SOLUTIONS MANUAL
TIM BRITT
ALGEBRA AND
TRIGONOMETRY
TWELFTH EDITION
Michael Sullivan
, 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.
TIM BRITT
ALGEBRA AND
TRIGONOMETRY
TWELFTH EDITION
Michael Sullivan
, 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.
