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lesson_08 - 1361 e 4 LQSSOH 8 3 In Hrs[233mm N9 begin the...

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Unformatted text preview: 1361 e 4'? LQSSOH 8 3 In Hrs [233mm N9 begin the Sfudj Cr]— tijonometrfc functl'on5} whfch {5 H18 mast {mlmtant Subject of m PYECMCL/dus OUMFLQ’ahd is Verj cmdofi I—GY HWY study "of calm/[ms (n the future Read Sections 42,43; cavejuuj. That M4135 yam unders’rondt'nj of H19 deTfnffi'ons 04]- the sine and cosine JImen‘xma and their EMJaman’r 90,2“th Homemk 1R“ Lessm 8 Section 4‘2 Moi—numbered (gueshons 1 throufih 39 Section 455’ odd—numbeled i through 4% 52, 53, 54- . Paje 4-8’ 4.; Measw’xnj Anaks A“ (1an 00105615 Oj- JCWOFL Yo s U’tai'fviines) Hm OT‘jfina'Cg at a Common POM? rCh we wiildenou 0 One of the rays, is ended the Enih‘M side Called the VEYUX i win B -of the M382 and the other my ES Cod (ed {he ievrmnaf sick? An mate j-ofmed by me ocmlateig Yo‘tanofl is 360° 0 8 The malfqn measure ej- cm range? with \JQrfiz'K at H18 center CT A the unf‘figflcm («arr—L Yaclius =1) {8 the Lena'th of We We Made by the 61th - '. Sim {he Czrwmferencc of a unit meta <3 lJL Cm anan “made by one cem‘ntm wwtufahen has meqswe 27 mdmns Q 11 mdmns :: 360° . So 0 5’72" «- D .- Ex_ Express [35 Gnd 4-100 (h radians! and exrregg quians {n derees [55: 155 (lg—o ) 7: 31 radians; 4-120" : 4.20 “80) = :23. radians vrv H ~ 3.1—.— ‘mdtans : 5” . '30 :: I500 A‘Eth of conversfof' Aug] real number 15 veFVQSIEm‘S cm 91an . when t>0 “~19ij {s generafizd b3. refutinj Countfifd Oflkwlse mm the Josi'trve’X 0005 when tco 5mm Yo’cau‘en .‘3 cfockwme_ For exempts: (RIB Kyfl Page 4'7 LflLC—Lfi‘f I“ G We 01‘ Mus Y, the (9'13“ 3 07‘ an m W mat: Svadfans is 8:78. ,__.._.-:—'- 1-" ": AT?“ 0 G Chou!“ SQCW . In a Cl'rdg of Yadius Y, fhe area A of a elm/{by seem farmed by Om M55 0’} G TQdionS {S A: fife Remark y. To um they: ffimMaQ, We anjfia Wat be measured {n mafia“ E -Find the Length 0'] an (“C but“ 0‘an 4—50 {n 0 CL‘FCUJ Lmfi’cfi radius 2 111le SoLuHUY} _ 4-50 : FEE. _ Ave [Myth 2 N9 == 2‘7} == TEE—(mdm ). “Few“ Que-«d " ow awhmtren Wesfion .. {he answer new; to We HMS E): In ca ocrde 01L radius 5 mileslon ah: of Mid] 3mt€s has anij (9 Find we measure of Ehe thm {h dE‘jW—QS and radians 5mm _SoLMTw“_ 5:1’8. 9:»:— == % Yach‘qns I 5 :§‘ [30 ._ [OS'H o Emits” 5 "gr-“~— "771— #34233 B. Find {he area of the warm Seem with M362 30° in a cud? of mdl'us 4 (none: 30 _ 0:1 ‘51 —-_L li——.—L '2_]— H ._. km“ @_30 6 rod: hs. Aveq_ :2 1’82. 14 7;” m8’-%-i§f (inz) +3) The Sine and {03(th ‘unctr'ons FM “j W‘jmt, the initially aid-e 1‘s [shad on the posit'we X‘flxm‘. LJi the (ml/mind side 01 H16 anflmt {markers the unit (1”le (Ixfijj‘zn at the Pom-(- P“) will“! CWC‘MQTPJ (SCH), 1jHJ), De'JUHJ EMT—THU} and WET-:XH) _—.__.___ Since. PM): (’xiflfflfl) [3 my file unit cfircLQ 'Xl-rjlii. it (allows tth M W __~__________‘.______ Bwnds (am the Sine and Cosine -. Fania“ real? numbers 1‘, ___,__F___#_________ "I garnigl and -—l Soost SI figs {3 because the: lyem’rs (my) on (the circle 'Xl+jl=’ SanSjj -1S°ts’ and ~lsjsl and 5M r‘s 3mm bfj the 3-wc‘c‘nm J cast is the ’>C~CWC‘C’1GTD. Frcm the defmflm “T We and cosine, we see how the mains 0 3m and 0031' (“hen e, as deso'ibed inflow. If jochb {2(50 firm the clejgnimn‘ :13 Shawn Tkua , the cosine ‘hnch'on is Wen I and the SM? ’unch‘cn is odd, SINK the 0‘“ (‘35 tflfi and 't gm"? the Same {RVanmosidE-Z‘g Imahj rewohumbert Sin[t+1’TI):.—sfn’t’ lewd cosL't-flfi): 055i :>€VI'°¢["C FW‘CHW : A HOHCMS‘tr-mt function f {3 Said to be [Jera‘odic if 04 Foam»? humber T exists wl‘fh JCUHfl :fl-fi) j-m an t in the domm‘n of f “me SMaHesi Positive numtger T j—mwht‘ch tfia‘s e§uatron holds (5 the lfergod Dj’ 7L T119 sine and cosine functions are Perfocffc wi’m Erfu'd 291 ugqnj the definm'on of sine and Cosil19y_...a{ohj wr‘rh PYUPGYHGS of PM“? (190111903! we have He fcflfiwthj {GHQ j—M Some SFECFJthkS I which the sfuden’rS' H’IHSIL W memmze‘ Cost 1 if: i} 3'; o —1 0 1 . F'- Sw't 0 g2. 25—— 3.3.. 1 o wt 0 Page 5) Sim the sine and cosine funch‘ons are Pew/{cram wiffi {Jen-”ad 1): We have Srhff) =3int’c +211) =8mh+47€1 :5th +613) : ., - SW“ *= adv-17‘) = Sim—4H): SmH—M) =2 ~-- ('herause t:(’c-zfi)+1fi) T‘WS. 3mm: SmL’cHnFE) Mammary m5£fl=msfi+znm it“ anj auger n‘ -_______.._________._._————r—-—_________________._._—————- E Find the mules of SinT and 0051 j“ ““3 \‘aLMQ 01L 4‘ .9. tr?- 2 tr? 5- t=~§~ a t=315° Em ._ W- —— [1,1— :5 SoLqun a SM 4 ) #31“?— m) ~—~Sm +) .3. 95 ..r' _. L _. J3 @5(¢):“5f%‘1n)”m5[4)P—5 “r T . # t —,' -—..._‘. --— .L "I ,3 sin—Jig) mink“; +611) :si'n(§.): 1, ces£“%)—M( .1 fink—005(1) 0 £_ Not; Sm‘t {s cm add uncfr‘onr and Dost {5 ah even audio” 5 . r cast—+25) we?) =4; .5]. SMBISD] :: smBISUeBbo" :2 mp4?) = .. 3,‘n[4~5'°) : _ £1 . ' r— oostens") : us£3i5°»%0°) —; m(~+5°) z 003mg): 1} To walk out some other oomPuTations; Wei-use the ideas of we evenoz numbers For “3 Yeai humber'b, the reiel‘eMQ Number r asgogrm with ”t (3 the Shortes'f CIISWQ (caught in MdiahS) mic“? tke unit aerate from t h: tfie 09am; 7:61 ahfj t! the referehco number r is in E0, {1i E5. Find Hie N’QLHQS 0T Sjn'tk and Cast j-m the "Jab/(e cf 1 G ‘2 511. b "t — -— 37{ C = fl}: “'— 6 ' B SGWW‘” 3; . For ”E: E3 the YQIQYQMQ number Y:%. The anjUL fl (3 mike 2nd FémdmnT, So. 6 0 9c sine is IJDSEINQ, cosine is nejatrw Thus ENE) :5:n(lé-):-J— CofifflJ— 6‘35“)" 5 b e 2* 6 —‘ 75' “"3“ —-— 71‘? ““704 t: g? {s in fine 3rd gummy so bdth the sine and Define is nejafiv'€_ The re Irene: number viii} Thus 3m (—34—? :-—$;‘n(-Tq‘:) "7—31- .. Debbi; :~6q6(2’:.)=~£ .2 Page 52 In summary, an‘t (3 Btu“ to EhQ 3W QMO‘MIW : - ‘ v! ' {Engine ~1— CN __, Stjn' 5&1“!le j‘“ _ The VPTWE’MQ Number Y=% In ’6’“? 4th ngdmnT Sint <0 Cost >0 r Sii’l(:;r) -—- Sm[ §:—% Ex ma Ru mules 03‘ i We mm Em 1"] 3mm?) mm): FEL- Bobfiion 5mg: 09mm, 032t$4¢f Let smut, H1911 oqudi-fi The win; (n [0,1110 whom Slne _ 2 L ”In [1}? (gm ?,'rd,4-[‘h cguqdmlfix Y£T9|"Qn& humbey) :n '6 fiheve are {We MW Chaim TM 06 3.3T? & Swag szslfl' +1n: l??? a=‘l&£+m = (add one mm»: comriatg Yo’rcdfm) 13” 90 t: 7)? w": WW m _ ______.._.,— - h 7'!” Hr WV y THUS ZtFFIHZJ-IFEE'T: [2 3 Find on ”camera of Jc (11 E0: 1“] 9‘0” 5““st 2(3m)1+3003t : O Swim“ ‘ By the PjHOjcVeqn identity (Sr'th-k (matle, the 98mm» {‘3 Chanjvd 710 _______,__... F —— r2’ 2’ L2 aft—@atf]+30~vfi:0, be '[email protected])2+3mst+220 MultiPlj bLj —l. on botk sides 2(m3fffi3myt_)_:0, (2m3t+l){m5t~2)=o 3c, ZCQSJE'HT—‘O a 003t~2==0. Le CzoS‘tfzwi~ evocsfziz. 8m- ch‘tzg is imposnm (no sdqn'cn) 3(an 4.5005th 006t=~3§~ has twoSQLuTiens in farm] Yejaenctg number; 2 ) ...
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