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# 7.3 - for every value of.r for which both functions are...

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Unformatted text preview: for every value of. .r for which both functions are defined. Such an eque lion is referred to as; am identity. An equatirm that not an identity is called :51 conditional equation. Use A1 ebra to Sim 1i Tri onometric EX ressions. RCWI'lte cos2 x+cot2 x+ sin2 x 111 terms Ofcscx . ' “2 3 1 h I 2 , r 1 _ 2‘ '— CO\$X+\$mX riCo-i X E HAT-1L I : Swag 2 0V" 1Q ’4— Cor X Z 3 2: C536. Lx‘ =- - 'i- - £4" {5% C‘ZX t’VW “COM ,, 4L:{_t ‘33 COBGQD; C393 8; Sec.(—o):§ec8 LowE—S): win/lo; Co+(v0):'—Co}8 Simplify by rewriting 5m1+ COW—1 over a common denominator. COS x + \$111 x gin!" SEEN (fogx—i (COSX‘FE) anx (60” H 5 31% )6 Gas x H ) ’SIHD'ZX i-#[Co<3x‘——I)(COS‘X.+I ) "‘ (2.st ginX—‘r’ces’x‘m' — W’F—H ~ 5» ~ 3Cn>§ (60% H 9.04m“; ) (a) Simplify tan ‘9 sec 6 of sine and cosine functions. by rewriting each trigonometric function in terms tone —j— \$26 9 gfn L9 ,3; ‘ Cos 9 605 3 page i I S {@6- i (b) Show that 1:1“ 66 = Loos—Q by multiplying the numerator and cos sm . K,‘ _. (9 denominator by l—cost9 5mg - a 113:9 U.\-\i:<3939)Li—C’9393 marge “is ‘ _c:o23/e teas/E» r_- c539 ‘5 MN I *Cog’e) i . '2. ‘ ___ 1 . —— J i COS 9' I "L535 l C03 8’ _‘ ————— a \$an 1 1 Siﬁe ([241. (c) Simplify + 1-sinu l+sinu common denominator. (l—ﬁi‘nuMH—Sinu) ’.[_\$f bK-4—l ’gliﬂd -: & 1-3fnui)(i+\$rinbk) l-3fn1bL by rewriting the expression over a lcoszi/H’P) “wig “ 31 (PF-El; (d) Simplify —.———l— by factoring. " 38“. s1nv+cosvsmv Fri 1’— rib ' r— S {n I? 6 In l/ Establish Identities. Guidelines for Establishing Identities 1. It is almost always proferable to start with the side containing the more compiicatocl expression. 2. Rewrite sums or di‘ffcrenceg of quotients as a single quotient. 3. Sometimes; rewriting one side in terms of Sines and cosmos only will help. 4. Alwa keep your goal in mind. As you manipulate one side of the expres~ sion. you must keep in mind the form of the expmssion on the other side. Verify the following identities. 1 l \————+—:————=ZSecx (secx+tanx) (éecx—tanx l g) .Vl .__"l0/V\X (chHo x)l§£cx )ay QSQCX g efx «— to:le . g QCX Rikch (S! c “Pom )(Secx—iom Y) Sac x + \$QCX—H’ V»! t See Xll-lOmX) (\$0M -—-1LW\X> ' Ar + D; F" in P; smx = —cosxtan(—_x) goes): (~—) W I Coax hmv ,‘7 M. anx —;. [3m 1—csc9sin39f63359 l»— ._L. 8:“:ng- S" 9 Mid-Stnlaﬂ 3— 'v H. iCO\$9 ‘__i__,,‘ gas/209 W I csc6—sin6’ 9509 ’ . 9‘ t29=—-—~— . C0 sing 479 '— l(:lr12€’ , sip/9 \$12? 95.9.; "" S1 ' g‘l‘g- @032 grne -"“’ 1 ’ “‘ ‘~ ~77: Slﬁnzg— 3‘“ er- 3312C): 1. ‘C‘QSQEX’J sin2 6—tan6’ cos2 6—cott9 \gyog ‘ ‘7. 89 ‘ Gosefg‘fn‘D—B -" Sfﬁg (COS a" Coo ) «*ﬂ Case - ' KC-Ogb) I 7— srge C056 _%fm9 L 3-09 COS 8 -cage Mﬂ—a I Cogs. : Sfoﬁ §Cc39€os.9”g““& ' I Case- 3&1?) 0097—9 "COS 9 siné’ t cscB—cotﬁz 1+cosc9 She _ l-CoSf-i 1 +50 \$9 { ~60 S 9- 9’ “"Crﬂxgﬁj i .—-C¢9%LE«L Sim L0 I [—HGOS LC: sin 6(cot 6’ + tan 9) 2 sec 6 3'an 6&8 «kg-"r19 m 9 D" ) - 3‘ _ l :- a g. 9' 09b9 4. \$709 (371” . / (303.9 G039'+ gag—(9‘ @0319 -+ SmZ—(SL : ’ a: ‘ Cloga cos 6‘; ...
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