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

516 Pages·2016·23.12 MB·English

by  Andy Bulman-Fleming, James Stewart, Lothar Redlin, Saleem Watson

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
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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
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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]
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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
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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
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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
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