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Chapter 3 27 - SECTION 3.4 DERIVATIVES 0F TRIGONOMETRIC...

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Unformatted text preview: SECTION 3.4 DERIVATIVES 0F TRIGONOMETRIC FUNCTIONS 177 tan 6t sin 6t 1 t . 65in 6t . 1 , 2t ‘ 2‘ ——-——-——- =1 -1 -11m _ 37' i133 sin 2t PER) ( t cos 6t sinZt) 33(1) 6t £1115 cos 6t t—>0 25m 2t sin6t 1 1 . 2t 1 l = ' ~' ‘-1 :61-—~~1=3 6:11.135 6t 15%cos6t 2:3?)511121: M 1 2H c050—1 lim c0s0—1 _ -—> 0 38.11mfl:1im#=%2—20 0—)0 srnO 0—»0 sm6 . sm0 1 —— Jun 0 9—0 0 . sin(1im cos 6) . 39' hm sm(cos 0) : .9_,0 _ sml ¥ sin1 0—»0 sec 6 (11m) sec 6 1 . 2 . . . . 40. lim SID 3t 1 hm (SID 3t , 811132?) a lim Sin 3t ' hm Sln 3t t——>0 t2 t~90 t t t~>0 t t—>0 t . 2 . 2 sm 3t , 8111 323 2 (£135 t > (31% 3t > <3 > 9 , cot 2:1: , cos 2m sin m , (sin x)/m . i135 [(sm x)/x] 41. hm : 11m .‘ : hm cos 2m .—— = hm COS 227 fi 2&0 cscx z—>0 8111 23? 2—0 (s1n2w)/m 2—»0 2 hn(1)[(s1n2zr)/2m] I—} 1 1 2 1 - —— : — 2 - 1 2 , sinsc — cosm . sinzt — cosm , sincc — cosa: 42. hm a = hm fin : hm . . z—nr/4 cos 2m a:—)7'r/4 cos2 2: ~ sin cc z—v7r/4 (cos x + Sln :c)(cos m — 8111117) . *1 —1 —1 2 11m : _ ' 7r ' 7I' Iran/4 cos :c + smw cos I + sm Z fi 43. Divide numerator and denominator by 9. (sin 0 also works.) sin0 1' sine . sin0 . 9 92% 0 1 1 hm ‘ 2 hm . = . _ _ 9—»06+tant9 9—»0 s1n6I 1 , s1n0 . 1 1+1-1 2 1 —- 1+ hm — hm 6 c050 9—io 0 6—0 c050 , sin(w ~ 1) . sin(x ~ 1) . 1 , sin($ — 1) $131932+x—2 1131(m+2)(x~1) z1—>Inlilt+2;1—>rnl :c—l 3 1 3 d . h . _ . 2 . 2 45' (a) _tan$:ismw :> sec2$~ cosmcosa: s1nm( Sln$) _ cos m+sm m.Sosec2;v= 1 . d3: d9: cos 3: cos2 ac cos2 :1: cos2 a: d d 1 — 1 ' ' (b) —sec:c : — => secmtanx = w. Sosecattanm : smat- div dm cos m cos2 av cos2 :c . d 1+cotac (c) dx (smx +coszc) — E‘CSCCL‘ : 2 2 c — ‘ — — — cosx—sinx— scm( csc x) (l+c0ta:)( csccccotm) cscm [ CSC x+(1+c0ta:) cotm] CSC2$ cscza: —Csc2m+cot2m+cotzn _ —1+cotm cscw ‘ cscm . cotat~1 Socosac—smatz \. c502: ...
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