INSTRUCTOR’S SOLUTIONS
MANUAL
TIM BRITT
Jackson State Community College
ALGEBRA AND TRIGONOMETRY
E NHANCED WITH G RAPHING U TILITIES
E IGHTH E DITION
Michael Sullivan
Chicago State University
Michael Sullivan III
Joliet Junior College
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, Table of Contents
Chapter R Review
R.1 Real Numbers .......................................................................................................................... 1
R.2 Algebra Essentials ................................................................................................................... 5
R.3 Geometry Essentials .............................................................................................................. 11
R.4 Polynomials ........................................................................................................................... 16
R.5 Factoring Polynomials ........................................................................................................... 23
R.6 Synthetic Division ................................................................................................................. 28
R.7 Rational Expressions ............................................................................................................. 30
R.8 nth Roots; Rational Exponents .............................................................................................. 40
Chapter 1 Graphs, Equations, and Inequalities
1.1 Graphing Utilities; Introduction to Graphing Equations ....................................................... 50
1.2 Solving Equations Using a Graphing Utility; Linear and Rational Equations....................... 57
1.3 Quadratic Equations .............................................................................................................. 71
1.4 Complex Numbers; Quadratic Equations in the Complex Number System .......................... 90
1.5 Radical Equations; Equations Quadratic in Form; Absolute Value Equations;
Factorable Equations ............................................................................................................. 96
1.6 Problem Solving: Interest, Mixture, Uniform Motion, and Constant Rate Jobs .................. 117
1.7 Solving Inequalities ............................................................................................................. 125
Chapter Review ............................................................................................................................ 137
Chapter Test ................................................................................................................................. 147
Chapter Projects ........................................................................................................................... 151
Chapter 2 Graphs
2.1 The Distance and Midpoint Formulas ................................................................................. 152
2.2 Intercepts; Symmetry; Graphing Key Equations ................................................................. 165
2.3 Lines .................................................................................................................................... 182
2.4 Circles .................................................................................................................................. 200
2.5 Variation .............................................................................................................................. 215
Chapter Review ............................................................................................................................ 220
Chapter Test ................................................................................................................................. 226
Cumulative Review ...................................................................................................................... 228
Chapter Projects ........................................................................................................................... 230
Chapter 3 Functions and Their Graphs
3.1 Functions ............................................................................................................................. 231
3.2 The Graph of a Function ...................................................................................................... 249
3.3 Properties of Functions ........................................................................................................ 258
3.4 Library of Functions; Piecewise-defined Functions ............................................................ 275
3.5 Graphing Techniques: Transformations .............................................................................. 287
3.6 Mathematical Models: Building Functions.......................................................................... 305
Chapter Review ............................................................................................................................ 313
Chapter Test ................................................................................................................................. 320
Cumulative Review ...................................................................................................................... 323
Chapter Projects ........................................................................................................................... 327
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, Chapter 4 Linear and Quadratic Functions
4.1 Properties of Linear Functions and Linear Models.............................................................. 329
4.2 Building Linear Models from Data ...................................................................................... 340
4.3 Quadratic Functions and Their Properties ........................................................................... 346
4.4 Build Quadratic Models from Verbal Descriptions and from Data ..................................... 370
4.5 Inequalities Involving Quadratic Functions ......................................................................... 378
Chapter Review ............................................................................................................................ 397
Chapter Test ................................................................................................................................. 405
Cumulative Review ...................................................................................................................... 408
Chapter Projects ........................................................................................................................... 411
Chapter 5 Polynomial and Rational Functions
5.1 Polynomial Functions .......................................................................................................... 414
5.2 The Graph of a Polynomial Function; Models .................................................................... 425
5.3 The Real Zeros of a Polynomial Function ........................................................................... 445
5.4 Complex Zeros; Fundamental Theorem of Algebra ............................................................ 482
5.5 Properties of Rational Functions ......................................................................................... 491
5.6 The Graph of a Rational Function ....................................................................................... 501
5.7 Polynomial and Rational Inequalities .................................................................................. 557
Chapter Review ............................................................................................................................ 579
Chapter Test ................................................................................................................................. 593
Cumulative Review ...................................................................................................................... 597
Chapter Projects ........................................................................................................................... 602
Chapter 6 Exponential and Logarithmic Functions
6.1 Composite Functions ........................................................................................................... 603
6.2 One-to-One Functions; Inverse Functions ........................................................................... 621
6.3 Exponential Functions ......................................................................................................... 644
6.4 Logarithmic Functions ......................................................................................................... 665
6.5 Properties of Logarithms ..................................................................................................... 687
6.6 Logarithmic and Exponential Equations.............................................................................. 696
6.7 Financial Models ................................................................................................................. 717
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models ............................................................................................................... 725
6.9 Building Exponential, Logarithmic, and Logistic Models from Data ................................. 736
Chapter Review ............................................................................................................................ 741
Chapter Test ................................................................................................................................. 763
Cumulative Review ...................................................................................................................... 757
Chapter Projects ........................................................................................................................... 760
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, Chapter 7 Trigonometric Functions
7.1 Angles, Arc Length, and Circular Motion ........................................................................... 763
7.2 Right Triangle Trigonometry ............................................................................................... 772
7.3 Computing the Values of Trigonometric Functions of Acute Angles ................................. 788
7.4 Trigonometric Functions of Any Angle............................................................................... 801
7.5 Unit Circle Approach; Properties of the Trigonometric Functions...................................... 817
7.6 Graphs of the Sine and Cosine Functions ............................................................................ 826
7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions................................... 848
7.8 Phase Shift; Sinusoidal Curve Fitting .................................................................................. 858
Chapter Review ............................................................................................................................ 871
Chapter Test ................................................................................................................................. 880
Cumulative Review ...................................................................................................................... 884
Chapter Projects ........................................................................................................................... 888
Chapter 8 Analytic Trigonometry
8.1 The Inverse Sine, Cosine, and Tangent Functions ............................................................... 891
8.2 The Inverse Trigonometric Functions (Continued) ............................................................. 905
8.3 Trigonometric Equations ..................................................................................................... 917
8.4 Trigonometric Identities ...................................................................................................... 938
8.5 Sum and Difference Formulas ............................................................................................. 951
8.6 Double-Angle and Half-Angle Formulas ............................................................................ 976
8.7 Product-to-Sum and Sum-to-Product Formulas................................................................. 1004
Chapter Review .......................................................................................................................... 1017
Chapter Test ............................................................................................................................... 1032
Cumulative Review .................................................................................................................... 1037
Chapter Projects ......................................................................................................................... 1043
Chapter 9 Applications of Trigonometric Functions
9.1 Applications Involving Right Triangles ............................................................................ 1047
9.2 The Law of Sines ............................................................................................................... 1055
9.3 The Law of Cosines ........................................................................................................... 1070
9.4 Area of a Triangle .............................................................................................................. 1082
9.5 Simple Harmonic Motion; Damped Motion; Combining Waves ...................................... 1092
Chapter Review .......................................................................................................................... 1102
Chapter Test ............................................................................................................................... 1108
Cumulative Review .................................................................................................................... 1111
Chapter Projects ......................................................................................................................... 1117
Chapter 10 Polar Coordinates; Vectors
10.1 Polar Coordinates .............................................................................................................. 1121
10.2 Polar Equations and Graphs............................................................................................... 1130
10.3 The Complex Plane; De Moivre’s Theorem ...................................................................... 1159
10.4 Vectors ............................................................................................................................... 1172
10.5 The Dot Product................................................................................................................. 1185
Chapter Review .......................................................................................................................... 1191
Chapter Test ............................................................................................................................... 1200
Cumulative Review .................................................................................................................... 1203
Chapter Projects ......................................................................................................................... 1205
Copyright © 2021 Pearson Education, Inc.
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MANUAL
TIM BRITT
Jackson State Community College
ALGEBRA AND TRIGONOMETRY
E NHANCED WITH G RAPHING U TILITIES
E IGHTH E DITION
Michael Sullivan
Chicago State University
Michael Sullivan III
Joliet Junior College
elitedocs elitedocs
, Table of Contents
Chapter R Review
R.1 Real Numbers .......................................................................................................................... 1
R.2 Algebra Essentials ................................................................................................................... 5
R.3 Geometry Essentials .............................................................................................................. 11
R.4 Polynomials ........................................................................................................................... 16
R.5 Factoring Polynomials ........................................................................................................... 23
R.6 Synthetic Division ................................................................................................................. 28
R.7 Rational Expressions ............................................................................................................. 30
R.8 nth Roots; Rational Exponents .............................................................................................. 40
Chapter 1 Graphs, Equations, and Inequalities
1.1 Graphing Utilities; Introduction to Graphing Equations ....................................................... 50
1.2 Solving Equations Using a Graphing Utility; Linear and Rational Equations....................... 57
1.3 Quadratic Equations .............................................................................................................. 71
1.4 Complex Numbers; Quadratic Equations in the Complex Number System .......................... 90
1.5 Radical Equations; Equations Quadratic in Form; Absolute Value Equations;
Factorable Equations ............................................................................................................. 96
1.6 Problem Solving: Interest, Mixture, Uniform Motion, and Constant Rate Jobs .................. 117
1.7 Solving Inequalities ............................................................................................................. 125
Chapter Review ............................................................................................................................ 137
Chapter Test ................................................................................................................................. 147
Chapter Projects ........................................................................................................................... 151
Chapter 2 Graphs
2.1 The Distance and Midpoint Formulas ................................................................................. 152
2.2 Intercepts; Symmetry; Graphing Key Equations ................................................................. 165
2.3 Lines .................................................................................................................................... 182
2.4 Circles .................................................................................................................................. 200
2.5 Variation .............................................................................................................................. 215
Chapter Review ............................................................................................................................ 220
Chapter Test ................................................................................................................................. 226
Cumulative Review ...................................................................................................................... 228
Chapter Projects ........................................................................................................................... 230
Chapter 3 Functions and Their Graphs
3.1 Functions ............................................................................................................................. 231
3.2 The Graph of a Function ...................................................................................................... 249
3.3 Properties of Functions ........................................................................................................ 258
3.4 Library of Functions; Piecewise-defined Functions ............................................................ 275
3.5 Graphing Techniques: Transformations .............................................................................. 287
3.6 Mathematical Models: Building Functions.......................................................................... 305
Chapter Review ............................................................................................................................ 313
Chapter Test ................................................................................................................................. 320
Cumulative Review ...................................................................................................................... 323
Chapter Projects ........................................................................................................................... 327
Copyright © 2021 Pearson Education, Inc.
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, Chapter 4 Linear and Quadratic Functions
4.1 Properties of Linear Functions and Linear Models.............................................................. 329
4.2 Building Linear Models from Data ...................................................................................... 340
4.3 Quadratic Functions and Their Properties ........................................................................... 346
4.4 Build Quadratic Models from Verbal Descriptions and from Data ..................................... 370
4.5 Inequalities Involving Quadratic Functions ......................................................................... 378
Chapter Review ............................................................................................................................ 397
Chapter Test ................................................................................................................................. 405
Cumulative Review ...................................................................................................................... 408
Chapter Projects ........................................................................................................................... 411
Chapter 5 Polynomial and Rational Functions
5.1 Polynomial Functions .......................................................................................................... 414
5.2 The Graph of a Polynomial Function; Models .................................................................... 425
5.3 The Real Zeros of a Polynomial Function ........................................................................... 445
5.4 Complex Zeros; Fundamental Theorem of Algebra ............................................................ 482
5.5 Properties of Rational Functions ......................................................................................... 491
5.6 The Graph of a Rational Function ....................................................................................... 501
5.7 Polynomial and Rational Inequalities .................................................................................. 557
Chapter Review ............................................................................................................................ 579
Chapter Test ................................................................................................................................. 593
Cumulative Review ...................................................................................................................... 597
Chapter Projects ........................................................................................................................... 602
Chapter 6 Exponential and Logarithmic Functions
6.1 Composite Functions ........................................................................................................... 603
6.2 One-to-One Functions; Inverse Functions ........................................................................... 621
6.3 Exponential Functions ......................................................................................................... 644
6.4 Logarithmic Functions ......................................................................................................... 665
6.5 Properties of Logarithms ..................................................................................................... 687
6.6 Logarithmic and Exponential Equations.............................................................................. 696
6.7 Financial Models ................................................................................................................. 717
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models ............................................................................................................... 725
6.9 Building Exponential, Logarithmic, and Logistic Models from Data ................................. 736
Chapter Review ............................................................................................................................ 741
Chapter Test ................................................................................................................................. 763
Cumulative Review ...................................................................................................................... 757
Chapter Projects ........................................................................................................................... 760
Copyright © 2021 Pearson Education, Inc.
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, Chapter 7 Trigonometric Functions
7.1 Angles, Arc Length, and Circular Motion ........................................................................... 763
7.2 Right Triangle Trigonometry ............................................................................................... 772
7.3 Computing the Values of Trigonometric Functions of Acute Angles ................................. 788
7.4 Trigonometric Functions of Any Angle............................................................................... 801
7.5 Unit Circle Approach; Properties of the Trigonometric Functions...................................... 817
7.6 Graphs of the Sine and Cosine Functions ............................................................................ 826
7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions................................... 848
7.8 Phase Shift; Sinusoidal Curve Fitting .................................................................................. 858
Chapter Review ............................................................................................................................ 871
Chapter Test ................................................................................................................................. 880
Cumulative Review ...................................................................................................................... 884
Chapter Projects ........................................................................................................................... 888
Chapter 8 Analytic Trigonometry
8.1 The Inverse Sine, Cosine, and Tangent Functions ............................................................... 891
8.2 The Inverse Trigonometric Functions (Continued) ............................................................. 905
8.3 Trigonometric Equations ..................................................................................................... 917
8.4 Trigonometric Identities ...................................................................................................... 938
8.5 Sum and Difference Formulas ............................................................................................. 951
8.6 Double-Angle and Half-Angle Formulas ............................................................................ 976
8.7 Product-to-Sum and Sum-to-Product Formulas................................................................. 1004
Chapter Review .......................................................................................................................... 1017
Chapter Test ............................................................................................................................... 1032
Cumulative Review .................................................................................................................... 1037
Chapter Projects ......................................................................................................................... 1043
Chapter 9 Applications of Trigonometric Functions
9.1 Applications Involving Right Triangles ............................................................................ 1047
9.2 The Law of Sines ............................................................................................................... 1055
9.3 The Law of Cosines ........................................................................................................... 1070
9.4 Area of a Triangle .............................................................................................................. 1082
9.5 Simple Harmonic Motion; Damped Motion; Combining Waves ...................................... 1092
Chapter Review .......................................................................................................................... 1102
Chapter Test ............................................................................................................................... 1108
Cumulative Review .................................................................................................................... 1111
Chapter Projects ......................................................................................................................... 1117
Chapter 10 Polar Coordinates; Vectors
10.1 Polar Coordinates .............................................................................................................. 1121
10.2 Polar Equations and Graphs............................................................................................... 1130
10.3 The Complex Plane; De Moivre’s Theorem ...................................................................... 1159
10.4 Vectors ............................................................................................................................... 1172
10.5 The Dot Product................................................................................................................. 1185
Chapter Review .......................................................................................................................... 1191
Chapter Test ............................................................................................................................... 1200
Cumulative Review .................................................................................................................... 1203
Chapter Projects ......................................................................................................................... 1205
Copyright © 2021 Pearson Education, Inc.
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