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Unformatted text preview: TRIGGNOMETRY Definition of the Six Trigonometric Functions Right triangle deﬁnitions, where 0 < 9 < 17/ 2. Adjacent Circular function deﬁm'rr'ons, where I9 is any angle. 2 :1 co | I“: O m o q: l i‘ﬁ co 0 o U) a: ll HIV: "ll-H ‘1 o m 9. 2 Cb Cb || ll Hark Hl'wkdlw K? a Reciprocal Identities - . i I 1 sm x = —---* set: .‘r = tan x = csc x cos x cot x csr x — —1- cos x *- 1 co1 x m l " sin .1: " ' soc x " tan x longest and Botasgent Identities Pythagorean lu‘eui‘ities Sin-2 x + cos2 x = ] i+ian2x==seczx l+cot2x=csc2x Cofunction Identities I sit: -x) == cos x cosGI—x) = sin x ‘17 11' csc.:{§- ) = sec 1: tan(E—x) = cot x f1.” 7r seclK-g—x =cscx cot 3-): =tanx Reduction Formulas sinﬁx} = "sin x cos(—-x) = cos x csc(-x) = ~csc .1- tan(~—x) = “tanx sec(-x) = secx cot(—x) = —cotx Sum and Difference Formulas sincfuiv) = sin .5: cos v 1- cos u sin v cos(u:-‘:v) =- cos u cos v \$ sin u sin v tan a 1: tan v ‘31: :v==—..—-—-——- ‘ {u ) I+tanutaﬁv sin 8 = 23-54 csc 3 = gag? C . . 6°°\$ d. 9390‘ Opposite COS I9 = {1% sec 9 = Li; a tan 9 = _:3?' cot 9 = ~—adJ' Double-Angle Formulas sin2u=2sinucosu cosZu=cosZu—siuzu=2coszu—l=l—2\$in2u Ztanu 1b'mzu=l-—tanzu Power-Reducing Formulas 2 1—005 2:: u = "—3— 2 I+cos 2:: cos a = —— sin 2 1—003 Eu l+cos 2n tanzu Sum-to-Produot Formulas . . . u+v u—v 5111 u + 5m v = 2 sm(—-) cos(—-—-—) 2 2 . . n+1) . H“? smu—smv=2cos— sun—— ( 2 ) 2 u+ u—v cosu+cosv=2cos J) cos -— 2 , 2 cos u co 2 5m “+1, lnru—ﬂ" _ v = _ . s 2 s K 2 Product-to-Sum Formulas sin n sin v = %{c05(u-v) — cos(u+v)] cos u cos v = éIcosGr—v) + cos(u+v)} sin n cos v = %[sin(u+v) + sintfw—m cos a sin v = %[sin(u+v) — sin(u—v)] DERIVATIVES AND INTEGRALS Basic Differentiation Ruies LEIcul=cu 2. E[uiv}=u .-_v 3. ﬁlm] = m" + 114' 4_ = d ._ d n _ ﬂ"i " 5. dxk‘] — 6. dxml me u d d u — = . — = — ’, =ﬁ 7. dx[.‘(] 1 8 dxﬂui] lulw) u D d u’ d u _ u , 9. Elma-E 10. Eie]—eu 11 i[" ] — (cos u)u' 12 £[ 0‘; u] = -{sin u)u’ . (ix am it ~ . . dx 0. 13 31m 1 = (sec2 Low 14 —d-[c0t u] = "*(cscz u)u' . (ix nu . dz 15 it ] = (sec-u tan uiu’ 16 i csc u} = —(csc u cot u) ' . dx secu . drl u d - a ___H' 9. _ ;L_ 17. EiaIcsm It] — v.1. _ “2 18. dxiarccos u} w W 9' u' d —u’ 19. Ewctan u] — 1 + “2 20. Eiarccot u] — -l-+ “3 d . u' d -u’ 21.—"sa l=—~-- 22.—- c = - —- filial-C c u‘ u a: - 1 £11th SC “1 lath/1:1 Basia: integration Formulas l. Ikﬂu) du = k Jﬂu} do: 2. [{ﬂu) i g(u)] do: = J-ﬂu) do: i [3(a) (it: n “n+1 3.J’du=u+C 4.1!}: du—n+1+C, n=F-—1_ du 5- j=lnlui+C 6.Jeudu=eu—.C 7.stinudu=-cosu+C 8.]cosudu=sinu+C 9. Itanudu=-1nlcosui+c 10. Icotudu=lnlsinug+c 11. [secudu =1nlsecu+ tanul +C 12. [cscudu = —in]cscu + cotul + C 13.J’sec2udu=tanu+C 14.Icsc3udu=-cotu+C 15.Jser:utanudu=sccu+c 16.J-csc»rcotudu=—csc:x+C 1?. I in; = arcsin E + C J- ada 7 = larctan E + C Va“ _ “L a a- + u' a a (1:: 1 .u 19. J-——-— =ﬂarcscc—+C uVuZ ‘- a2 ‘1 ...
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## This note was uploaded on 02/09/2012 for the course MATH 112 taught by Professor Jarvis during the Winter '08 term at BYU.

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