SOLUTIONS MANUAL Algebra and
N
Trigonometry 4th Edition Stewart
CONTENTS
¥ PROLOGUE:NPrinciplesofProblemSolvingN N 1
CHAPTER N P PREREQUISITES 3
P.1 ModelingtheRealNWorldwithNAlgebraN N 3
P.2 RealNNumbersN N 4
P.3 IntegerNExponentsNandNScientificNNotation 9
P.4 RationalExponentsandRadicalsN N 14
P.5 AlgebraicExpressionsN 18
P.6 FactoringN 22
P.7 RationalExpressionsN 27
P.8 SolvingBasicEquationsN N 34
P.9 ModelingwithEquationsN N 39
ChapterNPReviewN N 45
ChapterPTestN 51
¥ FOCUSONMODELING:MakingtheBestDecisions 54
CHAPTER N 1 EQUATIONS AND GRAPHS
N N 57
1.1 TheCoordinatePlaneN N 57
1.2 GraphsNofNEquationsNinNTwoNVariables;NCircles 65
1.3 LinesN 79
1.4 SolvingQuadraticEquationsN 90
1.5 ComplexNumbersN 98
1.6 SolvingOtherTypesofEquationsN N 101
1.7 SolvingNInequalitiesN N 110
1.8 SolvingN AbsoluteN ValueNEquationsN andN Inequalities 129
1.9 SolvingNEquationsNandNInequalitiesNGraphically 131
1.10 ModelingNVariationN 139
ChapterN1NReviewN N 143
Chapter1TestN 161
iii
,iv Contents
¥ FOCUSNONNMODELING:NFittingNLinestoNData 165
CHAPTER N 2 FUNCTIONS 169
2.1 FunctionsN 169
2.2 GraphsofFunctionsN N 178
2.3 GettingInformationfromtheGraphofaFunctionN N 190
2.4 AverageRateofNChangeofaFunctionN N 201
2.5 LinearFunctionsandModelsN N 206
2.6 TransformationsofFunctionsN 212
2.7 CombiningFunctionsN N 226
2.8 One-to-OneNFunctionsNandTheirNInverses 234
ChapterN2NReviewN N 243
Chapter2TestN 255
¥ FOCUSONMODELING:ModelingwithFunctionsN N 259
CHAPTER N 3 POLYNOMIAL AND RATIONAL FUNCTIONS
N N N 267
3.1 QuadraticNFunctionsandNModels 267
3.2 PolynomialNFunctionsNandNTheirNGraphs 276
3.3 DividingPolynomialsN N 291
3.4 RealZerosofPolynomialsN N 301
3.5 ComplexZerosandtheFundamentalTheoremofAlgebra 334
3.6 RationalFunctionsN N 344
ChapterN3NReviewN N 377
Chapter3TestN 395
¥ FOCUSONMODELING:FittingPolynomialCurvestoData 398
CHAPTER N 4 EXPONENTIALAND LOGARITHMIC FUNCTIONS
N N 401
4.1 ExponentialFunctionsN 401
4.2 TheNaturalExponentialFunctionN 409
4.3 LogarithmicFunctionsN 414
4.4 LawsNofNLogarithms 422
4.5 ExponentialandLogarithmicEquationsN 426
, Contents v
4.6 ModelingwithExponentialFunctionsN 433
4.7 LogarithmicNScalesN N 438
ChapterN4NReviewN N 440
Chapter4TestN 448
¥ FOCUSONMODELING:FittingExponentialandPowerCurvestoDataN N 450
CHAPTER N 5 TRIGONOMETRIC FUNCTIONS: RIGHT TRIANGLE APPROACH
N N N N 455
5.1 AngleMeasureN N 455
5.2 TrigonometryN ofRightNTriangles 459
5.3 TrigonometricFunctionsofAnglesN 464
5.4 nverseTrigonometricFunctionsandRightTrianglesN 468
5.5 TheLawofSinesN N 471
5.6 TheLawNofNCosinesN N 476
ChapterN5NReviewN N 481
Chapter5TestN 486
¥ FOCUSNONNMODELING:NSurveyingN N 536
CHAPTER N 6 TRIGONOMETRIC FUNCTIONS: UNIT CIRCLE APPROACH
N N N N 491
6.1 TheUnitNCircleN N 491
6.2 TrigonometricNFunctionsNofRealNNumbers 495
6.3 TrigonometricNGraphs 500
6.4 MoreNTrigonometricNGraphs 511
6.5 nverseNTrigonometricNFunctionsNandTheirNGraphs 519
6.6 ModelingHarmonicMotionN 521
ChapterN6NReviewN N 527
Chapter6TestN 534
¥ FOCUSONMODELING:FittingSinusoidalCurvestoDataN N 487
CHAPTER N 7 ANALYTIC TRIGONOMETRY
N 541
7.1 TrigonometricNIdentities 541
7.2 AdditionandSubtractionFormulasN 549
7.3 Double-Angle,NHalf-Angle,NandNProduct-SumNFormulas 556
, vi Contents
BasicTrigonometricEquations 567
MoreNTrigonometricNEquations 571NChapterN7
Review 578
Chapter7TestN 584
¥NFOCUSONMODELING:TravelingandStandingWaves 586
CHAPTER N 8 POLAR COORDINATES AND PARAMETRIC EQUATIONS
N N N N N 589
8.1 PolarCoordinatesN 589
8.2 GraphsofPolarEquationsN N 593
8.3 PolarNFormNofNComplexNNumbers;NDeNMoivre’sNTheorem 600
8.4 PlaneNCurvesNandParametricNEquations 612
ChapterN8NReviewN N 623
Chapter8TestN 630
¥ FOCUSNONMODELING:NThePathofaProjectileN N 631
CHAPTER N 9 VECTORS IN TWO AND THREE DIMENSIONS
N N N N N 635
9.1 VectorsinTwoDimensionsN N 635
9.2 TheDotProductN N 641
9.3 Three-DimensionalNCoordinateNGeometry 644
9.4 VectorsinThreeDimensionsN 646
9.5 TheCrossProductN N 649
9.6 EquationsofLinesandPlanesN N 652
ChapterN9NReviewN N 654
Chapter9TestN 658
¥ FOCUSONMODELING:NVectorFieldsN N 659
CHAPTER N 10 SYSTEMS OF EQUATIONS AND INEQUALITIES
N N N N 663
10.1 SystemsofLinearEquationsinTwoVariablesN N 663
10.2 SystemsofLinearEquationsinSeveralVariablesN N 670
10.3 PartialFractionsN N 678
10.4 SystemsofNonlinearEquationsN 689
10.5 SystemsofInequalitiesN N 696
N
Trigonometry 4th Edition Stewart
CONTENTS
¥ PROLOGUE:NPrinciplesofProblemSolvingN N 1
CHAPTER N P PREREQUISITES 3
P.1 ModelingtheRealNWorldwithNAlgebraN N 3
P.2 RealNNumbersN N 4
P.3 IntegerNExponentsNandNScientificNNotation 9
P.4 RationalExponentsandRadicalsN N 14
P.5 AlgebraicExpressionsN 18
P.6 FactoringN 22
P.7 RationalExpressionsN 27
P.8 SolvingBasicEquationsN N 34
P.9 ModelingwithEquationsN N 39
ChapterNPReviewN N 45
ChapterPTestN 51
¥ FOCUSONMODELING:MakingtheBestDecisions 54
CHAPTER N 1 EQUATIONS AND GRAPHS
N N 57
1.1 TheCoordinatePlaneN N 57
1.2 GraphsNofNEquationsNinNTwoNVariables;NCircles 65
1.3 LinesN 79
1.4 SolvingQuadraticEquationsN 90
1.5 ComplexNumbersN 98
1.6 SolvingOtherTypesofEquationsN N 101
1.7 SolvingNInequalitiesN N 110
1.8 SolvingN AbsoluteN ValueNEquationsN andN Inequalities 129
1.9 SolvingNEquationsNandNInequalitiesNGraphically 131
1.10 ModelingNVariationN 139
ChapterN1NReviewN N 143
Chapter1TestN 161
iii
,iv Contents
¥ FOCUSNONNMODELING:NFittingNLinestoNData 165
CHAPTER N 2 FUNCTIONS 169
2.1 FunctionsN 169
2.2 GraphsofFunctionsN N 178
2.3 GettingInformationfromtheGraphofaFunctionN N 190
2.4 AverageRateofNChangeofaFunctionN N 201
2.5 LinearFunctionsandModelsN N 206
2.6 TransformationsofFunctionsN 212
2.7 CombiningFunctionsN N 226
2.8 One-to-OneNFunctionsNandTheirNInverses 234
ChapterN2NReviewN N 243
Chapter2TestN 255
¥ FOCUSONMODELING:ModelingwithFunctionsN N 259
CHAPTER N 3 POLYNOMIAL AND RATIONAL FUNCTIONS
N N N 267
3.1 QuadraticNFunctionsandNModels 267
3.2 PolynomialNFunctionsNandNTheirNGraphs 276
3.3 DividingPolynomialsN N 291
3.4 RealZerosofPolynomialsN N 301
3.5 ComplexZerosandtheFundamentalTheoremofAlgebra 334
3.6 RationalFunctionsN N 344
ChapterN3NReviewN N 377
Chapter3TestN 395
¥ FOCUSONMODELING:FittingPolynomialCurvestoData 398
CHAPTER N 4 EXPONENTIALAND LOGARITHMIC FUNCTIONS
N N 401
4.1 ExponentialFunctionsN 401
4.2 TheNaturalExponentialFunctionN 409
4.3 LogarithmicFunctionsN 414
4.4 LawsNofNLogarithms 422
4.5 ExponentialandLogarithmicEquationsN 426
, Contents v
4.6 ModelingwithExponentialFunctionsN 433
4.7 LogarithmicNScalesN N 438
ChapterN4NReviewN N 440
Chapter4TestN 448
¥ FOCUSONMODELING:FittingExponentialandPowerCurvestoDataN N 450
CHAPTER N 5 TRIGONOMETRIC FUNCTIONS: RIGHT TRIANGLE APPROACH
N N N N 455
5.1 AngleMeasureN N 455
5.2 TrigonometryN ofRightNTriangles 459
5.3 TrigonometricFunctionsofAnglesN 464
5.4 nverseTrigonometricFunctionsandRightTrianglesN 468
5.5 TheLawofSinesN N 471
5.6 TheLawNofNCosinesN N 476
ChapterN5NReviewN N 481
Chapter5TestN 486
¥ FOCUSNONNMODELING:NSurveyingN N 536
CHAPTER N 6 TRIGONOMETRIC FUNCTIONS: UNIT CIRCLE APPROACH
N N N N 491
6.1 TheUnitNCircleN N 491
6.2 TrigonometricNFunctionsNofRealNNumbers 495
6.3 TrigonometricNGraphs 500
6.4 MoreNTrigonometricNGraphs 511
6.5 nverseNTrigonometricNFunctionsNandTheirNGraphs 519
6.6 ModelingHarmonicMotionN 521
ChapterN6NReviewN N 527
Chapter6TestN 534
¥ FOCUSONMODELING:FittingSinusoidalCurvestoDataN N 487
CHAPTER N 7 ANALYTIC TRIGONOMETRY
N 541
7.1 TrigonometricNIdentities 541
7.2 AdditionandSubtractionFormulasN 549
7.3 Double-Angle,NHalf-Angle,NandNProduct-SumNFormulas 556
, vi Contents
BasicTrigonometricEquations 567
MoreNTrigonometricNEquations 571NChapterN7
Review 578
Chapter7TestN 584
¥NFOCUSONMODELING:TravelingandStandingWaves 586
CHAPTER N 8 POLAR COORDINATES AND PARAMETRIC EQUATIONS
N N N N N 589
8.1 PolarCoordinatesN 589
8.2 GraphsofPolarEquationsN N 593
8.3 PolarNFormNofNComplexNNumbers;NDeNMoivre’sNTheorem 600
8.4 PlaneNCurvesNandParametricNEquations 612
ChapterN8NReviewN N 623
Chapter8TestN 630
¥ FOCUSNONMODELING:NThePathofaProjectileN N 631
CHAPTER N 9 VECTORS IN TWO AND THREE DIMENSIONS
N N N N N 635
9.1 VectorsinTwoDimensionsN N 635
9.2 TheDotProductN N 641
9.3 Three-DimensionalNCoordinateNGeometry 644
9.4 VectorsinThreeDimensionsN 646
9.5 TheCrossProductN N 649
9.6 EquationsofLinesandPlanesN N 652
ChapterN9NReviewN N 654
Chapter9TestN 658
¥ FOCUSONMODELING:NVectorFieldsN N 659
CHAPTER N 10 SYSTEMS OF EQUATIONS AND INEQUALITIES
N N N N 663
10.1 SystemsofLinearEquationsinTwoVariablesN N 663
10.2 SystemsofLinearEquationsinSeveralVariablesN N 670
10.3 PartialFractionsN N 678
10.4 SystemsofNonlinearEquationsN 689
10.5 SystemsofInequalitiesN N 696
