Stewart redlin watson algebra and trigonometry 3rd txtbk

www.elsolucionario.net http://www.elsolucionario.net LIBROS UNIVERISTARIOS Y SOLUCIONARIOS DE MUCHOS DE ESTOS LIBROS LOS SOLUCIONARIOS CONTIENEN TODOS LOS EJERCICIOS DEL LIBRO RESUELTOS Y EXPLICADOS DE FORMA CLARA VISITANOS PARA DESARGALOS GRATIS www.elsolucionario.net EXPONENTS AND RADICALS x ᎏᎏn ϭ x mϪn x x Ϫn ϭ ᎏᎏn x x n xn aᎏyᎏb ϭ ᎏyᎏn x m x n ϭ x mϩn 1x m2 n ϭ x m n 1xy2 n ϭ x n y n n x1͞n ϭ ͙xෆ n n ෆ ϭ ͙xෆ ͙yෆ ͙xy n ͙xෆ Ίᎏᎏ๶y ϭ ᎏᎏ ͙ෆy x n n ͙͙ ෆෆ ෆ x ϭ͙͙ ෆෆ ෆ x ϭ ͙xෆ n m Formulas for area A, perimeter P, circumference C, volume V: Rectangle mn Box A ϭ l„ m x m͞n ϭ ͙xෆෆ ϭ Q͙xෆR n n m n GEOMETRIC FORMULAS m n V ϭ l„ h P ϭ 2l ϩ 2„ m h „ SPECIAL PRODUCTS 1x ϩ y2 ϭ x ϩ xy ϩ y Triangle 2 1x Ϫ y2 ϭ x Ϫ xy ϩ y 2 „ l l Pyramid V ϭ ᎏ13ᎏ A ϭ ᎏ12ᎏ bh 1x ϩ y23 ϭ x ϩ 3x y ϩ 3xy ϩ y 1x Ϫ y23 ϭ x Ϫ 3x y ϩ 3xy Ϫ y h h a FACTORING FORMULAS a b x Ϫ y ϭ 1x ϩ y21x Ϫ y2 Circle x ϩ 2xy ϩ y ϭ 1x ϩ y22 A ϭ ␲r x Ϫ 2xy ϩ y ϭ 1x Ϫ y22 x ϩ y ϭ 1x ϩ y21x Ϫ xy ϩ y 2 Sphere V ϭ ᎏ43ᎏ ␲ r C ϭ 2␲ r A ϭ 4␲ r x Ϫ y ϭ 1x Ϫ y21x ϩ xy ϩ y 2 r r QUADRATIC FORMULA Cylinder If ax ϩ bx ϩ c ϭ 0, then Ϫb Ϯ ͙ෆbෆ Ϫෆ ෆ 4ෆaෆc x ϭ ᎏᎏ 2a Cone V ϭ ␲ r 2h V ϭ ᎏ13ᎏ ␲ r 2h r INEQUALITIES AND ABSOLUTE VALUE h h If a Ͻ b and b Ͻ c, then a Ͻ c r If a Ͻ b, then a ϩ c Ͻ b ϩ c If a Ͻ b and c Ͼ 0, then ca Ͻ cb HERON’S FORMULA If a Ͻ b and c Ͻ 0, then ca Ͼ cb If a Ͼ 0, then ⏐x⏐ ϭ a means x ϭ a or x ϭ Ϫa ⏐x⏐ Ͻ a means Ϫa Ͻ x Ͻ a ⏐x⏐ Ͼ a means x Ͼ a or x Ͻ Ϫa B Area ϭ ͙ෆ s sෆෆ Ϫෆaෆ 21 sෆϪ ෆෆbෆ 21 sෆϪ ෆෆcෆ2 aϩbϩc where s ϭ ᎏᎏ www.elsolucionario.net c A a b C DISTANCE AND MIDPOINT FORMULAS GRAPHS OF FUNCTIONS Distance between P11x1 , y12 and P2 1x , y2 : Linear functions: f1x2 ϭ mx ϩ b ෆෆ d ϭ ͙ෆ 1xෆ ෆෆxෆ 1ෆ y2ෆ Ϫෆyෆ 2Ϫ 12 ෆϩ 12 ෆ Midpoint of P1P2: y x1 ϩ x2 y1 ϩ y2 a ᎏᎏ, ᎏᎏb 2 y b b LINES Slope of line through P11x1 , y12 and P2 1x , y2 Slope-intercept equation of line with slope m and y-intercept b y ϭ mx ϩ b Two-intercept equation of line with x-intercept a and y-intercept b x y ᎏᎏ ϩ ᎏᎏ ϭ a b Power functions: f1x2 ϭ x n y y x x Ï=≈ Ï=x£ f 1x2 ϭ ͙xළ n Root functions: LOGARITHMS y ϭ log a x Ï=mx+b Ï=b y Ϫ y1 ϭ m 1x Ϫ x12 Point-slope equation of line through P11x1, y12 with slope m x x y2 Ϫ y1 m ϭ ᎏᎏ x Ϫ x1 y y means a y ϭ x log a a x ϭ x a log a x ϭ x log a ϭ log a a ϭ log x ϭ log10 x ln x ϭ log e x log a xy ϭ log a x ϩ log a y log a aᎏxᎏb ϭ log a x Ϫ log a y y log a x b ϭ b log a x log b x ϭ x x Ï=£œx ∑ Ï=œ∑ x log a x log a b Reciprocal functions: f 1x2 ϭ 1/x n y y EXPONENTIAL AND LOGARITHMIC FUNCTIONS y y y=a˛ a>1 x x y=a˛ 00 b+ hyp opp ă _a x radians sin cos ␪ tan ␪ 0° 30° 45° 60° 90° 180° 270° ␲͞6 ␲͞4 ␲͞3 ␲͞2 ␲ 3␲͞2 1͞2 ͙ෆ2͞2 ͙ෆ3͞2 Ϫ1 ͙ෆ3͞2 ͙ෆ2͞2 1͞2 Ϫ1 0 ͙ෆ3͞3 ͙ෆ3 — — b _a One period b+ 2π x k One period period: 2␲͞k amplitude: ⏐a ⏐ ␪ a>0 a 2π k b adj SPECIAL VALUES OF THE TRIGONOMETRIC FUNCTIONS y ϭ a cos k 1x Ϫ b2 1k Ͼ 02 phase shift: b GRAPHS OF THE INVERSE TRIGONOMETRIC FUNCTIONS y ϭ sinϪ1 x _1 y ϭ cosϪ1 x y ϭ tanϪ1 x y y y π π π π _2 www.elsolucionario.net π x _1 x x π _2 FUNDAMENTAL IDENTITIES FORMULAS FOR REDUCING POWERS sec x ϭ cos x csc x ϭ sin x tan x ϭ sin x cos x cot x ϭ tan x Ϫ cos 2x sin x ϭ ᎏᎏ sin x ϩ cos x ϭ 1 ϩ tan x ϭ sec x ϩ cot2 x ϭ csc x sin1Ϫx2 ϭ Ϫsin x cos1Ϫx2 ϭ cos x tan1Ϫx2 ϭ Ϫtan x ␲ sin aᎏᎏ Ϫ xb ϭ cos x ␲ cos aᎏᎏ Ϫ xb ϭ sin x ␲ tan aᎏᎏ Ϫ xb ϭ cot x ␲ cot aᎏᎏ Ϫ xb ϭ tan x ␲ sec aᎏᎏ Ϫ xb ϭ csc x ␲ csc aᎏᎏ Ϫ xb ϭ sec x HALF-ANGLE FORMULAS ϩ cos u u cos ᎏᎏ ϭ Ϯ B 2 sin u Ϫ cos u u tan ᎏᎏ ϭ ᎏᎏ ϭ ᎏᎏ sin u ϩ cos u PRODUCT-TO-SUM AND SUM-TO-PRODUCT IDENTITIES sin u cos √ ϭ ᎏ1ᎏ ͓sin1u ϩ √ ϩ sin1u Ϫ √ 2͔ cos u sin √ ϭ ᎏ1ᎏ ͓sin1u ϩ √ Ϫ sin1u Ϫ √ 2͔ REDUCTION IDENTITIES ␲ sin ax ϩ ᎏᎏb ϭ cos x sin1x ϩ ␲2 ϭ Ϫsin x cos1x ϩ ␲2 ϭ Ϫcos x ␲ cos ax ϩ ᎏᎏb ϭ Ϫsin x tan1x ϩ ␲2 ϭ tan x ␲ tan ax ϩ ᎏᎏb ϭ Ϫcot x ADDITION AND SUBTRACTION FORMULAS sin u sin √ ϭ ᎏᎏ ͓cos1u Ϫ √ Ϫ cos1u ϩ √ 2͔ xϩy xϪy sin x ϩ sin y ϭ sin ᎏᎏ cos ᎏᎏ 2 xϩy xϪy sin x Ϫ sin y ϭ cos ᎏᎏ sin ᎏᎏ 2 xϩy xϪy cos x Ϫ cos y ϭ Ϫ2 sin ᎏᎏ sin ᎏᎏ 2 sin1x Ϫ y2 ϭ sin x cos y Ϫ cos x sin y cos1x ϩ y2 ϭ cos x cos y Ϫ sin x sin y THE LAWS OF SINES AND COSINES cos1x Ϫ y2 ϭ cos x cos y ϩ sin x sin y tan x ϩ tan y tan1x ϩ y2 ϭ ᎏᎏ Ϫ tan x tan y cos u cos √ ϭ ᎏ1ᎏ ͓cos1u ϩ √ ϩ cos1u Ϫ √ 2͔ xϩy xϪy cos x ϩ cos y ϭ cos ᎏᎏ cos ᎏᎏ 2 sin1x ϩ y2 ϭ sin x cos y ϩ cos x sin y tan x Ϫ tan y tan1x Ϫ y2 ϭ ᎏᎏ ϩ tan x tan y DOUBLE-ANGLE FORMULAS The Law of Sines B a sin A sin B sin C ᎏᎏ ϭ ᎏᎏ ϭ ᎏᎏ a b c C cos 2x ϭ cos x Ϫ sin x 2 ϭ cos x Ϫ tan x tan 2x ϭ ᎏᎏ Ϫ tan x Ϫ cos x tan x ϭ ᎏᎏ ϩ cos x Ϫ cos u u sin ᎏᎏ ϭ Ϯ B 2 COFUNCTION IDENTITIES sin 2x ϭ sin x cos x ϩ cos 2x cos2 x ϭ ᎏᎏ ϭ Ϫ sin x c The Law of Cosines a ϭ b ϩ c Ϫ 2bc cos A b b ϭ a ϩ c Ϫ 2ac cos B c ϭ a ϩ b Ϫ 2ab cos C A www.elsolucionario.net ... analysis Stewart, Redlin, and Watson have also published Precalculus: Mathematics for Calculus, College Algebra, Trigonometry, and (with Phyllis Panman) College Algebra: Concepts and Contexts A... Spain • United Kingdom • United States www.elsolucionario.net Algebra and Trigonometry, Third Edition James Stewart, Lothar Redlin, Saleem Watson Acquisitions Editor: Gary Whalen Developmental Editor:... the text to graph and analyze functions, families of functions, and sequences; to calculate and graph regression curves; to perform matrix algebra; to graph linear inequalities; and other powerful