,SOLUTION MANUAL Algebra and Trigonometry,
12th 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
TIM BRITT
Jackson State Community College
ALGEBRA AND
TRIGONOMETRY
TWELFTH EDITION
Michael Sullivan
Chicago State University
,Copyright © 2025, 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: A103000353514
, 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 Equations and Inequalities
1.1 Linear Equations ...................................................................................................................... 50
1.2 Quadratic Equations................................................................................................................. 68
1.3 Complex Numbers; Quadratic Equations in the Complex Number System............................ 86
1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations................................ 92
1.5 Solving Inequalities ............................................................................................................... 116
1.6 Equations and Inequalities Involving Absolute Value .......................................................... 127
1.7 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications ...... 137
Chapter Review ............................................................................................................................ 145
Chapter Test .................................................................................................................................. 153
Chapter Projects ............................................................................................................................ 155
Chapter 2 Graphs
2.1 The Distance and Midpoint Formulas ................................................................................... 156
2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry ............................................. 169
2.3 Lines ...................................................................................................................................... 183
2.4 Circles .................................................................................................................................... 201
2.5 Variation ................................................................................................................................ 215
Chapter Review ............................................................................................................................ 221
Chapter Test .................................................................................................................................. 227
Cumulative Review ...................................................................................................................... 229
Chapter Project ............................................................................................................................. 231
Chapter 3 Functions and Their Graphs
3.1 Functions................................................................................................................................ 232
3.2 The Graph of a Function ........................................................................................................ 250
3.3 Properties of Functions .......................................................................................................... 259
3.4 Library of Functions; Piecewise-defined Functions .............................................................. 276
3.5 Graphing Techniques: Transformations ................................................................................ 288
3.6 Mathematical Models: Building Functions ........................................................................... 306
Chapter Review ............................................................................................................................ 314
Chapter Test .................................................................................................................................. 321
Cumulative Review ...................................................................................................................... 324
Chapter Projects ............................................................................................................................ 328
iii
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,Chapter 4 Linear and Quadratic Functions
4.1 Properties of Linear Functions and Linear Models ............................................................... 330
4.2 Building Linear Functions from Data .................................................................................... 341
4.3 Quadratic Functions and Their Properties ............................................................................. 347
4.4 Build Quadratic Models from Verbal Descriptions and from Data ...................................... 371
4.5 Inequalities Involving Quadratic Functions........................................................................... 378
Chapter Review ............................................................................................................................ 398
Chapter Test .................................................................................................................................. 406
Cumulative Review ...................................................................................................................... 408
Chapter Projects ............................................................................................................................ 411
Chapter 5 Polynomial and Rational Functions
5.1 Polynomial Functions ............................................................................................................ 414
5.2 Graphing Polynomial Functions; Models ............................................................................... 424
5.3 Properties of Rational Functions ........................................................................................... 440
5.4 The Graph of a Rational Function ......................................................................................... 450
5.5 Polynomial and Rational Inequalities .................................................................................... 506
5.6 The Real Zeros of a Polynomial Function ............................................................................. 527
5.7 Complex Zeros; Fundamental Theorem of Algebra .............................................................. 558
Chapter Review ............................................................................................................................ 567
Chapter Test .................................................................................................................................. 582
Cumulative Review ...................................................................................................................... 586
Chapter Projects ............................................................................................................................ 591
Chapter 6 Exponential and Logarithmic Functions
6.1 Composite Functions ............................................................................................................. 593
6.2 One-to-One Functions; Inverse Functions ............................................................................. 611
6.3 Exponential Functions ........................................................................................................... 634
6.4 Logarithmic Functions ........................................................................................................... 655
6.5 Properties of Logarithms ....................................................................................................... 677
6.6 Logarithmic and Exponential Equations................................................................................ 686
6.7 Financial Models ................................................................................................................... 707
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models ............................................................................................................... 715
6.9 Building Exponential, Logarithmic, and Logistic Models from Data ................................... 725
Chapter Review ............................................................................................................................ 729
Chapter Test .................................................................................................................................. 742
Cumulative Review ...................................................................................................................... 746
Chapter Projects ............................................................................................................................ 749
iv
Copyright © 2025 Pearson Education, Inc.
,Chapter 7 Trigonometric Functions
7.1 Angles, Arc Length, and Circular Motion ............................................................................. 752
7.2 Right Triangle Trigonometry ................................................................................................. 761
7.3 Computing the Values of Trigonometric Functions of Acute Angles ................................... 777
7.4 Trigonometric Functions of Any Angle ................................................................................ 790
7.5 Unit Circle Approach: Properties of the Trigonometric Functions ....................................... 806
7.6 Graphs of the Sine and Cosine Functions .............................................................................. 815
7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions .................................... 837
7.8 Phase Shift; Sinusoidal Curve Fitting .................................................................................... 847
Chapter Review ............................................................................................................................ 860
Chapter Test .................................................................................................................................. 869
Cumulative Review ...................................................................................................................... 873
Chapter Projects ............................................................................................................................ 877
Chapter 8 Analytic Trigonometry
8.1 The Inverse Sine, Cosine, and Tangent Functions................................................................. 881
8.2 The Inverse Trigonometric Functions (Continued) ............................................................... 895
8.3 Trigonometric Equations ....................................................................................................... 907
8.4 Trigonometric Identities ........................................................................................................ 928
8.5 Sum and Difference Formulas ............................................................................................... 941
8.6 Double-angle and Half-angle Formulas................................................................................. 966
8.7 Product-to-Sum and Sum-to-Product Formulas .................................................................... 994
Chapter Review .......................................................................................................................... 1007
Chapter Test ................................................................................................................................ 1022
Cumulative Review .................................................................................................................... 1027
Chapter Projects .......................................................................................................................... 1033
Chapter 9 Applications of Trigonometric Functions
9.1 Applications Involving Right Triangles .............................................................................. 1037
9.2 The Law of Sines ................................................................................................................. 1045
9.3 The Law of Cosines ............................................................................................................. 1060
9.4 Area of a Triangle ................................................................................................................ 1072
9.5 Simple Harmonic Motion; Damped Motion; Combining Waves ........................................ 1082
Chapter Review .......................................................................................................................... 1092
Chapter Test ................................................................................................................................ 1098
Cumulative Review .................................................................................................................... 1101
Chapter Projects .......................................................................................................................... 1107
Chapter 10 Polar Coordinates; Vectors
10.1 Polar Coordinates............................................................................................................... 1111
10.2 Polar Equations and Graphs............................................................................................... 1120
10.3 The Complex Plane; De Moivre’s Theorem ...................................................................... 1149
10.4 Vectors ............................................................................................................................... 1163
10.5 The Dot Product ................................................................................................................. 1176
Chapter Review .......................................................................................................................... 1182
Chapter Test ................................................................................................................................ 1190
Cumulative Review .................................................................................................................... 1194
Chapter Projects .......................................................................................................................... 1196
v
Copyright © 2025 Pearson Education, Inc.
,Chapter 11 Analytic Geometry
11.2 The Parabola ...................................................................................................................... 1199
11.3 The Ellipse ......................................................................................................................... 1215
11.4 The Hyperbola ................................................................................................................... 1232
11.5 Rotation of Axes; General Form of a Conic ...................................................................... 1252
11.6 Polar Equations of Conics ................................................................................................. 1265
11.7 Plane Curves and Parametric Equations ............................................................................ 1274
Chapter Review .......................................................................................................................... 1289
Chapter Test ................................................................................................................................ 1298
Cumulative Review .................................................................................................................... 1303
Chapter Projects .......................................................................................................................... 1305
Chapter 12 Systems of Equations and Inequalities
12.1 Systems of Linear Equations: Substitution and Elimination ............................................. 1309
12.2 Systems of Linear Equations: Matrices ............................................................................. 1332
12.3 Systems of Linear Equations: Determinants...................................................................... 1356
12.4 Matrix Algebra................................................................................................................... 1370
12.5 Partial Fraction Decomposition ......................................................................................... 1389
12.6 Systems of Nonlinear Equations ........................................................................................ 1407
12.7 Systems of Inequalities ...................................................................................................... 1435
12.8 Linear Programming .......................................................................................................... 1450
Chapter Review .......................................................................................................................... 1464
Chapter Test ................................................................................................................................ 1479
Cumulative Review .................................................................................................................... 1487
Chapter Projects .......................................................................................................................... 1491
Chapter 13 Sequences; Induction; the Binomial Theorem
13.1 Sequences .......................................................................................................................... 1493
13.2 Arithmetic Sequences ........................................................................................................ 1503
13.3 Geometric Sequences; Geometric Series ........................................................................... 1512
13.4 Mathematical Induction ..................................................................................................... 1524
13.5 The Binomial Theorem ...................................................................................................... 1533
Chapter Review .......................................................................................................................... 1540
Chapter Test ................................................................................................................................ 1544
Cumulative Review .................................................................................................................... 1547
Chapter Projects .......................................................................................................................... 1550
vi
Copyright © 2025 Pearson Education, Inc.
,Chapter 14 Counting and Probability
14.1 Counting ............................................................................................................................ 1553
14.2 Permutations and Combinations ........................................................................................ 1556
14.3 Probability.......................................................................................................................... 1561
Chapter Review .......................................................................................................................... 1568
Chapter Test ................................................................................................................................ 1570
Cumulative Review .................................................................................................................... 1571
Chapter Projects .......................................................................................................................... 1574
Appendix Graphing Utilities
Section 1 The Viewing Rectangle ............................................................................................. 1577
Section 2 Using a Graphing Utility to Graph Equations ........................................................... 1578
Section 3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry ................. 1583
Section 5 Square Screens ........................................................................................................... 1585
vii
Copyright © 2025 Pearson Education, Inc.
,
12th 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
TIM BRITT
Jackson State Community College
ALGEBRA AND
TRIGONOMETRY
TWELFTH EDITION
Michael Sullivan
Chicago State University
,Copyright © 2025, 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: A103000353514
, 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 Equations and Inequalities
1.1 Linear Equations ...................................................................................................................... 50
1.2 Quadratic Equations................................................................................................................. 68
1.3 Complex Numbers; Quadratic Equations in the Complex Number System............................ 86
1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations................................ 92
1.5 Solving Inequalities ............................................................................................................... 116
1.6 Equations and Inequalities Involving Absolute Value .......................................................... 127
1.7 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications ...... 137
Chapter Review ............................................................................................................................ 145
Chapter Test .................................................................................................................................. 153
Chapter Projects ............................................................................................................................ 155
Chapter 2 Graphs
2.1 The Distance and Midpoint Formulas ................................................................................... 156
2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry ............................................. 169
2.3 Lines ...................................................................................................................................... 183
2.4 Circles .................................................................................................................................... 201
2.5 Variation ................................................................................................................................ 215
Chapter Review ............................................................................................................................ 221
Chapter Test .................................................................................................................................. 227
Cumulative Review ...................................................................................................................... 229
Chapter Project ............................................................................................................................. 231
Chapter 3 Functions and Their Graphs
3.1 Functions................................................................................................................................ 232
3.2 The Graph of a Function ........................................................................................................ 250
3.3 Properties of Functions .......................................................................................................... 259
3.4 Library of Functions; Piecewise-defined Functions .............................................................. 276
3.5 Graphing Techniques: Transformations ................................................................................ 288
3.6 Mathematical Models: Building Functions ........................................................................... 306
Chapter Review ............................................................................................................................ 314
Chapter Test .................................................................................................................................. 321
Cumulative Review ...................................................................................................................... 324
Chapter Projects ............................................................................................................................ 328
iii
Copyright © 2025 Pearson Education, Inc.
,Chapter 4 Linear and Quadratic Functions
4.1 Properties of Linear Functions and Linear Models ............................................................... 330
4.2 Building Linear Functions from Data .................................................................................... 341
4.3 Quadratic Functions and Their Properties ............................................................................. 347
4.4 Build Quadratic Models from Verbal Descriptions and from Data ...................................... 371
4.5 Inequalities Involving Quadratic Functions........................................................................... 378
Chapter Review ............................................................................................................................ 398
Chapter Test .................................................................................................................................. 406
Cumulative Review ...................................................................................................................... 408
Chapter Projects ............................................................................................................................ 411
Chapter 5 Polynomial and Rational Functions
5.1 Polynomial Functions ............................................................................................................ 414
5.2 Graphing Polynomial Functions; Models ............................................................................... 424
5.3 Properties of Rational Functions ........................................................................................... 440
5.4 The Graph of a Rational Function ......................................................................................... 450
5.5 Polynomial and Rational Inequalities .................................................................................... 506
5.6 The Real Zeros of a Polynomial Function ............................................................................. 527
5.7 Complex Zeros; Fundamental Theorem of Algebra .............................................................. 558
Chapter Review ............................................................................................................................ 567
Chapter Test .................................................................................................................................. 582
Cumulative Review ...................................................................................................................... 586
Chapter Projects ............................................................................................................................ 591
Chapter 6 Exponential and Logarithmic Functions
6.1 Composite Functions ............................................................................................................. 593
6.2 One-to-One Functions; Inverse Functions ............................................................................. 611
6.3 Exponential Functions ........................................................................................................... 634
6.4 Logarithmic Functions ........................................................................................................... 655
6.5 Properties of Logarithms ....................................................................................................... 677
6.6 Logarithmic and Exponential Equations................................................................................ 686
6.7 Financial Models ................................................................................................................... 707
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models ............................................................................................................... 715
6.9 Building Exponential, Logarithmic, and Logistic Models from Data ................................... 725
Chapter Review ............................................................................................................................ 729
Chapter Test .................................................................................................................................. 742
Cumulative Review ...................................................................................................................... 746
Chapter Projects ............................................................................................................................ 749
iv
Copyright © 2025 Pearson Education, Inc.
,Chapter 7 Trigonometric Functions
7.1 Angles, Arc Length, and Circular Motion ............................................................................. 752
7.2 Right Triangle Trigonometry ................................................................................................. 761
7.3 Computing the Values of Trigonometric Functions of Acute Angles ................................... 777
7.4 Trigonometric Functions of Any Angle ................................................................................ 790
7.5 Unit Circle Approach: Properties of the Trigonometric Functions ....................................... 806
7.6 Graphs of the Sine and Cosine Functions .............................................................................. 815
7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions .................................... 837
7.8 Phase Shift; Sinusoidal Curve Fitting .................................................................................... 847
Chapter Review ............................................................................................................................ 860
Chapter Test .................................................................................................................................. 869
Cumulative Review ...................................................................................................................... 873
Chapter Projects ............................................................................................................................ 877
Chapter 8 Analytic Trigonometry
8.1 The Inverse Sine, Cosine, and Tangent Functions................................................................. 881
8.2 The Inverse Trigonometric Functions (Continued) ............................................................... 895
8.3 Trigonometric Equations ....................................................................................................... 907
8.4 Trigonometric Identities ........................................................................................................ 928
8.5 Sum and Difference Formulas ............................................................................................... 941
8.6 Double-angle and Half-angle Formulas................................................................................. 966
8.7 Product-to-Sum and Sum-to-Product Formulas .................................................................... 994
Chapter Review .......................................................................................................................... 1007
Chapter Test ................................................................................................................................ 1022
Cumulative Review .................................................................................................................... 1027
Chapter Projects .......................................................................................................................... 1033
Chapter 9 Applications of Trigonometric Functions
9.1 Applications Involving Right Triangles .............................................................................. 1037
9.2 The Law of Sines ................................................................................................................. 1045
9.3 The Law of Cosines ............................................................................................................. 1060
9.4 Area of a Triangle ................................................................................................................ 1072
9.5 Simple Harmonic Motion; Damped Motion; Combining Waves ........................................ 1082
Chapter Review .......................................................................................................................... 1092
Chapter Test ................................................................................................................................ 1098
Cumulative Review .................................................................................................................... 1101
Chapter Projects .......................................................................................................................... 1107
Chapter 10 Polar Coordinates; Vectors
10.1 Polar Coordinates............................................................................................................... 1111
10.2 Polar Equations and Graphs............................................................................................... 1120
10.3 The Complex Plane; De Moivre’s Theorem ...................................................................... 1149
10.4 Vectors ............................................................................................................................... 1163
10.5 The Dot Product ................................................................................................................. 1176
Chapter Review .......................................................................................................................... 1182
Chapter Test ................................................................................................................................ 1190
Cumulative Review .................................................................................................................... 1194
Chapter Projects .......................................................................................................................... 1196
v
Copyright © 2025 Pearson Education, Inc.
,Chapter 11 Analytic Geometry
11.2 The Parabola ...................................................................................................................... 1199
11.3 The Ellipse ......................................................................................................................... 1215
11.4 The Hyperbola ................................................................................................................... 1232
11.5 Rotation of Axes; General Form of a Conic ...................................................................... 1252
11.6 Polar Equations of Conics ................................................................................................. 1265
11.7 Plane Curves and Parametric Equations ............................................................................ 1274
Chapter Review .......................................................................................................................... 1289
Chapter Test ................................................................................................................................ 1298
Cumulative Review .................................................................................................................... 1303
Chapter Projects .......................................................................................................................... 1305
Chapter 12 Systems of Equations and Inequalities
12.1 Systems of Linear Equations: Substitution and Elimination ............................................. 1309
12.2 Systems of Linear Equations: Matrices ............................................................................. 1332
12.3 Systems of Linear Equations: Determinants...................................................................... 1356
12.4 Matrix Algebra................................................................................................................... 1370
12.5 Partial Fraction Decomposition ......................................................................................... 1389
12.6 Systems of Nonlinear Equations ........................................................................................ 1407
12.7 Systems of Inequalities ...................................................................................................... 1435
12.8 Linear Programming .......................................................................................................... 1450
Chapter Review .......................................................................................................................... 1464
Chapter Test ................................................................................................................................ 1479
Cumulative Review .................................................................................................................... 1487
Chapter Projects .......................................................................................................................... 1491
Chapter 13 Sequences; Induction; the Binomial Theorem
13.1 Sequences .......................................................................................................................... 1493
13.2 Arithmetic Sequences ........................................................................................................ 1503
13.3 Geometric Sequences; Geometric Series ........................................................................... 1512
13.4 Mathematical Induction ..................................................................................................... 1524
13.5 The Binomial Theorem ...................................................................................................... 1533
Chapter Review .......................................................................................................................... 1540
Chapter Test ................................................................................................................................ 1544
Cumulative Review .................................................................................................................... 1547
Chapter Projects .......................................................................................................................... 1550
vi
Copyright © 2025 Pearson Education, Inc.
,Chapter 14 Counting and Probability
14.1 Counting ............................................................................................................................ 1553
14.2 Permutations and Combinations ........................................................................................ 1556
14.3 Probability.......................................................................................................................... 1561
Chapter Review .......................................................................................................................... 1568
Chapter Test ................................................................................................................................ 1570
Cumulative Review .................................................................................................................... 1571
Chapter Projects .......................................................................................................................... 1574
Appendix Graphing Utilities
Section 1 The Viewing Rectangle ............................................................................................. 1577
Section 2 Using a Graphing Utility to Graph Equations ........................................................... 1578
Section 3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry ................. 1583
Section 5 Square Screens ........................................................................................................... 1585
vii
Copyright © 2025 Pearson Education, Inc.
,
