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SOLUTIONS MANUAL
TIM BRITT
ALGEBRA AND
TRIGONOMETRY
TWELFTH EDITION
Michael Sullivan 1 / 4
Copyright © 2025 Pearson Education, Inc.
iii 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
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iv
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
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v
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
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