,SOLUTION MANUAL Algebra and Trigonometry
Enhanced with Graphing Utilities, 9th edition
Sullivan
Notes
1- The file is chapter after chapter.
2- We have shown you few pages sample.
3- The file contains all Appendix and Excel sheet
if it exists.
4- We have all what you need, we make update
at every time. There are many new editions
waiting you.
5- If you think you purchased the wrong file You
can contact us at every time, we can replace it
with true one.
6- The answers are at the end of the file
Our email:
, INSTRUCTOR’S SOLUTIONS
MANUAL
GEX INC.
ALGEBRA & TRIGONOMETRY
ENHANCED WITH GRAPHING
UTILITIES
NINTH EDITION
Michael Sullivan
Chicago State University
Michael Sullivan, III
Joliet Junior College
and
Florida SouthWestern State College
,Copyright © 2026, 2021, 2017 by Pearson Education, Inc. or its affiliates. All Rights Reserved. Manufactured in the
United States of America. This publication is protected by copyright, and permission should be obtained from the
publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any
means, electronic, mechanical, photocopying, recording, or otherwise. For information regarding permissions, request
forms, and the appropriate contacts within the Pearson Education Global Rights and Permissions department, please
visit www.pearsoned.com/permissions/.
PEARSON and MYLAB are exclusive trademarks owned by Pearson Education, Inc. or its affiliates in the U.S.
and/or other countries.
Unless otherwise indicated herein, any third-party trademarks, logos, or icons that may appear in this work are the
property of their respective owners, and any references to third-party trademarks, logos, icons, or other trade dress are
for demonstrative or descriptive purposes only. Such references are not intended to imply any sponsorship,
endorsement, authorization, or promotion of Pearson’s products by the owners of such marks, or any relationship
between the owner and Pearson Education, Inc., or its affiliates, authors, licensees, or distributors.
PPID: A103000398499
, 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 .......................... 89
1.5 Radical Equations; Equations Quadratic in Form; Absolute Value Equations;
Factorable Equations ............................................................................................................. 95
1.6 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate
Job Applications .................................................................................................................. 115
1.7 Solving Inequalities ............................................................................................................. 123
Chapter Review ............................................................................................................................ 134
Chapter Test ................................................................................................................................. 144
Chapter Project ............................................................................................................................. 149
Chapter 2 Graphs
2.1 The Distance and Midpoint Formulas ................................................................................. 150
2.2 Intercepts; Symmetry; Graphing Key Equations ................................................................. 162
2.3 Lines .................................................................................................................................... 178
2.4 Circles .................................................................................................................................. 195
2.5 Variation .............................................................................................................................. 208
Chapter Review ............................................................................................................................ 214
Chapter Test ................................................................................................................................. 220
Cumulative Review ...................................................................................................................... 221
Chapter Project ............................................................................................................................. 224
Chapter 3 Functions and Their Graphs
3.1 Functions ............................................................................................................................. 225
3.2 The Graph of a Function ...................................................................................................... 243
3.3 Properties of Functions ........................................................................................................ 252
3.4 Library of Functions; Piecewise-defined Functions ............................................................ 269
3.5 Graphing Techniques: Transformations .............................................................................. 282
3.6 Mathematical Models: Building Functions.......................................................................... 300
Chapter Review ............................................................................................................................ 307
Chapter Test ................................................................................................................................. 314
Cumulative Review ...................................................................................................................... 318
Chapter Projects ........................................................................................................................... 321
Copyright © 2026 Pearson Education, Inc.
,Chapter 4 Linear and Quadratic Functions
4.1 Properties of Linear Functions and Linear Models.............................................................. 322
4.2 Building Linear Models from Data ...................................................................................... 333
4.3 Quadratic Functions and Their Properties ........................................................................... 339
4.4 Build Quadratic Models from Verbal Descriptions and from Data ..................................... 363
4.5 Inequalities Involving Quadratic Functions ......................................................................... 371
Chapter Review ............................................................................................................................ 390
Chapter Test ................................................................................................................................. 398
Cumulative Review ...................................................................................................................... 400
Chapter Project ............................................................................................................................. 403
Chapter 5 Polynomial and Rational Functions
5.1 Polynomial Functions .......................................................................................................... 404
5.2 The Graph of a Polynomial Function; Models .................................................................... 414
5.3 The Real Zeros of a Polynomial Function ........................................................................... 435
5.4 Complex Zeros; Fundamental Theorem of Algebra ............................................................ 472
5.5 Properties of Rational Functions ......................................................................................... 481
5.6 The Graph of a Rational Function ....................................................................................... 491
5.7 Polynomial and Rational Inequalities .................................................................................. 546
Chapter Review ............................................................................................................................ 567
Chapter Test ................................................................................................................................. 582
Cumulative Review ...................................................................................................................... 587
Chapter Project ............................................................................................................................. 591
Chapter 6 Exponential and Logarithmic Functions
6.1 Composite Functions ........................................................................................................... 592
6.2 One-to-One Functions; Inverse Functions ........................................................................... 610
6.3 Exponential Functions ......................................................................................................... 633
6.4 Logarithmic Functions ......................................................................................................... 654
6.5 Properties of Logarithms ..................................................................................................... 676
6.6 Logarithmic and Exponential Equations.............................................................................. 685
6.7 Financial Models ................................................................................................................. 708
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models ............................................................................................................... 716
6.9 Building Exponential, Logarithmic, and Logistic Models from Data ................................. 728
Chapter Review ............................................................................................................................ 734
Chapter Test ................................................................................................................................. 746
Cumulative Review ...................................................................................................................... 750
Chapter Project ............................................................................................................................. 753
Copyright © 2026 Pearson Education, Inc.
,Chapter 7 Trigonometric Functions
7.1 Angles, Arc Length, and Circular Motion ........................................................................... 754
7.2 Right Triangle Trigonometry ............................................................................................... 763
7.3 Computing the Values of Trigonometric Functions of Acute Angles ................................. 779
7.4 Trigonometric Functions of Any Angle............................................................................... 791
7.5 Unit Circle Approach; Properties of the Trigonometric Functions...................................... 807
7.6 Graphs of the Sine and Cosine Functions ............................................................................ 817
7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions................................... 838
7.8 Phase Shift; Sinusoidal Curve Fitting .................................................................................. 848
Chapter Review ............................................................................................................................ 860
Chapter Test ................................................................................................................................. 869
Cumulative Review ...................................................................................................................... 873
Chapter Project ............................................................................................................................. 877
Chapter 8 Analytic Trigonometry
8.1 The Inverse Sine, Cosine, and Tangent Functions ............................................................... 878
8.2 The Inverse Trigonometric Functions (Continued) ............................................................. 892
8.3 Trigonometric Equations ..................................................................................................... 904
8.4 Trigonometric Identities ...................................................................................................... 925
8.5 Sum and Difference Formulas ............................................................................................. 938
8.6 Double-angle and Half-angle Formulas ............................................................................... 963
8.7 Product-to-Sum and Sum-to-Product Formulas................................................................... 991
Chapter Review .......................................................................................................................... 1003
Chapter Test ............................................................................................................................... 1018
Cumulative Review .................................................................................................................... 1023
Chapter Project ........................................................................................................................... 1028
Chapter 9 Applications of Trigonometric Functions
9.1 Applications Involving Right Triangles ............................................................................ 1029
9.2 The Law of Sines ............................................................................................................... 1037
9.3 The Law of Cosines ........................................................................................................... 1052
9.4 Area of a Triangle .............................................................................................................. 1064
9.5 Simple Harmonic Motion; Damped Motion; Combining Waves ...................................... 1074
Chapter Review .......................................................................................................................... 1084
Chapter Test ............................................................................................................................... 1090
Cumulative Review .................................................................................................................... 1093
Chapter Projects ......................................................................................................................... 1099
Chapter 10 Polar Coordinates; Vectors
10.1 Polar Coordinates .............................................................................................................. 1101
10.2 Polar Equations and Graphs............................................................................................... 1110
10.3 The Complex Plane; De Moivre’s Theorem ...................................................................... 1139
10.4 Vectors ............................................................................................................................... 1152
10.5 The Dot Product................................................................................................................. 1165
Chapter Review .......................................................................................................................... 1171
Chapter Test ............................................................................................................................... 1180
Cumulative Review .................................................................................................................... 1183
Chapter Project ........................................................................................................................... 1185
Copyright © 2026 Pearson Education, Inc.
,Chapter 11 Analytic Geometry
11.2 The Parabola ...................................................................................................................... 1186
11.3 The Ellipse ......................................................................................................................... 1202
11.4 The Hyperbola ................................................................................................................... 1219
11.5 Rotation of Axes; General Form of a Conic ...................................................................... 1239
11.6 Polar Equations of Conics ................................................................................................. 1252
11.7 Plane Curves and Parametric Equations ............................................................................ 1261
Chapter Review .......................................................................................................................... 1276
Chapter Test ............................................................................................................................... 1285
Cumulative Review .................................................................................................................... 1290
Chapter Project ........................................................................................................................... 1292
Chapter 12 Systems of Equations and Inequalities
12.1 Systems of Linear Equations: Substitution and Elimination ............................................. 1293
12.2 Systems of Linear Equations: Matrices ............................................................................. 1315
12.3 Systems of Linear Equations: Determinants ...................................................................... 1340
12.4 Matrix Algebra .................................................................................................................. 1355
12.5 Partial Fraction Decomposition ......................................................................................... 1373
12.6 Systems of Nonlinear Equations ........................................................................................ 1391
12.7 Systems of Inequalities ...................................................................................................... 1419
12.8 Linear Programming .......................................................................................................... 1434
Chapter Review .......................................................................................................................... 1448
Chapter Test ............................................................................................................................... 1463
Cumulative Review .................................................................................................................... 1471
Chapter Project........................................................................................................................... 1475
Chapter 13 Sequences; Induction; the Binomial Theorem
13.1 Sequences .......................................................................................................................... 1476
13.2 Arithmetic Sequences ........................................................................................................ 1489
13.3 Geometric Sequences; Geometric Series ........................................................................... 1498
13.4 The Limit of a Sequence; Infinite Series ........................................................................... 1510
13.5 Mathematical Induction ..................................................................................................... 1514
13.6 The Binomial Theorem ...................................................................................................... 1524
Chapter Review .......................................................................................................................... 1531
Chapter Test ............................................................................................................................... 1535
Cumulative Review .................................................................................................................... 1538
Chapter Project ........................................................................................................................... 1541
Chapter 14 Counting and Probability
14.1 Counting ............................................................................................................................ 1542
14.2 Permutations and Combinations ........................................................................................ 1545
14.3 Probability ......................................................................................................................... 1550
Chapter Review .......................................................................................................................... 1557
Chapter Test ............................................................................................................................... 1559
Cumulative Review .................................................................................................................... 1560
Chapter Project ........................................................................................................................... 1563
Copyright © 2026 Pearson Education, Inc.
, Chapter R
Review
Section R.1 16. ( A ∩ B) ∪ C
= ({1, 3, 4,5, 9} ∩ {2, 4, 6, 7,8} ) ∪ {1,3, 4, 6}
1. rational
= {4} ∪ {1, 3, 4, 6}
2. 4 + 5 ⋅ 6 − 3 = 4 + 30 − 3 = 31
= {1,3, 4, 6}
3. Distributive
17. A = {0, 2, 6, 7, 8}
4. c
5. a 18. C = {0, 2, 5, 7, 8, 9}
6. b 19. A ∩ B = {1, 3, 4, 5, 9} ∩ {2, 4, 6, 7, 8}
7. True = {4} = {0, 1, 2, 3, 5, 6, 7, 8, 9}
8. False; The Zero-Product Property states that if a
product equals 0, then at least one of the factors 20. B ∪ C = {2, 4, 6, 7, 8} ∪ {1, 3, 4, 6}
must equal 0.
= {1, 2, 3, 4, 6, 7, 8} = {0, 5, 9}
9. False; 6 is the Greatest Common Factor of 12
and 18. The Least Common Multiple is the 21. A ∪ B = {0, 2, 6, 7, 8} ∪ {0, 1, 3, 5, 9}
smallest value that both numbers will divide
= {0, 1, 2, 3, 5, 6, 7, 8, 9}
evenly. The LCM for 12 and 18 is 36.
10. True 22. B ∩ C = {0, 1, 3, 5, 9} ∩ {0, 2, 5, 7, 8, 9}
= {0, 5, 9}
11. A ∪ B = {1, 3, 4,5, 9} ∪ {2, 4, 6, 7,8}
= {1, 2,3, 4, 5, 6, 7,8, 9}
23. a. {2,5}
12. A ∪ C = {1, 3, 4,5, 9} ∪ {1, 3, 4, 6} b. {−6, 2,5}
= {1, 3, 4, 5, 6, 9}
13. A ∩ B = {1, 3, 4,5, 9} ∩ {2, 4, 6, 7,8} = {4}
c. { 1
−6, , −1.333... = −1.3, 2,5
2 }
d. {π }
14. A ∩ C = {1, 3, 4,5, 9} ∩ {1, 3, 4, 6} = {1, 3, 4}
15. ( A ∪ B) ∩ C
e. { 1
−6, , −1.333... = −1.3, π , 2,5
2 }
= ({1, 3, 4,5, 9} ∪ {2, 4, 6, 7,8} ) ∩ {1,3, 4, 6} 24. a. {1}
= {1, 2,3, 4,5, 6, 7,8,9} ∩ {1,3, 4, 6}
b. {0,1}
= {1, 3, 4, 6}
c. { 5
− , 2.060606... = 2.06,1.25, 0,1
3 }
d. { 5}
1
Copyright © 2026 Pearson Education, Inc.
, Chapter R: Review
e. { 5
− , 2.060606... = 2.06,1.25, 0,1, 5
3 } 34. a.
35. a.
0.054
9.999
b.
b.
0.053
9.998
25. a. {1} 36. a. 1.001 b. 1.000
b. {0,1} 37. a. 0.429 b. 0.428
c. { 1 1 1
0,1, , ,
2 3 4 } 38. a. 0.556 b. 0.555
d. None 39. a. 34.733 b. 34.733
e. { 1 1 1
0,1, , ,
2 3 4 } 40. a. 16.200
41. 3 + 2 = 5
b. 16.200
26. a. None
42. 5 ⋅ 2 = 10
b. {−1}
43. x + 2 = 3 ⋅ 4
c. {−1.3, −1.2, −1.1, −1}
44. 3 + y = 2 + 2
d. None
e. {−1.3, −1.2, −1.1, −1} 45. 3 y = 1 + 2
46. 2 x = 4 ⋅ 6
27. a. None
b. None 47. x − 2 = 6
c. None
48. 2 − y = 6
d. { 2, π , 2 + 1, π +
1
2 } 49.
x
=6
2
e. { 2, π , 2 + 1, π +
1
2 } 50.
2
=6
x
28. a. None
b. None 51. 9 − 4 + 2 = 5 + 2 = 7
c. { 1
2 }
+ 10.3
52. 6 − 4 + 3 = 2 + 3 = 5
53. −6 + 4 ⋅ 3 = −6 + 12 = 6
d. {− 2, π + 2 } 54. 8 − 4 ⋅ 2 = 8 − 8 = 0
e. { 1
− 2, π + 2, + 10.3
2 } 55. 18 − 5 ⋅ 2 = 18 − 10 = 8
56. 100 − 10 ⋅ 2 = 100 − 20 = 80
29. a. 18.953 b. 18.952
1 12 + 1 13
30. a. 25.861 b. 25.861 57. 4 + = =
3 3 3
31. a. 28.653 b. 28.653
1 4 −1 3
58. 2 − = =
32. a. 99.052 b. 99.052 2 2 2
33. a. 0.063 b. 0.062
2
Copyright © 2026 Pearson Education, Inc.
Enhanced with Graphing Utilities, 9th edition
Sullivan
Notes
1- The file is chapter after chapter.
2- We have shown you few pages sample.
3- The file contains all Appendix and Excel sheet
if it exists.
4- We have all what you need, we make update
at every time. There are many new editions
waiting you.
5- If you think you purchased the wrong file You
can contact us at every time, we can replace it
with true one.
6- The answers are at the end of the file
Our email:
, INSTRUCTOR’S SOLUTIONS
MANUAL
GEX INC.
ALGEBRA & TRIGONOMETRY
ENHANCED WITH GRAPHING
UTILITIES
NINTH EDITION
Michael Sullivan
Chicago State University
Michael Sullivan, III
Joliet Junior College
and
Florida SouthWestern State College
,Copyright © 2026, 2021, 2017 by Pearson Education, Inc. or its affiliates. All Rights Reserved. Manufactured in the
United States of America. This publication is protected by copyright, and permission should be obtained from the
publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any
means, electronic, mechanical, photocopying, recording, or otherwise. For information regarding permissions, request
forms, and the appropriate contacts within the Pearson Education Global Rights and Permissions department, please
visit www.pearsoned.com/permissions/.
PEARSON and MYLAB are exclusive trademarks owned by Pearson Education, Inc. or its affiliates in the U.S.
and/or other countries.
Unless otherwise indicated herein, any third-party trademarks, logos, or icons that may appear in this work are the
property of their respective owners, and any references to third-party trademarks, logos, icons, or other trade dress are
for demonstrative or descriptive purposes only. Such references are not intended to imply any sponsorship,
endorsement, authorization, or promotion of Pearson’s products by the owners of such marks, or any relationship
between the owner and Pearson Education, Inc., or its affiliates, authors, licensees, or distributors.
PPID: A103000398499
, 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 .......................... 89
1.5 Radical Equations; Equations Quadratic in Form; Absolute Value Equations;
Factorable Equations ............................................................................................................. 95
1.6 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate
Job Applications .................................................................................................................. 115
1.7 Solving Inequalities ............................................................................................................. 123
Chapter Review ............................................................................................................................ 134
Chapter Test ................................................................................................................................. 144
Chapter Project ............................................................................................................................. 149
Chapter 2 Graphs
2.1 The Distance and Midpoint Formulas ................................................................................. 150
2.2 Intercepts; Symmetry; Graphing Key Equations ................................................................. 162
2.3 Lines .................................................................................................................................... 178
2.4 Circles .................................................................................................................................. 195
2.5 Variation .............................................................................................................................. 208
Chapter Review ............................................................................................................................ 214
Chapter Test ................................................................................................................................. 220
Cumulative Review ...................................................................................................................... 221
Chapter Project ............................................................................................................................. 224
Chapter 3 Functions and Their Graphs
3.1 Functions ............................................................................................................................. 225
3.2 The Graph of a Function ...................................................................................................... 243
3.3 Properties of Functions ........................................................................................................ 252
3.4 Library of Functions; Piecewise-defined Functions ............................................................ 269
3.5 Graphing Techniques: Transformations .............................................................................. 282
3.6 Mathematical Models: Building Functions.......................................................................... 300
Chapter Review ............................................................................................................................ 307
Chapter Test ................................................................................................................................. 314
Cumulative Review ...................................................................................................................... 318
Chapter Projects ........................................................................................................................... 321
Copyright © 2026 Pearson Education, Inc.
,Chapter 4 Linear and Quadratic Functions
4.1 Properties of Linear Functions and Linear Models.............................................................. 322
4.2 Building Linear Models from Data ...................................................................................... 333
4.3 Quadratic Functions and Their Properties ........................................................................... 339
4.4 Build Quadratic Models from Verbal Descriptions and from Data ..................................... 363
4.5 Inequalities Involving Quadratic Functions ......................................................................... 371
Chapter Review ............................................................................................................................ 390
Chapter Test ................................................................................................................................. 398
Cumulative Review ...................................................................................................................... 400
Chapter Project ............................................................................................................................. 403
Chapter 5 Polynomial and Rational Functions
5.1 Polynomial Functions .......................................................................................................... 404
5.2 The Graph of a Polynomial Function; Models .................................................................... 414
5.3 The Real Zeros of a Polynomial Function ........................................................................... 435
5.4 Complex Zeros; Fundamental Theorem of Algebra ............................................................ 472
5.5 Properties of Rational Functions ......................................................................................... 481
5.6 The Graph of a Rational Function ....................................................................................... 491
5.7 Polynomial and Rational Inequalities .................................................................................. 546
Chapter Review ............................................................................................................................ 567
Chapter Test ................................................................................................................................. 582
Cumulative Review ...................................................................................................................... 587
Chapter Project ............................................................................................................................. 591
Chapter 6 Exponential and Logarithmic Functions
6.1 Composite Functions ........................................................................................................... 592
6.2 One-to-One Functions; Inverse Functions ........................................................................... 610
6.3 Exponential Functions ......................................................................................................... 633
6.4 Logarithmic Functions ......................................................................................................... 654
6.5 Properties of Logarithms ..................................................................................................... 676
6.6 Logarithmic and Exponential Equations.............................................................................. 685
6.7 Financial Models ................................................................................................................. 708
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models ............................................................................................................... 716
6.9 Building Exponential, Logarithmic, and Logistic Models from Data ................................. 728
Chapter Review ............................................................................................................................ 734
Chapter Test ................................................................................................................................. 746
Cumulative Review ...................................................................................................................... 750
Chapter Project ............................................................................................................................. 753
Copyright © 2026 Pearson Education, Inc.
,Chapter 7 Trigonometric Functions
7.1 Angles, Arc Length, and Circular Motion ........................................................................... 754
7.2 Right Triangle Trigonometry ............................................................................................... 763
7.3 Computing the Values of Trigonometric Functions of Acute Angles ................................. 779
7.4 Trigonometric Functions of Any Angle............................................................................... 791
7.5 Unit Circle Approach; Properties of the Trigonometric Functions...................................... 807
7.6 Graphs of the Sine and Cosine Functions ............................................................................ 817
7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions................................... 838
7.8 Phase Shift; Sinusoidal Curve Fitting .................................................................................. 848
Chapter Review ............................................................................................................................ 860
Chapter Test ................................................................................................................................. 869
Cumulative Review ...................................................................................................................... 873
Chapter Project ............................................................................................................................. 877
Chapter 8 Analytic Trigonometry
8.1 The Inverse Sine, Cosine, and Tangent Functions ............................................................... 878
8.2 The Inverse Trigonometric Functions (Continued) ............................................................. 892
8.3 Trigonometric Equations ..................................................................................................... 904
8.4 Trigonometric Identities ...................................................................................................... 925
8.5 Sum and Difference Formulas ............................................................................................. 938
8.6 Double-angle and Half-angle Formulas ............................................................................... 963
8.7 Product-to-Sum and Sum-to-Product Formulas................................................................... 991
Chapter Review .......................................................................................................................... 1003
Chapter Test ............................................................................................................................... 1018
Cumulative Review .................................................................................................................... 1023
Chapter Project ........................................................................................................................... 1028
Chapter 9 Applications of Trigonometric Functions
9.1 Applications Involving Right Triangles ............................................................................ 1029
9.2 The Law of Sines ............................................................................................................... 1037
9.3 The Law of Cosines ........................................................................................................... 1052
9.4 Area of a Triangle .............................................................................................................. 1064
9.5 Simple Harmonic Motion; Damped Motion; Combining Waves ...................................... 1074
Chapter Review .......................................................................................................................... 1084
Chapter Test ............................................................................................................................... 1090
Cumulative Review .................................................................................................................... 1093
Chapter Projects ......................................................................................................................... 1099
Chapter 10 Polar Coordinates; Vectors
10.1 Polar Coordinates .............................................................................................................. 1101
10.2 Polar Equations and Graphs............................................................................................... 1110
10.3 The Complex Plane; De Moivre’s Theorem ...................................................................... 1139
10.4 Vectors ............................................................................................................................... 1152
10.5 The Dot Product................................................................................................................. 1165
Chapter Review .......................................................................................................................... 1171
Chapter Test ............................................................................................................................... 1180
Cumulative Review .................................................................................................................... 1183
Chapter Project ........................................................................................................................... 1185
Copyright © 2026 Pearson Education, Inc.
,Chapter 11 Analytic Geometry
11.2 The Parabola ...................................................................................................................... 1186
11.3 The Ellipse ......................................................................................................................... 1202
11.4 The Hyperbola ................................................................................................................... 1219
11.5 Rotation of Axes; General Form of a Conic ...................................................................... 1239
11.6 Polar Equations of Conics ................................................................................................. 1252
11.7 Plane Curves and Parametric Equations ............................................................................ 1261
Chapter Review .......................................................................................................................... 1276
Chapter Test ............................................................................................................................... 1285
Cumulative Review .................................................................................................................... 1290
Chapter Project ........................................................................................................................... 1292
Chapter 12 Systems of Equations and Inequalities
12.1 Systems of Linear Equations: Substitution and Elimination ............................................. 1293
12.2 Systems of Linear Equations: Matrices ............................................................................. 1315
12.3 Systems of Linear Equations: Determinants ...................................................................... 1340
12.4 Matrix Algebra .................................................................................................................. 1355
12.5 Partial Fraction Decomposition ......................................................................................... 1373
12.6 Systems of Nonlinear Equations ........................................................................................ 1391
12.7 Systems of Inequalities ...................................................................................................... 1419
12.8 Linear Programming .......................................................................................................... 1434
Chapter Review .......................................................................................................................... 1448
Chapter Test ............................................................................................................................... 1463
Cumulative Review .................................................................................................................... 1471
Chapter Project........................................................................................................................... 1475
Chapter 13 Sequences; Induction; the Binomial Theorem
13.1 Sequences .......................................................................................................................... 1476
13.2 Arithmetic Sequences ........................................................................................................ 1489
13.3 Geometric Sequences; Geometric Series ........................................................................... 1498
13.4 The Limit of a Sequence; Infinite Series ........................................................................... 1510
13.5 Mathematical Induction ..................................................................................................... 1514
13.6 The Binomial Theorem ...................................................................................................... 1524
Chapter Review .......................................................................................................................... 1531
Chapter Test ............................................................................................................................... 1535
Cumulative Review .................................................................................................................... 1538
Chapter Project ........................................................................................................................... 1541
Chapter 14 Counting and Probability
14.1 Counting ............................................................................................................................ 1542
14.2 Permutations and Combinations ........................................................................................ 1545
14.3 Probability ......................................................................................................................... 1550
Chapter Review .......................................................................................................................... 1557
Chapter Test ............................................................................................................................... 1559
Cumulative Review .................................................................................................................... 1560
Chapter Project ........................................................................................................................... 1563
Copyright © 2026 Pearson Education, Inc.
, Chapter R
Review
Section R.1 16. ( A ∩ B) ∪ C
= ({1, 3, 4,5, 9} ∩ {2, 4, 6, 7,8} ) ∪ {1,3, 4, 6}
1. rational
= {4} ∪ {1, 3, 4, 6}
2. 4 + 5 ⋅ 6 − 3 = 4 + 30 − 3 = 31
= {1,3, 4, 6}
3. Distributive
17. A = {0, 2, 6, 7, 8}
4. c
5. a 18. C = {0, 2, 5, 7, 8, 9}
6. b 19. A ∩ B = {1, 3, 4, 5, 9} ∩ {2, 4, 6, 7, 8}
7. True = {4} = {0, 1, 2, 3, 5, 6, 7, 8, 9}
8. False; The Zero-Product Property states that if a
product equals 0, then at least one of the factors 20. B ∪ C = {2, 4, 6, 7, 8} ∪ {1, 3, 4, 6}
must equal 0.
= {1, 2, 3, 4, 6, 7, 8} = {0, 5, 9}
9. False; 6 is the Greatest Common Factor of 12
and 18. The Least Common Multiple is the 21. A ∪ B = {0, 2, 6, 7, 8} ∪ {0, 1, 3, 5, 9}
smallest value that both numbers will divide
= {0, 1, 2, 3, 5, 6, 7, 8, 9}
evenly. The LCM for 12 and 18 is 36.
10. True 22. B ∩ C = {0, 1, 3, 5, 9} ∩ {0, 2, 5, 7, 8, 9}
= {0, 5, 9}
11. A ∪ B = {1, 3, 4,5, 9} ∪ {2, 4, 6, 7,8}
= {1, 2,3, 4, 5, 6, 7,8, 9}
23. a. {2,5}
12. A ∪ C = {1, 3, 4,5, 9} ∪ {1, 3, 4, 6} b. {−6, 2,5}
= {1, 3, 4, 5, 6, 9}
13. A ∩ B = {1, 3, 4,5, 9} ∩ {2, 4, 6, 7,8} = {4}
c. { 1
−6, , −1.333... = −1.3, 2,5
2 }
d. {π }
14. A ∩ C = {1, 3, 4,5, 9} ∩ {1, 3, 4, 6} = {1, 3, 4}
15. ( A ∪ B) ∩ C
e. { 1
−6, , −1.333... = −1.3, π , 2,5
2 }
= ({1, 3, 4,5, 9} ∪ {2, 4, 6, 7,8} ) ∩ {1,3, 4, 6} 24. a. {1}
= {1, 2,3, 4,5, 6, 7,8,9} ∩ {1,3, 4, 6}
b. {0,1}
= {1, 3, 4, 6}
c. { 5
− , 2.060606... = 2.06,1.25, 0,1
3 }
d. { 5}
1
Copyright © 2026 Pearson Education, Inc.
, Chapter R: Review
e. { 5
− , 2.060606... = 2.06,1.25, 0,1, 5
3 } 34. a.
35. a.
0.054
9.999
b.
b.
0.053
9.998
25. a. {1} 36. a. 1.001 b. 1.000
b. {0,1} 37. a. 0.429 b. 0.428
c. { 1 1 1
0,1, , ,
2 3 4 } 38. a. 0.556 b. 0.555
d. None 39. a. 34.733 b. 34.733
e. { 1 1 1
0,1, , ,
2 3 4 } 40. a. 16.200
41. 3 + 2 = 5
b. 16.200
26. a. None
42. 5 ⋅ 2 = 10
b. {−1}
43. x + 2 = 3 ⋅ 4
c. {−1.3, −1.2, −1.1, −1}
44. 3 + y = 2 + 2
d. None
e. {−1.3, −1.2, −1.1, −1} 45. 3 y = 1 + 2
46. 2 x = 4 ⋅ 6
27. a. None
b. None 47. x − 2 = 6
c. None
48. 2 − y = 6
d. { 2, π , 2 + 1, π +
1
2 } 49.
x
=6
2
e. { 2, π , 2 + 1, π +
1
2 } 50.
2
=6
x
28. a. None
b. None 51. 9 − 4 + 2 = 5 + 2 = 7
c. { 1
2 }
+ 10.3
52. 6 − 4 + 3 = 2 + 3 = 5
53. −6 + 4 ⋅ 3 = −6 + 12 = 6
d. {− 2, π + 2 } 54. 8 − 4 ⋅ 2 = 8 − 8 = 0
e. { 1
− 2, π + 2, + 10.3
2 } 55. 18 − 5 ⋅ 2 = 18 − 10 = 8
56. 100 − 10 ⋅ 2 = 100 − 20 = 80
29. a. 18.953 b. 18.952
1 12 + 1 13
30. a. 25.861 b. 25.861 57. 4 + = =
3 3 3
31. a. 28.653 b. 28.653
1 4 −1 3
58. 2 − = =
32. a. 99.052 b. 99.052 2 2 2
33. a. 0.063 b. 0.062
2
Copyright © 2026 Pearson Education, Inc.
