Algebra and Trigonometry 4th Edition Stewart SOLUTIONS MANUAL
CONTENTS
¥ PROLOGUE:XPrinciplesofProblemSolvingX X 1
CHAPTER X P PREREQUISITES 3
P.1 ModelingtheRealXWorldwithXAlgebraX X 3
P.2 RealXNumbersX X 4
P.3 IntegerXExponentsXandXScientificXNotation 9
P.4 RationalExponentsandRadicalsX X 14
P.5 AlgebraicExpressionsX 18
P.6 FactoringX 22
P.7 RationalExpressionsX 27
P.8 SolvingBasicEquationsX X 34
P.9 ModelingwithEquationsX X 39
ChapterXPReviewX X 45
ChapterPTestX 51
¥ FOCUSONMODELING:MakingtheBestDecisions 54
CHAPTER X 1 EQUATIONS AND GRAPHS
X X 57
1.1 TheCoordinatePlaneX X 57
1.2 GraphsXofXEquationsXinXTwoXVariables;XCircles 65
1.3 LinesX 79
1.4 SolvingQuadraticEquationsX 90
1.5 ComplexNumbersX 98
1.6 SolvingOtherTypesofEquationsX X 101
1.7 SolvingXInequalitiesX X 110
1.8 SolvingX AbsoluteX ValueXEquationsX andX Inequalities 129
1.9 SolvingXEquationsXandXInequalitiesXGraphically 131
1.10 ModelingXVariationX 139
ChapterX1XReviewX X 143
Chapter1TestX 161
iii
,iv Contents
¥ FOCUSXONXMODELING:XFittingXLinestoXData 165
CHAPTER X 2 FUNCTIONS 169
2.1 FunctionsX 169
2.2 GraphsofFunctionsX X 178
2.3 GettingInformationfromtheGraphofaFunctionX X 190
2.4 AverageRateofXChangeofaFunctionX X 201
2.5 LinearFunctionsandModelsX X 206
2.6 TransformationsofFunctionsX 212
2.7 CombiningFunctionsX X 226
2.8 One-to-OneXFunctionsXandTheirXInverses 234
ChapterX2XReviewX X 243
Chapter2TestX 255
¥ FOCUSONMODELING:ModelingwithFunctionsX X 259
CHAPTER X 3 POLYNOMIAL AND RATIONAL FUNCTIONS
X X X 267
3.1 QuadraticXFunctionsandXModels 267
3.2 PolynomialXFunctionsXandXTheirXGraphs 276
3.3 DividingPolynomialsX X 291
3.4 RealZerosofPolynomialsX X 301
3.5 ComplexZerosandtheFundamentalTheoremofAlgebra 334
3.6 RationalFunctionsX X 344
ChapterX3XReviewX X 377
Chapter3TestX 395
¥ FOCUSONMODELING:FittingPolynomialCurvestoData 398
CHAPTER X 4 EXPONENTIALAND LOGARITHMIC FUNCTIONS
X X 401
4.1 ExponentialFunctionsX 401
4.2 TheNaturalExponentialFunctionX 409
4.3 LogarithmicFunctionsX 414
4.4 LawsXofXLogarithms 422
4.5 ExponentialandLogarithmicEquationsX 426
, Contents v
4.6 ModelingwithExponentialFunctionsX 433
4.7 LogarithmicXScalesX X 438
ChapterX4XReviewX X 440
Chapter4TestX 448
¥ FOCUSONMODELING:FittingExponentialandPowerCurvestoDataX X 450
CHAPTER X 5 TRIGONOMETRIC FUNCTIONS: RIGHT TRIANGLE APPROACH
X X X X 455
5.1 AngleMeasureX X 455
5.2 TrigonometryX ofRightXTriangles 459
5.3 TrigonometricFunctionsofAnglesX 464
5.4 nverseTrigonometricFunctionsandRightTrianglesX 468
5.5 TheLawofSinesX X 471
5.6 TheLawXofXCosinesX X 476
ChapterX5XReviewX X 481
Chapter5TestX 486
¥ FOCUSXONXMODELING:XSurveyingX X 536
CHAPTER X 6 TRIGONOMETRIC FUNCTIONS: UNIT CIRCLE APPROACH
X X X X 491
6.1 TheUnitXCircleX X 491
6.2 TrigonometricXFunctionsXofRealXNumbers 495
6.3 TrigonometricXGraphs 500
6.4 MoreXTrigonometricXGraphs 511
6.5 nverseXTrigonometricXFunctionsXandTheirXGraphs 519
6.6 ModelingHarmonicMotionX 521
ChapterX6XReviewX X 527
Chapter6TestX 534
¥ FOCUSONMODELING:FittingSinusoidalCurvestoDataX X 487
CHAPTER X 7 ANALYTIC TRIGONOMETRY
X 541
7.1 TrigonometricXIdentities 541
7.2 AdditionandSubtractionFormulasX 549
7.3 Double-Angle,XHalf-Angle,XandXProduct-SumXFormulas 556
, vi Contents
BasicTrigonometricEquations 567
MoreXTrigonometricXEquations 571XChapterX7
Review 578
Chapter7TestX 584
¥XFOCUSONMODELING:TravelingandStandingWaves 586
CHAPTER 8 X X POLAR COORDINATES AND PARAMETRIC EQUATIONS
X X X X 589
8.1 PolarCoordinatesX 589
8.2 GraphsofPolarEquationsX X 593
8.3 PolarXFormXofXComplexXNumbers;XDeXMoivre’sXTheorem 600
8.4 PlaneXCurvesXandParametricXEquations 612
ChapterX8XReviewX X 623
Chapter8TestX 630
¥ FOCUSXONMODELING:XThePathofaProjectileX X 631
CHAPTER X 9 VECTORS IN TWO AND THREE DIMENSIONS
X X X X X 635
9.1 VectorsinTwoDimensionsX X 635
9.2 TheDotProductX X 641
9.3 Three-DimensionalXCoordinateXGeometry 644
9.4 VectorsinThreeDimensionsX 646
9.5 TheCrossProductX X 649
9.6 EquationsofLinesandPlanesX X 652
ChapterX9XReviewX X 654
Chapter9TestX 658
¥ FOCUSONMODELING:XVectorFieldsX X 659
CHAPTER X 10 SYSTEMS OF EQUATIONS AND INEQUALITIES
X X X X 663
10.1 SystemsofLinearEquationsinTwoVariablesX X 663
10.2 SystemsofLinearEquationsinSeveralVariablesX X 670
10.3 PartialFractionsX X 678
10.4 SystemsofNonlinearEquationsX 689
10.5 SystemsofInequalitiesX X 696
CONTENTS
¥ PROLOGUE:XPrinciplesofProblemSolvingX X 1
CHAPTER X P PREREQUISITES 3
P.1 ModelingtheRealXWorldwithXAlgebraX X 3
P.2 RealXNumbersX X 4
P.3 IntegerXExponentsXandXScientificXNotation 9
P.4 RationalExponentsandRadicalsX X 14
P.5 AlgebraicExpressionsX 18
P.6 FactoringX 22
P.7 RationalExpressionsX 27
P.8 SolvingBasicEquationsX X 34
P.9 ModelingwithEquationsX X 39
ChapterXPReviewX X 45
ChapterPTestX 51
¥ FOCUSONMODELING:MakingtheBestDecisions 54
CHAPTER X 1 EQUATIONS AND GRAPHS
X X 57
1.1 TheCoordinatePlaneX X 57
1.2 GraphsXofXEquationsXinXTwoXVariables;XCircles 65
1.3 LinesX 79
1.4 SolvingQuadraticEquationsX 90
1.5 ComplexNumbersX 98
1.6 SolvingOtherTypesofEquationsX X 101
1.7 SolvingXInequalitiesX X 110
1.8 SolvingX AbsoluteX ValueXEquationsX andX Inequalities 129
1.9 SolvingXEquationsXandXInequalitiesXGraphically 131
1.10 ModelingXVariationX 139
ChapterX1XReviewX X 143
Chapter1TestX 161
iii
,iv Contents
¥ FOCUSXONXMODELING:XFittingXLinestoXData 165
CHAPTER X 2 FUNCTIONS 169
2.1 FunctionsX 169
2.2 GraphsofFunctionsX X 178
2.3 GettingInformationfromtheGraphofaFunctionX X 190
2.4 AverageRateofXChangeofaFunctionX X 201
2.5 LinearFunctionsandModelsX X 206
2.6 TransformationsofFunctionsX 212
2.7 CombiningFunctionsX X 226
2.8 One-to-OneXFunctionsXandTheirXInverses 234
ChapterX2XReviewX X 243
Chapter2TestX 255
¥ FOCUSONMODELING:ModelingwithFunctionsX X 259
CHAPTER X 3 POLYNOMIAL AND RATIONAL FUNCTIONS
X X X 267
3.1 QuadraticXFunctionsandXModels 267
3.2 PolynomialXFunctionsXandXTheirXGraphs 276
3.3 DividingPolynomialsX X 291
3.4 RealZerosofPolynomialsX X 301
3.5 ComplexZerosandtheFundamentalTheoremofAlgebra 334
3.6 RationalFunctionsX X 344
ChapterX3XReviewX X 377
Chapter3TestX 395
¥ FOCUSONMODELING:FittingPolynomialCurvestoData 398
CHAPTER X 4 EXPONENTIALAND LOGARITHMIC FUNCTIONS
X X 401
4.1 ExponentialFunctionsX 401
4.2 TheNaturalExponentialFunctionX 409
4.3 LogarithmicFunctionsX 414
4.4 LawsXofXLogarithms 422
4.5 ExponentialandLogarithmicEquationsX 426
, Contents v
4.6 ModelingwithExponentialFunctionsX 433
4.7 LogarithmicXScalesX X 438
ChapterX4XReviewX X 440
Chapter4TestX 448
¥ FOCUSONMODELING:FittingExponentialandPowerCurvestoDataX X 450
CHAPTER X 5 TRIGONOMETRIC FUNCTIONS: RIGHT TRIANGLE APPROACH
X X X X 455
5.1 AngleMeasureX X 455
5.2 TrigonometryX ofRightXTriangles 459
5.3 TrigonometricFunctionsofAnglesX 464
5.4 nverseTrigonometricFunctionsandRightTrianglesX 468
5.5 TheLawofSinesX X 471
5.6 TheLawXofXCosinesX X 476
ChapterX5XReviewX X 481
Chapter5TestX 486
¥ FOCUSXONXMODELING:XSurveyingX X 536
CHAPTER X 6 TRIGONOMETRIC FUNCTIONS: UNIT CIRCLE APPROACH
X X X X 491
6.1 TheUnitXCircleX X 491
6.2 TrigonometricXFunctionsXofRealXNumbers 495
6.3 TrigonometricXGraphs 500
6.4 MoreXTrigonometricXGraphs 511
6.5 nverseXTrigonometricXFunctionsXandTheirXGraphs 519
6.6 ModelingHarmonicMotionX 521
ChapterX6XReviewX X 527
Chapter6TestX 534
¥ FOCUSONMODELING:FittingSinusoidalCurvestoDataX X 487
CHAPTER X 7 ANALYTIC TRIGONOMETRY
X 541
7.1 TrigonometricXIdentities 541
7.2 AdditionandSubtractionFormulasX 549
7.3 Double-Angle,XHalf-Angle,XandXProduct-SumXFormulas 556
, vi Contents
BasicTrigonometricEquations 567
MoreXTrigonometricXEquations 571XChapterX7
Review 578
Chapter7TestX 584
¥XFOCUSONMODELING:TravelingandStandingWaves 586
CHAPTER 8 X X POLAR COORDINATES AND PARAMETRIC EQUATIONS
X X X X 589
8.1 PolarCoordinatesX 589
8.2 GraphsofPolarEquationsX X 593
8.3 PolarXFormXofXComplexXNumbers;XDeXMoivre’sXTheorem 600
8.4 PlaneXCurvesXandParametricXEquations 612
ChapterX8XReviewX X 623
Chapter8TestX 630
¥ FOCUSXONMODELING:XThePathofaProjectileX X 631
CHAPTER X 9 VECTORS IN TWO AND THREE DIMENSIONS
X X X X X 635
9.1 VectorsinTwoDimensionsX X 635
9.2 TheDotProductX X 641
9.3 Three-DimensionalXCoordinateXGeometry 644
9.4 VectorsinThreeDimensionsX 646
9.5 TheCrossProductX X 649
9.6 EquationsofLinesandPlanesX X 652
ChapterX9XReviewX X 654
Chapter9TestX 658
¥ FOCUSONMODELING:XVectorFieldsX X 659
CHAPTER X 10 SYSTEMS OF EQUATIONS AND INEQUALITIES
X X X X 663
10.1 SystemsofLinearEquationsinTwoVariablesX X 663
10.2 SystemsofLinearEquationsinSeveralVariablesX X 670
10.3 PartialFractionsX X 678
10.4 SystemsofNonlinearEquationsX 689
10.5 SystemsofInequalitiesX X 696
