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Cost + tan t 2 i — sins sin! — sinr tan(s — I) cos(s — t) sin(s — t) - t — I 2 2cos \ 1 + cost /----——— 2 — t) s—I - s+t - I r) 2t tan— 2 tan 2 tsar I — Cost sort 1 —tant - sirs sint ± cos (s — t) = — . s+r S—t 2Cos—--—coc—-—- = sina - ? -2bc os a Sifl stny s+t S—f coas —Cost =—2sin----——sin------- Coss +cost = Laws of Sines and Cosines V coss — tan 1 -I- tan a tan = Cos(s + Factoring Formulas 2cos——-sIn-—,-— — cott 2sinssint =Cos(s—t) —cos(5 +r) 2 cos a cost Product Formulas 2 1 cos± — cost + sins tan .c cos 1 + COtf = CSCf + cos 2t taft I tan —i) = —tan 1 5jn? cott sins cost Half Angle Formulas = sin(s + n + sin(s sins — sint sins — Double Angle Formulas tan s tan t — sin , = 1 — 2sin’t t 2 sinr Addition Formulas ——-—— .1 — COSt ---——- — cos (—t) = Cost 2coccsinr=sin(s + t) —sin(s— r) 2 sinscost 2 \ = cos t 2 cos( Odd-even Identities tans + tan t - 2 srnr cost Sin—± t cos2t sin 2r tan(s -It) Sin, srnt Cofunction Identities CSC t = COtt Cost Basic Identities sinscost + coss sins —sin cos(s + r = cos a cost sin(s + t) sin (—t) cost scct sin(- —t) = I — cost =--— Sect = taft Sin, - = = Vt x = - 3-V; V=SeCT tanG 0 .fifl tant sin t = Sin 1’ t = x v — x — r a — a b = iy=CSCII = = b) - L 1 J 0 Cos 0 Cot I = Cot cost Graphs 0) TRIGONOMETRY U- 5) - V = v (1 = x v.0 cos°(1,x) = SeC tan y—/2 7 - x + + + + + — +.. -I- (p’ k) +x) ± 2 p(p—l ) )(p— k! i .t x sinh x <1 ± e) coshx srnh x 1 (e’ ac/2 /2 +, —1< —1x1 —I <x<1 csch x cosh = sr,y < y < (p —k +1) + 2 x C’ 6 .t coshxl ±—±-±-- = cos x =1 — — el+x++j+ 5 X+X-+X-± Series tan°xx—--+——-—±. sinh x y Hyperbolic Functions — e’) cosh x —--1 I —x sech x 5+ x secix sec’ x tan tx sinhx tanhx=— cosh x sinh x siny,—n-/2 yCOSx+?X=CoSv,0yar = sin°x +s x = Inverse Trigonometric Functions y area rr + crr’v r + h 4 I liter t000 cubic centimeters = 7.48 gallons 453.6 grams 1 pound 1 cubic foot 2.20 pounds 180 degrees = 0.62 miles 1 .057 quarts 1 kilometer 1’ =-rr - 2 = irr h 2 = 2 S = 42cr CONVERSIONS Volume Surface Spheres Volume Surface area S V = 7rrh Volume Cones 2 + 2crrh S = 2irr Surface area radians = I liter A = Area CIinders C = 27cr Circumference Cirdes 2.54 centimeter5 cç + b = 1 kiloeram = 1 inch O Any triangle Right triangle a2 Pythagorean Theorem Triangles GEOMETRY 0 U- (U / 19. 18. 17. 16. 15. 14. 13. 12. ii. 10. 9. 8. 7. 6. secu + C u do — cot UI + C = In Isec u + tan UI + C csc u do = In ese o sec cotu du = Inlsinol + C tanu do = —Inicosul + C csc u cot u do = sc o + C seco tano do csc u 2 du = —cotu ± C o do = tanu + C 2 sec do 2 = a J zi\/ — 1 a a In a [—r==du =-sec’ / +u2 J •\/5_. a + C + C C 1 —--rdu=sin± a 1 2---—du tan1+C J a f f J f f J —cosu + C ma cosudo = sinu + C sinudu a”du j 5. c’ + C j c’ do 4. +C,n —1 do —u’ — fidt=lnIu!+c fundu oc 3 2. 1. fu etc = INTEGRALS U- V. 0: cv D, tan x = Dsin’x DYer = Dr in x D, tanh x 1 1 + - 2x sech Dvsec’x x’Vx —1 =— D, cos’ x = 1 x In a Dra’ = a’lna D, log., x D, cschx = —cschxcothx D,sechx = —sechxanhx D,cothx = —csch x 2 Dr sinh x = cosh x sinh x D,cscx = —cscxcotx Drsecx = secxtanx D, cosh x 2x Dr cot x = —csc D cos x = —sin x x x 2 Drtanx = sec Drsinx = cosx D,x’ = r’ 1 DERIVATIVES Varberg, Purcell, and Rigdon CALCULUS, 9/E to accompany Formula Card