6974732E28692E652E2C20> Tj 1 0 0 1 136.08 111.42 Tm <697420> Tj 1 0 0 1 145.80 111.42 Tm <697320> Tj 1 0 0 1 156.96 111.42 Tm <61776C617661726420> Tj 1 0 0 1 203.40 111.06 Tm <746F20> Tj 1 0 0 1 215.82 111.06 Tm <6861766520> Tj 1 0 0 1 241.92 110.88 Tm <427820> Tj 1 0 0 1 259.20 110.88 Tm <65787072657373656420> Tj 1 0 0 1 309.42 110.70 Tm <696E20> Tj 1 0 0 1 321.48 110.70 Tm <72616469616E7320> Tj 1 0 0 1 360.00 110.52 Tm <616E6420> Tj 1 0 0 1 380.34 110.52 Tm <6420> Tj 1 0 0 1 389.34 110.52 Tm <696E20> Tj 1 0 0 1 401.76 110.34 Tm <646567726565732E29> Tj ET endstream endobj 4 0 obj 14023 endobj 5 0 obj << /Type /Font /Subtype /Type1 /BaseFont /Helvetica /Encoding /WinAnsiEncoding >> endobj 6 0 obj << /Length 7 0 R >> stream Graphing sine and cosine functionsAll sine and cosine graphs can be charactenzedby four values: the amplitude, the period,the phase shift, and the vertical translation. All four of these values can be obtained fromthe graph or from the equation of the fuirction. Sine and cosine functions are written as: (x): A sin (Bx + C) + D e(x):Acos(Bx+C)+D From earlier chapters, w know that sin(x) : cos(x-9Oo), so all of these formulas andideas will hold fiue for both functions.The amplitude is equal to one-half the vertical distance from the minimum value to themaximum value of the graph and is equal to A in the function's equation.The period of a graph is the distance from any point on the gaph to the correspondingpoint on the gaph in the next cycle. Ma,rimums and minimums are easy choices, but anypoint can be used to find the period from the graph. From the equation of a function, theperiod can be found by the following formula: The period, T : 2nB 36fin radians, or T :1- in degees.BV The vertical translation of a graph is the amount by which it is shifted up or down. Thestandard sine and cosine graphs both have an average value of 0, but the graphs can moveaway from this position. The amount by which this value is shifted is equal to D in thefunction's equation. From a graph, it is found by taking the average of the minimum andmaximum values.The phase shift, 0, is often the most troublesome to find. It is the amowrt by which thewhole graph is shifted left or right from its standard position. The phase shift is found byusing the following formula:0- -cB*Note: It is best, though not always required, for the phase shift and Bx to have the sameunits.(i.e., it is awlavard to have Bx expressed in radians and d in degrees.) endstream endobj 7 0 obj 1740 endobj 8 0 obj << /Length 27 >> stream % CANON_PFINF_TYPE0_TEXTON endstream endobj 9 0 obj << /Length 44 >> stream q 612.18 0 0 792.00 0.00 0.00 cm /Obj2 Do Q endstream endobj 10 0 obj << /Type /Page /MediaBox [ 0 0 612.18 792.00 ] /Parent 11 0 R /Resources << /Font << /F3 5 0 R >> /XObject << /Obj2 2 0 R >> /Subtype 6 0 R /ProcSet [ /PDF /Text /ImageB /ImageC /ImageI ] >> /Contents [ 8 0 R 9 0 R 3 0 R ] >> endobj 13 0 obj << /Type /XObject /Subtype /Image /Width 3401 /Height 4400 /BitsPerComponent 1 /ColorSpace /DeviceGray /Filter /CCITTFaxDecode /DecodeParms << /K -1 /Columns 3401 >> /Length 45192 >> stream >58;kL(F\DfBMљ!-k +&0 '`ӄ0p OM>"+> N%4> ۻBv5CT0h!Cڏꖓ/O*OĈF *^R`*f)"2'8E-PuTDW2vwqC"C Bd*QPT@B0L0, $r9 r90k2IsD5$9*LPJ`0ϠU aABa=@R@@0 aB„@АӠhD&SLMS!&aPaB 5'Pa=0AuUYzj"RUM§PH*xT4i7- .WMm𨋔U "XlDD^uI//I\\o }6Ez:"M,ȸA"Ƃ Fg  g{0S;motmn}P K !4B-p\XN& Jzupx0AmW!bSi7^z: MuӤZ^7^j߯?} ޵o-]&.V뮿Kkui[#&פ[_?k5`ߠZ{o}o[a/ȣ `rkKS6k?wt?_[qzAWA__ Aᇿ; w oH7] o7 a ߿}b:]w]ι7o_!?|=b ji޿_0~Ia޷o{m.[k׭i{_v߶{{i:_iRkoﯴn׵} V!޽|X %`va_ 0J'3h-K]^ W hcn+Aݱkv_u -pvjFtH4zM}1Iam8| lm0a(an֐rwV`l0@q@`gi*( 0EC @v  qPuPMm0&:i 4V6 u MH6(NC05JV 5Xa}KXa+ d:&N2%yd~~SYᦘM;!  <0DȣN"""""")b DDD0a0C 0@H @A4F""Fad!aZPDN4J𭈈zKӯL%ᯐƋ]„PD6JE2#8 gr"#-2G&*CJFv5g;Erl)e5ȇhDndTTAIYd|jvwjhDC a}Wa}hRd<\ ,z/!;TA5[w~ִ߭anºkt״*>k%[K3e::8AxtdtPD]!QLgXBb,hOe-$wDWa9A& (  9  V?RA APa B+'TB˅-}00>(@vD `AN,&H88D D=`aϐ eBqni;L&wmaBvNa5[NzNAN`B!ӷl1v~{4a~mL! $#= "{[!.â"k Am'x|&Iރ]]t`tt}mhm[x^:Wavnm'M&E=M 1?dRaA z*A!vK ݭ.)tKH[ }]%[@֭it%zoƗ]u}_͠t~W}J뷹N>#i!_;GiUEzT  7z_k  ޵_N  ^XDQ{_E]j"n߰:ntֻoo[] }/ޯۻun_n/_z{~F ݒ.o+!~^-7jB{jwיuupkkK^/l?~a/[T/,]W{kC_ $Ɲ1ŮKV] [v߾ kkhl8 ];^o_ث |4 f=9'*itI&4i>GVi'kvjEy7H,1;ipm:zm5I _V'حmZ W -m+ 6 {L;M](a0i4A 4Zh6P 4-ؤӌ`*}p .DpL MCI2 eV hP0Lp@ɋ)x2Й3}k  r4IG#GˊG28G f28FG ]tlT c.tn.ds'G$#لpI吰`5BG>G\5H̏ `yPf\ro$99C"d""""""=aP;uf9Pacl)9P~ x a#°*A:(8ffZhZ<E """"""wy{0F6]""""""?e0ɺzY0S- qfvKdZ2;8@P0 (U;R;LULȀ jPA{OjIxeﯢWofBW9@e#mYn w&"T]tu~ݯ:]%_}WI~G?^O]5Bi4d1Ip󨀈A%f#\0!|!!N" B̩; ʛUW0B N &@hXA 43Y"pа A, fa2@4a, 6 $šš—.N`̈́4!A'k##((BLȰ8@DC!5/ /@M5MS&jB-0PTUL&OoA[A4 (& O;]A&dL TS=&"ÑLDG _$h|"#"qjCN4ރH0IkL(M4ioM:|&T&Aa 'L&L(Aa0U##Ɖ{AA&}:%D 'A[i 0KNjO]546QiƘvM5T ''IÞ~AZ!tzM܃DPwDD~d">r !BDvQxiAE@  >aڴGGi " 4Ev#%oM=~xN]?O#:AwpOO82 845U ;H- h m+I3=/ >ש?߭?ڳO!<'ޝN齽&JI;֓j!9p&d&44 :NT }+?MNh4lRA^{}t.?ߤO"pJ ^ i/}޶_ '۷CVm?i4״_Jf}n_~[ۤnIҴ}n/خ,%7#{~/n߫}=. 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128.88 Tm <766572746963616C20> Tj 1 0 0 1 147.96 128.70 Tm <7472616E736C6174696F6E20> Tj 1 0 0 1 202.14 128.52 Tm <697320> Tj 1 0 0 1 213.84 129.24 Tm <28332B20> Tj 1 0 0 1 234.54 130.86 Tm <2D6C2920> Tj 1 0 0 1 249.84 128.52 Tm <4920> Tj 1 0 0 1 256.32 128.52 Tm <323A20> Tj 1 0 0 1 276.30 128.52 Tm <6C2C20> Tj 1 0 0 1 287.28 128.34 Tm <736F20> Tj 1 0 0 1 300.60 128.34 Tm <4420> Tj 1 0 0 1 312.12 131.04 Tm <2D20> Tj 1 0 0 1 323.10 128.34 Tm <3120> Tj 1 0 0 1 331.20 128.34 Tm <616E64> Tj 0.18 Tc 1 0 0 1 87.12 114.66 Tm <54686520> Tj 1 0 0 1 108.90 114.66 Tm <506861736520> Tj 1 0 0 1 140.40 114.66 Tm <736869667420> Tj 1 0 0 1 164.34 114.66 Tm <697320> Tj 1 0 0 1 175.32 114.66 Tm <302C20> Tj 1 0 0 1 187.56 114.66 Tm <736F20> Tj 1 0 0 1 201.78 114.48 Tm <4320> Tj 1 0 0 1 212.76 117.36 Tm <3A20> Tj 1 0 0 1 222.84 114.48 Tm <302E20> Tj 1 0 0 1 234.90 115.02 Tm <284E6F746520> Tj 1 0 0 1 264.60 114.48 Tm <7468617420> Tj 1 0 0 1 285.48 114.48 Tm <74686520> Tj 1 0 0 1 302.94 114.48 Tm <766572746963616C20> Tj 1 0 0 1 342.36 114.30 Tm <736869667420> Tj 1 0 0 1 367.02 114.30 Tm <736F6D6574696D657320> Tj 1 0 0 1 421.20 114.30 Tm <63617573657320> Tj 1 0 0 1 456.12 114.12 Tm <697420> Tj 1 0 0 1 465.84 114.12 Tm <746F20> Tj 1 0 0 1 478.80 114.12 Tm <6C6F6F6B20> Tj 1 0 0 1 503.10 114.12 Tm <6C696B65> Tj 0.18 Tc 1 0 0 1 86.76 100.98 Tm <776520> Tj 1 0 0 1 104.22 100.80 Tm <6861766520> Tj 1 0 0 1 129.96 100.80 Tm <6120> Tj 1 0 0 1 138.06 101.16 Tm <706861736520> Tj 1 0 0 1 168.66 100.62 Tm <73686966742C20> Tj 1 0 0 1 195.84 100.62 Tm <62757420> Tj 1 0 0 1 215.10 100.62 Tm <7468697320> Tj 1 0 0 1 235.62 100.62 Tm <697320> Tj 1 0 0 1 246.42 100.62 Tm <6E6F7420> Tj 1 0 0 1 264.60 100.44 Tm <74686520> Tj 1 0 0 1 282.42 100.44 Tm <6361736529> Tj 1.50 Tc 1 0 0 1 225.54 86.04 Tm <73696E20> Tj 1 0 0 1 242.46 87.84 Tm <2820> Tj 1 0 0 1 250.02 85.68 Tm <25782920> Tj 1 0 0 1 277.20 87.12 Tm <2B6C> Tj 0.00 Tc /F3 9.0 Tf 1 0 0 1 169.74 563.76 Tm <34> Tj 0.00 Tc 1 0 0 1 170.10 548.64 Tm <33> Tj 0.00 Tc 1 0 0 1 169.92 532.98 Tm <32> Tj 0.00 Tc 1 0 0 1 170.46 518.22 Tm <31> Tj 0.72 Tc 1 0 0 1 199.98 489.96 Tm <302E35> Tj 1.44 Tc 1 0 0 1 250.02 489.96 Tm <312E35> Tj 0.90 Tc 1 0 0 1 299.16 489.78 Tm <322E35> Tj 0.18 Tc /F3 11.0 Tf 1 0 0 1 86.94 86.22 Tm <5468657265666F72652C20> Tj 1 0 0 1 140.58 86.22 Tm <6F757220> Tj 1 0 0 1 159.84 86.22 Tm <6571756174696F6E20> Tj 1 0 0 1 204.48 86.22 Tm <6973> Tj ET endstream endobj 15 0 obj 7964 endobj 16 0 obj << /Length 17 0 R >> stream Graphing sine and cosine functions Graphins Recinrocal Trigonometric FunctionsThe cosecant and secant graphs are not very easy to draw, but they become much easier ifwe first draw the graphs of their related sine or cosine graphs. To turn a sine into acosecant or a cosine into a secant, simply take the reciprocals of a few points. The zeroesof the sine and cosine graph become asymptotes of the reciprocal graphs, and thema:rimums become minimums and minimums become manimums. Ex. Given the following sine gaph, find an equation. 1.57 3.14 4.71 6.28 7. 12.5614.13 15.7 17.27 18 One-half the vertical distance from the min to the max is %*(3--1) : 2, so A:2,The period is (12.7-3.14) : 44 so B - 2rl4r: Y2,The vertical translation is (3+ -l) I 2: l, so D - 1 andThe Phase shift is 0, so C : 0. (Note that the vertical shift sometimes causes it to look like we have a phase shift, but this is not the case) sin ( %x) +l 4321 0.5 1.5 2.5 Therefore, our equation is endstream endobj 17 0 obj 964 endobj 18 0 obj << /Length 27 >> stream % CANON_PFINF_TYPE0_TEXTON endstream endobj 19 0 obj << /Length 45 >> stream q 612.18 0 0 792.00 0.00 0.00 cm /Obj13 Do Q endstream endobj 20 0 obj << /Type /Page /MediaBox [ 0 0 612.18 792.00 ] /Parent 11 0 R /Resources << /Font << /F3 5 0 R >> /XObject << /Obj13 13 0 R >> /Subtype 16 0 R /ProcSet [ /PDF /Text /ImageB /ImageC /ImageI ] >> /Contents [ 18 0 R 19 0 R 14 0 R ] >> endobj 11 0 obj << /Kids [ 10 0 R 20 0 R ] /Count 2 /Type /Pages >> endobj 12 0 obj << /Pages 11 0 R /Type /Catalog >> endobj xref 0 21 0000000000 65535 f 0000000015 00000 n 0000000110 00000 n 0000058364 00000 n 0000072441 00000 n 0000072463 00000 n 0000072566 00000 n 0000074359 00000 n 0000074380 00000 n 0000074458 00000 n 0000074553 00000 n 0000129726 00000 n 0000129799 00000 n 0000074802 00000 n 0000120213 00000 n 0000128233 00000 n 0000128255 00000 n 0000129274 00000 n 0000129295 00000 n 0000129374 00000 n 0000129471 00000 n trailer << /Size 21 /Info 1 0 R /Root 12 0 R /ID [<2ccb534c9b11f1386cab10531a3b183e><2ccb534c9b11f1386cab10531a3b183e>] >> startxref 129854 %%EOF