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Student solutions manual : Algebra and trigonometry, fourth edition, James Stewart, Lothar Redlin, Saleem Watson (Compressed) PDF

516 Pages·2016·23.12 MB·English
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Preview Student solutions manual : Algebra and trigonometry, fourth edition, James Stewart, Lothar Redlin, Saleem Watson (Compressed)

Algebra and Trigonometry FOURTH EDITION James Stewart McMaster University and University of Toronto The Pennsylvania State University California State University, Long Beach Prepared by Andy Bulman-Fleming eo » CENGAGE ** Learning’ Australia + Brazil * Mexico » Singapore * United Kingdom + United States CENGAGE Learning © 2016 Cengage Learning ISBN: 978-1-305-11815-7 WCN: 01-100-101 Cengage Learning 20 Channel Center Street ALL RIGHTS RESERVED. No part of this work covered by the Boston, MA 02210 copyright herein may be reproduced, transmitted, stored, or USA used in any form or by any means graphic, electronic, or mechanical, including but not limited to photocopying, Cengage Learning is a leading provider of customized recording, scanning, digitizing, taping, Web distribution, learning solutions with office locations around the globe, information networks, or information storage and retrieval including Singapore, the United Kingdom, Australia, systems, except as permitted under Section 107 or 108 of the Mexico, Brazil, and Japan. Locate your local office at: 1976 United States Copyright Act, without the prior written www.cengage.com/global. permission of the publisher. Cengage Learning products are represented in Canada by Nelson Education, Ltd. For product information and technology assistance, contact us at To learn more about Cengage Learning Solutions, Cengage Learning Customer & Sales Support, 1-800-354-9706. visit www.cengage.com. For permission to use material from this text or product, submit Purchase any of our products at your local college store or all requests online at www.cengage.com/permissions at our preferred online store www.cengagebrain.com. Further permissions questions can be emailed to [email protected]. Printed in the United States of America Print Number: 02 Print Year: 2015 ty. tt CONTENTS m PROLPrincOipleGs ofU ProbElem :Sol ving 1 CHAPTER P_ PREREQUISITES 3 P.1 Modeling the Real World with Algebra 3 P.2 RealNumbers 3 P.3 Integer Exponents and Scientific Notation 6 P.4 Rational Exponents and Radicals 8 P.5 Algebraic Expressions 11 P.6 Factoring 13 P.7 Rational Expressions 16 P.8 Solving Basic Equations 19 P.9 Modeling with Equations 22 Chapter P Review 25 ChapterPTest 28 w FOCUS ON MODELING: Making the Best Decisions 29 CHAPTER 1 EQUATIONASN D GRAPHS 33 1.1. TheCoordinate Plane 33 1.2 Graopf Ehquastio ns in Two Variables; Circles 38 1.3 Lines 45 1.4 Solving Quadratic Equations 50 1.5 ComplexNumbers 55 1.6 Solving Other Types of Equations 56 1.7 Solving Inequalities 60 1.8 Solving Absolute Value Equations and Inequalities 70 1.9 Solving Equations and Inequalities Graphically 71 1.10 Modeling Variation 74 Chapt1R eevrie w 77 - Chapt1eT res t 86 © 2016 Cengage Learning. AlJ Rights Reserved. May not be scanned, copied or duplicated, or posted to a.publicly accessible website, in whole or in part. iv Contents FOCUS ON MODELING: Fitting Lines to Data 89 CHAPTER 2 FUNCTIONS 91 2.1 Functions 91 2.2 Graphs of Functions 95 2.3 Getting Information from the Graph of aFunction 102 2.4 Average Rate of Change ofa Function 108 2.5 Linear Functions and Models = 111 2.6 Transformations of Functions 114 2.7 Combining Functions 121 2.8 One-to-One Functions and Their Inverses 125 Chapter2 R eview 130 Chapter 2 Test 137 FOCUS ON MODELING: Modeling with Functions 138 CHAPTER 3 POLYNOMIAL AND RATIONAL FUNCTIONS 143 3.1 Quadratic Functions and Models =1 43 3.2 Polynomial Functions and TheirGraphs 148 3.3 Dividing Polynomials 156 3.4 Real Zeros of Polynomials 160 3.5 Complex Zeros and the Fundamental Theorem of Algebra 176 3.6 Rational Functions 181 Chap3tR eevrie w 198 Chapter 3 Test 208 FOCUS ON MODELING: Fitting Polynomial Curves toData 210 CHAPTER 4 EXPONENTIAL AND LOGARITHMIC FUNCTIONS 213 4.1 Exponential Functions 213 4.2 The Natural Exponential Function 217 4.3 Logarithmic Functions 220 4.4 Laws of Logarithms 225 4.5 Exponential and Logarithmic Equations ©2 27 i] © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Contents v 4.6 Modeling with Exponential Functions 231 4.7 Logarithmic Scales 233 Chapter 4 Review 234 Chapter 4 Test 239 FOCUS ON MODELING: Fitting Exponential and Power Curves to Data 240 CHAPTER 5 TRIGONOMETRIC FUNCTIONS: RIGHT TRIANGLE APPROACH 243 5.1 Angle Measure 243 5.2 Trigonometry of Right Triangles 245 5.3 Trigonometric Functions of Angles 247 5.4 Inverse Trigonometric Functions and Right Triangles 250 5.5 The Law of Sines 252 5.6 The Law of Cosines 254 Chapter5 R eview 257 Chapter 5 Test 259 FOCUS ON MODELING: Surveying 287 CHAPTER 6 TRIGONOMETRIC FUNCTIONS: UNIT CIRCLE APPROACH 263 6.1 The Unit Circle 263 6.2 Trigonometric Functions of RealNumbers 265 6.3 Trigonometric Graphs 267 6.4 More Trigonometric Graphs 274 6.5 Inverse Trigonometric Functions‘and Their Graphs 277 6.6 Modeling Harmonic Motion 279 Chapter 6 Review 282 Chapter 6 Test 286 FOCUS ON MODELING: Fitting Sinusoidal Curves to Data 260 CHAPTER 7 ANALYTIC TRIGONOMETRY 291 7.1 Trigonometric Identities 291 7.2 Addition and Subtraction Formulas 295 7.3 Double-Angle, Half-Angle, and Product-Sum Formulas 298 © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. vi Contents 7.4 Basic Trigonometric Equations 304 7.5 More Trigonometric Equations 306 Chapter 7 Review 309 Chapter 7 Test 312 FOCUS ON MODELING: Traveling and Standing Waves 313 CHAPTER 8 POLAR COORDINATES AND PARAMETRIC EQUATIONS 315 8.1 Polar Coordinates 315 8.2 Graphs of Polar Equations 317 8.3 Polar Form of Complex Numbers; De Moivre’s Theorem 321 8.4 Plane Curves and Parametric Equations 327 Chapter 8 Review 334 Chapter 8 Test 337 FOCUS ON MODELING: The Path ofa P rojectile 338 CHAPTER 9 VECTORS IN TWO AND THREE DIMENSIONS 341 9.1 Vectors inTwo Dimensions 341 9.2 The Dot Product 344 9.3 Three-Dimensional Coordinate Geometry 346 98 Vectors in Three Dimensions 347 9.5 The Cross Product 349 9.6 Equations of Lines and Planes 350 Chapter9 Review 352 Chapter 9 Test 354 FOCUS ON MODELING: Vector Fields 355 CHAPTER 10 SYSTEMS OF EQUATIONS AND INEQUALITIES 357 ; 10.1 Systems of Linear Equations in Two Variables 357 10.2 Systems of Linear Equations in Several Variables 361 10.3 Partial Fractions 365 10.4 Systems of Nonlinear Equations 370 10.5 Systems of Inequalities 374 © 2016 Cengage Learning. All Rights Reserved, May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in-part. <a Contents vii Chapter 10 Review 380 Chapter 10 Test 384 FOCUS ON MODELING: Linear Programming 386 CHAPTER 11 MATRICES AND DETERMINANTS 391 11.1 Matrices and Systems of Linear Equations 391 11.2 The Algebra of Matrices 397 | 11.3 Inverses of Matrices and Matrix Equations 401 11.4 Determinants and Cramer's Rule 406 Chap1t1R eevrie w 413 Chapt1e1T res t 418 FOCUS ON MODELING: Computer Graphics 420 CHAPTER 12 CONIC SECTIONS 423 12.1 Parabolas 423 12.2 Ellipses 425 12.3 Hyperbolas 430 12.4 Shifted Conics 433 12.5 Rotation of Axes 439 12.6 Polar Equations of Conics 445 Chapter 12 Review 450 Chapter 12 Test 457 FOCUS ON MODELING: Conics in Architecture 458 CHAPTER 13 SEQUENCES AND SERIES 459 13.1 Sequences and Summation Notation 459 13.2 Arithmetic Sequences 461 - 13.3 Geometric Sequences 464 13.4 Mathematics of Finance 468 13.5 Mathematical Induction 470 13.6 The Binomial Theorem 475 Chapter 13 Review 477 © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. viii Contents Chapter 13 Test 481 m FOCUS ON MODELING: Modeling with Recursive Sequences 482 CHAPTER 14 COUNTING AND PROBABILITY 483 14.1 (Counting 483 14.2 Probability 486 14.3 Binomial Probability 490 14.4 ExpectedValue 493 Chapter 14 Review 494 Chapter 14 Test 497 m FOCUS ON MODELING: The Monte CarloMethod 497 APPENDIXES 499 A Geometry Review 499 Calculations and Significant Figures 499 C Graphing with a Graphing Calculator 500 © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a-publicly accessible website, in whole or in part.

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