Soluition Manual – Algebra and Trigonometry, 11th edition (Sullivan, 2019)

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Soluition Manual – Algebra and Trigonometry, 11th edition (Sullivan, 2019)

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 ………………………. 87

1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations …………………………. 93

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 ………………………………………………………………………………………………………………… 154

Chapter Projects …………………………………………………………………………………………………………… 156

Chapter 2 Graphs

2.1 The Distance and Midpoint Formulas ……………………………………………………………………….. 157

2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry……………………………………… 170

2.3 Lines …………………………………………………………………………………………………………………….. 184

2.4 Circles ………………………………………………………………………………………………………………….. 202

2.5 Variation ……………………………………………………………………………………………………………….. 216

Chapter Review ……………………………………………………………………………………………………………. 222

Chapter Test ………………………………………………………………………………………………………………… 228

Cumulative Review ………………………………………………………………………………………………………. 230

Chapter Project …………………………………………………………………………………………………………….. 232

Chapter 3 Functions and Their Graphs

3.1 Functions ………………………………………………………………………………………………………………. 233

3.2 The Graph of a Function …………………………………………………………………………………………. 251

3.3 Properties of Functions……………………………………………………………………………………………. 260

3.4 Library of Functions; Piecewise-defined Functions …………………………………………………….. 277

3.5 Graphing Techniques: Transformations …………………………………………………………………….. 289

3.6 Mathematical Models: Building Functions ………………………………………………………………… 307

Chapter Review ……………………………………………………………………………………………………………. 315

Chapter Test ………………………………………………………………………………………………………………… 322

Cumulative Review ………………………………………………………………………………………………………. 325

Chapter Projects …………………………………………………………………………………………………………… 329

Chapter 4 Linear and Quadratic Functions

4.1 Properties of Linear Functions and Linear Models ……………………………………………………… 331

4.2 Building Linear Functions from Data ……………………………………………………………………….. 342

4.3 Quadratic Functions and Their Properties ………………………………………………………………….. 348

4.4 Build Quadratic Models from Verbal Descriptions and from Data ……………………………….. 371

4.5 Inequalities Involving Quadratic Functions ……………………………………………………………….. 379

Chapter Review ……………………………………………………………………………………………………………. 399

Chapter Test ………………………………………………………………………………………………………………… 407

Cumulative Review ………………………………………………………………………………………………………. 409

Chapter Projects …………………………………………………………………………………………………………… 412

Chapter 5 Polynomial and Rational Functions

5.1 Polynomial Functions ……………………………………………………………………………………………… 415

5.2 Graphing Polynomial Functions; Models ……………………………………………………………………. 425

5.3 Properties of Rational Functions ………………………………………………………………………………. 441

5.4 The Graph of a Rational Function …………………………………………………………………………….. 451

5.5 Polynomial and Rational Inequalities ………………………………………………………………………… 507

5.6 The Real Zeros of a Polynomial Function ………………………………………………………………….. 528

5.7 Complex Zeros; Fundamental Theorem of Algebra …………………………………………………….. 559

Chapter Review ……………………………………………………………………………………………………………. 568

Chapter Test ………………………………………………………………………………………………………………… 583

Cumulative Review ………………………………………………………………………………………………………. 587

Chapter Projects …………………………………………………………………………………………………………… 592

Chapter 6 Exponential and Logarithmic Functions

6.1 Composite Functions ………………………………………………………………………………………………. 594

6.2 One-to-One Functions; Inverse Functions …………………………………………………………………. 612

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 ……………………………………………………………………………………………………. 706

6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth

and Decay Models ……………………………………………………………………………………………….. 714

6.9 Building Exponential, Logarithmic, and Logistic Models from Data …………………………….. 723

Chapter Review ……………………………………………………………………………………………………………. 729

Chapter Test ………………………………………………………………………………………………………………… 741

Cumulative Review ………………………………………………………………………………………………………. 745

Chapter Projects …………………………………………………………………………………………………………… 748

Chapter 7 Trigonometric Functions

7.1 Angles, Arc Length, and Circular Motion ………………………………………………………………….. 751

7.2 Right Triangle Trigonometry …………………………………………………………………………………… 760

7.3 Computing the Values of Trigonometric Functions of Acute Angles …………………………….. 776

7.4 Trigonometric Functions of Any Angle …………………………………………………………………….. 789

7.5 Unit Circle Approach: Properties of the Trigonometric Functions ………………………………… 805

7.6 Graphs of the Sine and Cosine Functions ………………………………………………………………….. 814

7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions ……………………………… 836

7.8 Phase Shift; Sinusoidal Curve Fitting ……………………………………………………………………….. 846

Chapter Review ……………………………………………………………………………………………………………. 857

Chapter Test ………………………………………………………………………………………………………………… 866

Cumulative Review ………………………………………………………………………………………………………. 870

Chapter Projects …………………………………………………………………………………………………………… 874

Chapter 8 Analytic Trigonometry

8.1 The Inverse Sine, Cosine, and Tangent Functions ………………………………………………………. 877

8.2 The Inverse Trigonometric Functions (Continued) ……………………………………………………… 890

8.3 Trigonometric Equations …………………………………………………………………………………………. 902

8.4 Trigonometric Identities ………………………………………………………………………………………….. 923

8.5 Sum and Difference Formulas ………………………………………………………………………………….. 936

8.6 Double-angle and Half-angle Formulas …………………………………………………………………….. 961

8.7 Product-to-Sum and Sum-to-Product Formulas ………………………………………………………….. 987

Chapter Review ………………………………………………………………………………………………………….. 1000

Chapter Test ………………………………………………………………………………………………………………. 1015

Cumulative Review …………………………………………………………………………………………………….. 1020

Chapter Projects …………………………………………………………………………………………………………. 1026

Chapter 9 Applications of Trigonometric Functions

9.1 Applications Involving Right Triangles …………………………………………………………………… 1030

9.2 The Law of Sines …………………………………………………………………………………………………. 1038

9.3 The Law of Cosines ……………………………………………………………………………………………… 1053

9.4 Area of a Triangle ………………………………………………………………………………………………… 1065

9.5 Simple Harmonic Motion; Damped Motion; Combining Waves …………………………………. 1075

Chapter Review ………………………………………………………………………………………………………….. 1085

Chapter Test ………………………………………………………………………………………………………………. 1091

Cumulative Review …………………………………………………………………………………………………….. 1094

Chapter Projects …………………………………………………………………………………………………………. 1100

Chapter 10 Polar Coordinates; Vectors

10.1 Polar Coordinates ……………………………………………………………………………………………….. 1104

10.2 Polar Equations and Graphs …………………………………………………………………………………. 1113

10.3 The Complex Plane; De Moivre’s Theorem …………………………………………………………… 1143

10.4 Vectors ……………………………………………………………………………………………………………… 1156

10.5 The Dot Product …………………………………………………………………………………………………. 1169

Chapter Review ………………………………………………………………………………………………………….. 1175

Chapter Test ………………………………………………………………………………………………………………. 1183

Cumulative Review …………………………………………………………………………………………………….. 1186

Chapter Projects …………………………………………………………………………………………………………. 1189

Chapter 11 Analytic Geometry

11.2 The Parabola ………………………………………………………………………………………………………. 1193

11.3 The Ellipse ………………………………………………………………………………………………………… 1208

11.4 The Hyperbola ……………………………………………………………………………………………………. 1225

11.5 Rotation of Axes; General Form of a Conic ……………………………………………………………. 1245

11.6 Polar Equations of Conics ……………………………………………………………………………………. 1258

11.7 Plane Curves and Parametric Equations …………………………………………………………………. 1267

Chapter Review ………………………………………………………………………………………………………….. 1282

Chapter Test ………………………………………………………………………………………………………………. 1291

Cumulative Review …………………………………………………………………………………………………….. 1296

Chapter Projects …………………………………………………………………………………………………………. 1298

Chapter 12 Systems of Equations and Inequalities

12.1 Systems of Linear Equations: Substitution and Elimination……………………………………… 1302

12.2 Systems of Linear Equations: Matrices ………………………………………………………………….. 1325

12.3 Systems of Linear Equations: Determinants …………………………………………………………… 1350

12.4 Matrix Algebra …………………………………………………………………………………………………… 1364

12.5 Partial Fraction Decomposition …………………………………………………………………………….. 1383

12.6 Systems of Nonlinear Equations …………………………………………………………………………… 1402

12.7 Systems of Inequalities ………………………………………………………………………………………… 1430

12.8 Linear Programming …………………………………………………………………………………………… 1446

Chapter Review ………………………………………………………………………………………………………….. 1459

Chapter Test ………………………………………………………………………………………………………………. 1474

Cumulative Review …………………………………………………………………………………………………….. 1483

Chapter Projects …………………………………………………………………………………………………………. 1486

Chapter 13 Sequences; Induction; the Binomial Theorem

13.1 Sequences ………………………………………………………………………………………………………….. 1489

13.2 Arithmetic Sequences ………………………………………………………………………………………….. 1499

13.3 Geometric Sequences; Geometric Series ……………………………………………………………….. 1508

13.4 Mathematical Induction ……………………………………………………………………………………….. 1520

13.5 The Binomial Theorem ……………………………………………………………………………………….. 1529

Chapter Review ………………………………………………………………………………………………………….. 1536

Chapter Test ………………………………………………………………………………………………………………. 1540

Cumulative Review …………………………………………………………………………………………………….. 1543

Chapter Projects …………………………………………………………………………………………………………. 1546

Chapter 14 Counting and Probability

14.1 Counting ……………………………………………………………………………………………………………. 1549

14.2 Permutations and Combinations ……………………………………………………………………………. 1552

14.3 Probability …………………………………………………………………………………………………………. 1557

Chapter Review ………………………………………………………………………………………………………….. 1564

Chapter Test ………………………………………………………………………………………………………………. 1566

Cumulative Review …………………………………………………………………………………………………….. 1567

Chapter Projects …………………………………………………………………………………………………………. 1570

Appendix Graphing Utilities

Section 1 The Viewing Rectangle ………………………………………………………………………………… 1573

Section 2 Using a Graphing Utility to Graph Equations ………………………………………………….. 1574

Section 3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry …………….. 1579

Section 5 Square Screens ……………………………………………………………………………………………. 1581