# trig - The Unit Circle (0,1) 90° = gm » 3: (IL—1) 270...

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Unformatted text preview: The Unit Circle (0,1) 90° = gm » 3: (IL—1) 270 :1;— Regprocal Idgnliiies I I sing = cscﬂ = — cscﬂ sinﬁ i l secﬂ = Quotient identities .' 6' tang = gm c019 = c059 c056 sinﬂ c0519 2 5663 c059 — I Pagagoraan Identiﬁes sin29+oosza=1 1+ not2 B = csc’ B tan39+1=secaﬂ #- Double-Angle Formulas cos2u=0052 u~sin2u =20052u-1 = 1 -23in’u tan 2U: Zianu 1-tan’u “my: cotﬂ sin (— B)=-sinB cos(-B}=cose tan(-B)=-tanﬂ cot(-B)=-ooie csc(-B)=-csc8 cotﬂ = m higgative Angie Identiiigs Produci-io—Sum Formulas sinusinv =‘Alcos(u-v)-cos{u+v)] COSUCOSV = V: [cos (u - V) + 605 (U + VT] Power Reducin Formulas #% sinucosv gsm uzi-co52u =I/2[5in(u+v)+sin(u-v)] 2 cosusinv Icoszu= 1+oo32u 2 =‘/2[51n(u+v)-5in(U'V)] tan2u=1-oo52u Half-Angie Formulas Ri hi Trian le Definitions: Lgiilgi fw_|._||_l_i__u_";|_l..'-i‘|?_3 sin 9. csc 9. tan 8. cm 8 my hyp Even Functions 0059 = -# sect? = —-* hyp adj cos 9. sec 8 d. WE m opp uPl3' adj a Coiunciion Ideniitieg, sin (90“- 9) = 005 9 cos (90°- 9) = sin 9 tan (90°- 9) = cotB no! (90°- 8) = tan 8 sec(90°—B)=csc8 csc(90”-e)=sec3 Sum & Difference Formulas '5in(u:v]=slnucosv1cosusinv ‘coe(u:i:v)=cosuousv:sinusinv tan{u1:v)= tanuitanv 1xtanutanv Sum-to-Product Formulas I _ H + v Slnu+ smv: 2sin[ 2 )cn{ I . Iii-V . Sll'lﬂ- SHIV: 2'00 2 Sin u+v cosu+ cosv= 2co ~3— co , u+ v cosu— cosv = —25m Graphs of the__Trig_on0metric Functions ) — sin .\ Symmetry: Odd y = est 3: Symmetry: Odd Domain: (- m. 00) Domain: all reals except x = 1m when: n = integer Range: [-1, 1] Range: (- m. -l], [1. r«2) Asymptotes: rm Period: 27: Period: 27: .‘ = cos x Symmetry: Even Domain: (- m. 0°) Domain: all reals except it = m2 + no where n -— imegur Range: [-1. ll Range: (- m, -l ]. ['l, w) Asymptotes: m’2 + an Period: 27: Period: 21: _\ '— Inn Symmetry: Odd - - - Symmetry: Odd Domain: all reals except x = m’Z + am when: n = inlcgcr Domain: all reals except x = am where n = imcgcr Range: (— co, m) Asymptotes: a0. + an Range: (- no. no) Asymptotes: rm Period: 7: Period: it ...
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## This note was uploaded on 12/13/2011 for the course MATH 142 taught by Professor Kustin during the Fall '11 term at South Carolina.

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trig - The Unit Circle (0,1) 90° = gm » 3: (IL—1) 270...

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