Algebra and Trigonometry – 5th Edition | Complete Text Summary and Problem Solutions | 2025/2026 NEW!! 100% VERIFIED CORRECT

Algebraand Trigonometry 5thEditionStewart SOLUTIONS MANUAL
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CONTENTS
¥ PROLOGUE:PrinciplesofProblemSolving lI I l I l 1

CHAPTER I l P PREREQUISITES 3
P.1 ModelingtheReal WorldwithAlgebra lI lI I l I l 3
P.2 RealNumbers 4
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P.3 Integer Exponents andScientificNotation
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P.4 RationalExponentsandRadicals I l I l 14
P.5 AlgebraicExpressions 18 I l




P.6 Factoring 22 I l




P.7 RationalExpressions I l 27
P.8 SolvingBasicEquations I l I l 34
P.9 ModelingwithEquations I l I l 39
ChapterPReview lI I l I l 45
ChapterPTest 51 I l




¥ FOCUSONMODELING:MakingtheBestDecisions 54

CHAPTER I l 1 EQUATIONS AND GRAPHS I L I L
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1.1 TheCoordinatePlane 57 I l I l




1.2 Graphs ofEquations in TwoVariables;Circles
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1.3 Lines 79 I l




1.4 SolvingQuadraticEquations I l 90
1.5 ComplexNumbers I l 98
1.6 SolvingOtherTypesofEquations I l I l 101
1.7 SolvingInequalities
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1.8 Solving Absolute Value Equations and Inequalities 129
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1.9 Solving Equations andInequalities Graphically
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1.10 ModelingVariation 139 lI I l




Chapter1Review lI lI I l I l 143
Chapter1Test 161 I l




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,viii Contents

¥ FOCUSON MODELING: Fitting Linesto Data
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CHAPTER I l 2 FUNCTIONS 169
2.1 Functions 169 I l




2.2 GraphsofFunctions I l I l 178
2.3 GettingInformationfromtheGraphofaFunction I l I l 190
2.4 AverageRateof ChangeofaFunction lI I l I l 201
2.5 LinearFunctionsandModels 206 I l I l




2.6 TransformationsofFunctions 212 I l




2.7 CombiningFunctions 226 I l I l




2.8 One-to-OneFunctionsandTheir Inverses lI lI Il 234
Chapter2Review 243 lI lI I l I l




Chapter2Test 255 I l




¥ FOCUSONMODELING:ModelingwithFunctions I l I l 259

CHAPTER I l 3 POLYNOMIAL AND RATIONAL FUNCTIONS IL IL I L 267
3.1 Quadratic Functionsand ModelsIl Il 267
3.2 Polynomial Functions andTheirGraphs Il Il lI lI 276
3.3 DividingPolynomials I l I l 291
3.4 RealZerosofPolynomials I l I l 301
3.5 ComplexZerosandtheFundamentalTheoremofAlgebra 334
3.6 RationalFunctions 344 I l I l




Chapter3Review 377 lI lI I l I l




Chapter3Test 395 I l




¥ FOCUSONMODELING:FittingPolynomialCurvestoData 398

CHAPTER I l 4 EXPONENTIALAND LOGARITHMIC FUNCTIONS IL IL 401
4.1 ExponentialFunctions 401 I l




4.2 TheNaturalExponentialFunction I l 409
4.3 LogarithmicFunctions I l 414
4.4 Laws of Logarithms
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4.5 ExponentialandLogarithmicEquations 426 I l

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4.6 ModelingwithExponentialFunctions I l 433
4.7 LogarithmicScales 438 lI I l I l




Chapter4Review lI lI I l I l 440
Chapter4Test 448 I l




¥ FOCUSONMODELING:FittingExponentialandPowerCurvestoData I l I l 450

CHAPTER I l 5 TRIGONOMETRIC FUNCTIONS: RIGHT TRIANGLE APPROACH I L I L I L I L
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5.1 AngleMeasure I l I l 455
5.2 Trigonometry ofRightTriangles Il lI 459
5.3 TrigonometricFunctionsofAngles I l 464
5.4 nverseTrigonometricFunctionsandRightTriangles 468 I l




5.5 TheLawofSines 471 I l I l




5.6 TheLaw ofCosines 476
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Chapter5Review 481 lI lI I l I l




Chapter5Test 486 I l




¥ FOCUS ONMODELING:Surveying 536
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CHAPTER I l 6 TRIGONOMETRIC FUNCTIONS: UNIT CIRCLE APPROACH I L I L I L I L 491
6.1 TheUnitCircle 491 lI I l I l




6.2 TrigonometricFunctionsofReal Numbers lI lI Il 495
6.3 Trigonometric Graphs 500 Il




6.4 MoreTrigonometricGraphs
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6.5 nverse TrigonometricFunctions andTheirGraphs
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6.6 ModelingHarmonicMotion 521 I l




Chapter6Review lI lI I l I l 527
Chapter6Test 534 I l




¥ FOCUSONMODELING:FittingSinusoidalCurvestoData I l I l 487

CHAPTER I l 7 ANALYTIC TRIGONOMETRY I L
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7.1 Trigonometric Identities 541 Il




7.2 AdditionandSubtractionFormulas 549 I l




7.3 Double-Angle, Half-Angle, and Product-Sum Formulas
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BasicTrigonometricEquations 567
MoreTrigonometricEquations
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Review 578
Chapter7Test 584 I l




¥ FOCUSONMODELING:TravelingandStandingWaves
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CHAPTER Il 8 POLARCOORDINATESANDPARAMETRICEQUATIONS
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8.1 PolarCoordinates 589 I l




8.2 GraphsofPolarEquations I l I l 593
8.3 Polar Form of Complex Numbers; De Moivre’s Theorem
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8.4 PlaneCurvesandParametric Equations
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Chapter8Review lI lI I l I l 623
Chapter8Test 630 I l




¥ FOCUS ONMODELING: ThePathofaProjectile
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CHAPTER I l 9 VECTORS IN TWO AND THREE DIMENSIONS IL IL IL IL IL 635
9.1 VectorsinTwoDimensions 635 I l I l




9.2 TheDotProduct 641 I l I l




9.3 Three-DimensionalCoordinateGeometry lI lI 644
9.4 VectorsinThreeDimensions 646 I l




9.5 TheCrossProduct 649 I l I l




9.6 EquationsofLinesandPlanes 652 I l I l




Chapter9Review lI lI I l I l 654
Chapter9Test 658 I l




¥ FOCUSONMODELING: VectorFields lI I l I l 659

CHAPTER I l 10 SYSTEMSOFEQUATIONSANDINEQUALITIES IL IL IL IL 663
10.1 SystemsofLinearEquationsinTwoVariables I l I l 663
10.2 SystemsofLinearEquationsinSeveralVariables I l I l 670
10.3 PartialFractions 678 I l I l




10.4 SystemsofNonlinearEquations I l 689
10.5 SystemsofInequalities I l I l 696