Algebra and Trigonometry 4th Edition Stewart SOLUTIONS MANUAL
CONTENTS
¥ PROLOGUE: PrinciplesofProblemSolving
QA Q A Q A 1
CHAPTER Q A P PREREQUISITES 3
P.1 ModelingtheReal Worldwith Algebra QA QA Q A Q A 3
P.2 Real Numbers 4
QA Q A Q A
P.3 Integer Exponents and Scientific Notation 9
QA QA QA QA
P.4 RationalExponentsandRadicals Q A Q A 14
P.5 AlgebraicExpressions Q A 18
P.6 Factoring 22 Q A
P.7 RationalExpressions Q A 27
P.8 SolvingBasicEquations Q A Q A 34
P.9 ModelingwithEquations Q A Q A 39
Chapter PReviewQA Q A Q A 45
ChapterPTest 51 Q A
¥ FOCUSONMODELING:MakingtheBestDecisions 54
CHAPTER Q A 1 EQUATIONS QA AND GRAPHS QA 57
1.1 TheCoordinatePlane 57 Q A Q A
1.2 Graphs of Equations in Two Variables; Circles 65
QA QA QA QA QA QA
1.3 Lines 79 Q A
1.4 SolvingQuadraticEquations Q A 90
1.5 ComplexNumbers Q A 98
1.6 SolvingOtherTypesofEquations Q A Q A 101
1.7 Solving Inequalities
QA Q A Q A 110
1.8 Solving Absolute Value Equations and Inequalitie 129
QA QA QA QA QA
s
1.9 Solving Equations and Inequalities Graphically 131
QA QA QA QA
1.10 Modeling Variation 139
QA Q A
Chapter 1 Review
QA QA Q A Q A 143
Chapter1Test 161 Q A
iii
,iv Contents
¥ FOCUS ON MODELING: Fitting Linesto Data 165
QA QA QA QA QA
CHAPTER Q A 2 FUNCTIONS 169
2.1 Functions 169 Q A
2.2 GraphsofFunctions Q A Q A 178
2.3 GettingInformationfromtheGraphofaFunction Q A Q A 190
2.4 AverageRateof ChangeofaFunction QA Q A Q A 201
2.5 LinearFunctionsandModels 206 Q A Q A
2.6 TransformationsofFunctions 212 Q A
2.7 CombiningFunctions 226 Q A Q A
2.8 One-to-One Functions andTheir Inverses
QA QA QA 234
Chapter 2 Review 243
QA QA Q A Q A
Chapter2Test 255 Q A
¥ FOCUSONMODELING:ModelingwithFunctions Q A Q A 259
CHAPTER Q A 3 POLYNOMIAL QA AND RATIONAL FUNCTIONS
QA QA 267
3.1 Quadratic Functionsand Models 267
QA QA
3.2 Polynomial Functions and Their Graphs 276
QA QA QA QA
3.3 DividingPolynomials Q A Q A 291
3.4 RealZerosofPolynomials Q A Q A 301
3.5 ComplexZerosandtheFundamentalTheoremofAlgebra 334
3.6 RationalFunctions 344 Q A Q A
Chapter 3 Review 377
QA QA Q A Q A
Chapter3Test 395 Q A
¥ FOCUSONMODELING:FittingPolynomialCurvestoData 398
CHAPTER Q A 4 EXPONENTIALAND LOGARITHMIC FUNCTIONS QA QA 401
4.1 ExponentialFunctions Q A 401
4.2 TheNaturalExponentialFunction Q A 409
4.3 LogarithmicFunctions Q A 414
4.4 Laws of Logarithms
QA QA 422
4.5 ExponentialandLogarithmicEquations Q A 426
, Contents v
4.6 ModelingwithExponentialFunctions Q A 433
4.7 Logarithmic Scales QA Q A Q A 438
Chapter 4 Review
QA QA Q A Q A 440
Chapter4Test 448 Q A
¥ FOCUSONMODELING:FittingExponentialandPowerCurvestoData Q A Q A 450
CHAPTER Q A 5 TRIGONOMETRIC QA FUNCTIONS: RIGHT TRIANGLE APPROACH QA QA QA 455
5.1 AngleMeasure Q A Q A 455
5.2 Trigonometry ofRight Triangles 459 QA QA
5.3 TrigonometricFunctionsofAngles Q A 464
5.4 nverseTrigonometricFunctionsandRightTriangles 468 Q A
5.5 TheLawofSines 471 Q A Q A
5.6 TheLaw of Cosines 476
QA QA Q A Q A
Chapter 5 Review 481
QA QA Q A Q A
Chapter5Test 486 Q A
¥ FOCUS ON MODELING: Surveying
QA QA QA Q A Q A 536
CHAPTER Q A 6 TRIGONOMETRIC QA FUNCTIONS: UNIT CIRCLE APPROACH QA QA QA 491
6.1 TheUnit Circle 491 QA Q A Q A
6.2 Trigonometric Functions ofReal Numbers 495 QA QA QA
6.3 Trigonometric Graphs 500 QA
6.4 More Trigonometric Graphs
QA QA 511
6.5 nverse Trigonometric Functions andTheir Graphs
QA QA QA QA 519
6.6 ModelingHarmonicMotion 521 Q A
Chapter 6 Review
QA QA Q A Q A 527
Chapter6Test 534 Q A
¥ FOCUSONMODELING:FittingSinusoidalCurvestoData Q A Q A 487
CHAPTER Q A 7 ANALYTIC QA TRIGONOMETRY 541
7.1 Trigonometric Identities 541 QA
7.2 AdditionandSubtractionFormulas 549 Q A
7.3 Double-Angle, Half-Angle, and Product-Sum Formulas 556
QA QA QA QA
, vi Contents
BasicTrigonometricEquations 567
More Trigonometric Equations
QA QA 571 Chapter 7QA QA
Review 578
Chapter7Test 584 Q A
¥ FOCUSONMODELING:TravelingandStandingWaves 586
QA
CHAPTER QA 8 POLAR COORDINATES AND PARAMETRIC EQUATIONS
Q A QA QA QA QA 589
8.1 PolarCoordinates 589 Q A
8.2 GraphsofPolarEquations Q A Q A 593
8.3 Polar Form of Complex Numbers; De Moivre’s Theore 600
QA QA QA QA QA QA QA
m
8.4 Plane Curves andParametric Equations 612
QA QA QA
Chapter 8 Review QA QA Q A Q A 623
Chapter8Test 630 Q A
¥ FOCUS ONMODELING: ThePathofaProjectile
QA QA Q A Q A 631
CHAPTER Q A 9 VECTORS IN TWO AND THREE DIMENSIONS QA QA QA QA QA 635
9.1 VectorsinTwoDimensions 635 Q A Q A
9.2 TheDotProduct 641 Q A Q A
9.3 Three-Dimensional Coordinate Geometry QA QA 644
9.4 VectorsinThreeDimensions 646 Q A
9.5 TheCrossProduct 649 Q A Q A
9.6 EquationsofLinesandPlanes 652 Q A Q A
Chapter 9 Review QA QA Q A Q A 654
Chapter9Test 658 Q A
¥ FOCUSONMODELING: VectorFields QA Q A Q A 659
CHAPTER Q A 10 SYSTEMS OF EQUATIONS AND INEQUALITIES QA QA QA QA 663
10.1 SystemsofLinearEquationsinTwoVariables Q A Q A 663
10.2 SystemsofLinearEquationsinSeveralVariables Q A Q A 670
10.3 PartialFractions 678 Q A Q A
10.4 SystemsofNonlinearEquations Q A 689
10.5 SystemsofInequalities Q A Q A 696
CONTENTS
¥ PROLOGUE: PrinciplesofProblemSolving
QA Q A Q A 1
CHAPTER Q A P PREREQUISITES 3
P.1 ModelingtheReal Worldwith Algebra QA QA Q A Q A 3
P.2 Real Numbers 4
QA Q A Q A
P.3 Integer Exponents and Scientific Notation 9
QA QA QA QA
P.4 RationalExponentsandRadicals Q A Q A 14
P.5 AlgebraicExpressions Q A 18
P.6 Factoring 22 Q A
P.7 RationalExpressions Q A 27
P.8 SolvingBasicEquations Q A Q A 34
P.9 ModelingwithEquations Q A Q A 39
Chapter PReviewQA Q A Q A 45
ChapterPTest 51 Q A
¥ FOCUSONMODELING:MakingtheBestDecisions 54
CHAPTER Q A 1 EQUATIONS QA AND GRAPHS QA 57
1.1 TheCoordinatePlane 57 Q A Q A
1.2 Graphs of Equations in Two Variables; Circles 65
QA QA QA QA QA QA
1.3 Lines 79 Q A
1.4 SolvingQuadraticEquations Q A 90
1.5 ComplexNumbers Q A 98
1.6 SolvingOtherTypesofEquations Q A Q A 101
1.7 Solving Inequalities
QA Q A Q A 110
1.8 Solving Absolute Value Equations and Inequalitie 129
QA QA QA QA QA
s
1.9 Solving Equations and Inequalities Graphically 131
QA QA QA QA
1.10 Modeling Variation 139
QA Q A
Chapter 1 Review
QA QA Q A Q A 143
Chapter1Test 161 Q A
iii
,iv Contents
¥ FOCUS ON MODELING: Fitting Linesto Data 165
QA QA QA QA QA
CHAPTER Q A 2 FUNCTIONS 169
2.1 Functions 169 Q A
2.2 GraphsofFunctions Q A Q A 178
2.3 GettingInformationfromtheGraphofaFunction Q A Q A 190
2.4 AverageRateof ChangeofaFunction QA Q A Q A 201
2.5 LinearFunctionsandModels 206 Q A Q A
2.6 TransformationsofFunctions 212 Q A
2.7 CombiningFunctions 226 Q A Q A
2.8 One-to-One Functions andTheir Inverses
QA QA QA 234
Chapter 2 Review 243
QA QA Q A Q A
Chapter2Test 255 Q A
¥ FOCUSONMODELING:ModelingwithFunctions Q A Q A 259
CHAPTER Q A 3 POLYNOMIAL QA AND RATIONAL FUNCTIONS
QA QA 267
3.1 Quadratic Functionsand Models 267
QA QA
3.2 Polynomial Functions and Their Graphs 276
QA QA QA QA
3.3 DividingPolynomials Q A Q A 291
3.4 RealZerosofPolynomials Q A Q A 301
3.5 ComplexZerosandtheFundamentalTheoremofAlgebra 334
3.6 RationalFunctions 344 Q A Q A
Chapter 3 Review 377
QA QA Q A Q A
Chapter3Test 395 Q A
¥ FOCUSONMODELING:FittingPolynomialCurvestoData 398
CHAPTER Q A 4 EXPONENTIALAND LOGARITHMIC FUNCTIONS QA QA 401
4.1 ExponentialFunctions Q A 401
4.2 TheNaturalExponentialFunction Q A 409
4.3 LogarithmicFunctions Q A 414
4.4 Laws of Logarithms
QA QA 422
4.5 ExponentialandLogarithmicEquations Q A 426
, Contents v
4.6 ModelingwithExponentialFunctions Q A 433
4.7 Logarithmic Scales QA Q A Q A 438
Chapter 4 Review
QA QA Q A Q A 440
Chapter4Test 448 Q A
¥ FOCUSONMODELING:FittingExponentialandPowerCurvestoData Q A Q A 450
CHAPTER Q A 5 TRIGONOMETRIC QA FUNCTIONS: RIGHT TRIANGLE APPROACH QA QA QA 455
5.1 AngleMeasure Q A Q A 455
5.2 Trigonometry ofRight Triangles 459 QA QA
5.3 TrigonometricFunctionsofAngles Q A 464
5.4 nverseTrigonometricFunctionsandRightTriangles 468 Q A
5.5 TheLawofSines 471 Q A Q A
5.6 TheLaw of Cosines 476
QA QA Q A Q A
Chapter 5 Review 481
QA QA Q A Q A
Chapter5Test 486 Q A
¥ FOCUS ON MODELING: Surveying
QA QA QA Q A Q A 536
CHAPTER Q A 6 TRIGONOMETRIC QA FUNCTIONS: UNIT CIRCLE APPROACH QA QA QA 491
6.1 TheUnit Circle 491 QA Q A Q A
6.2 Trigonometric Functions ofReal Numbers 495 QA QA QA
6.3 Trigonometric Graphs 500 QA
6.4 More Trigonometric Graphs
QA QA 511
6.5 nverse Trigonometric Functions andTheir Graphs
QA QA QA QA 519
6.6 ModelingHarmonicMotion 521 Q A
Chapter 6 Review
QA QA Q A Q A 527
Chapter6Test 534 Q A
¥ FOCUSONMODELING:FittingSinusoidalCurvestoData Q A Q A 487
CHAPTER Q A 7 ANALYTIC QA TRIGONOMETRY 541
7.1 Trigonometric Identities 541 QA
7.2 AdditionandSubtractionFormulas 549 Q A
7.3 Double-Angle, Half-Angle, and Product-Sum Formulas 556
QA QA QA QA
, vi Contents
BasicTrigonometricEquations 567
More Trigonometric Equations
QA QA 571 Chapter 7QA QA
Review 578
Chapter7Test 584 Q A
¥ FOCUSONMODELING:TravelingandStandingWaves 586
QA
CHAPTER QA 8 POLAR COORDINATES AND PARAMETRIC EQUATIONS
Q A QA QA QA QA 589
8.1 PolarCoordinates 589 Q A
8.2 GraphsofPolarEquations Q A Q A 593
8.3 Polar Form of Complex Numbers; De Moivre’s Theore 600
QA QA QA QA QA QA QA
m
8.4 Plane Curves andParametric Equations 612
QA QA QA
Chapter 8 Review QA QA Q A Q A 623
Chapter8Test 630 Q A
¥ FOCUS ONMODELING: ThePathofaProjectile
QA QA Q A Q A 631
CHAPTER Q A 9 VECTORS IN TWO AND THREE DIMENSIONS QA QA QA QA QA 635
9.1 VectorsinTwoDimensions 635 Q A Q A
9.2 TheDotProduct 641 Q A Q A
9.3 Three-Dimensional Coordinate Geometry QA QA 644
9.4 VectorsinThreeDimensions 646 Q A
9.5 TheCrossProduct 649 Q A Q A
9.6 EquationsofLinesandPlanes 652 Q A Q A
Chapter 9 Review QA QA Q A Q A 654
Chapter9Test 658 Q A
¥ FOCUSONMODELING: VectorFields QA Q A Q A 659
CHAPTER Q A 10 SYSTEMS OF EQUATIONS AND INEQUALITIES QA QA QA QA 663
10.1 SystemsofLinearEquationsinTwoVariables Q A Q A 663
10.2 SystemsofLinearEquationsinSeveralVariables Q A Q A 670
10.3 PartialFractions 678 Q A Q A
10.4 SystemsofNonlinearEquations Q A 689
10.5 SystemsofInequalities Q A Q A 696
