# Investigating College Algebra and Trigonometry with Technology with Trigonometry Chapters 12 and 13 Student CD-Rom and Access Code Card

# Investigating College Algebra and Trigonometry with Technology with Trigonometry Chapters 12 and 13 Student CD-Rom and Access Code Card

ISBN: 978-0-470-41332-6

Jun 2008

698 pages

$228.95

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## Description

Technology and an investigative pedagogy are powerful tools for fostering in-depth understanding of mathematics concepts.*Investigating College Algebra and Trigonometry with Technology*presents the core concepts of College Algebra and Trigonometry within a technology-oriented, data-driven, applied framework that embraces investigative, collaborative learning. With this text

*,*students use graphing calculators, and optionally Microsoft® Excel and other technologies, to explore patterns and to make, test, and generalize conjectures. Most importantly, investigations—which engage students in analysis of real-world data—promote collaboration and bring relevance to the mathematics students are learning.

The American Mathematical Association of Two-Year Colleges (AMATYC) and the Mathematical Association of America’s Committee on Undergraduate Programs in Mathematics (CUPM) set standards for meaningful and relevant mathematics and the refocusing of the College Algebra and Trigonometry course. This text follows their recommendations for using technology, experiencing varied applications of mathematics, and having opportunities to solve problems, reason critically, exhibit persistence, and test conjectures through investigations and data analysis.

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Annotated Contents vii

Preface xix

To the Student xxvii

To the Instructor xxix

Acknowledgments xxxi

Chapter 1: Problem Solving 1

1.1 Pictures, Graphs, and Diagrams 2

1.2 Symbolic Representation 9

1.3 Organizing Information 16

1.4 Measures of Central Tendency and Box Plots 24

1.5 Measures of Spread 31

Chapter 1 Review 45

Chapter 2: Patterns and Recursion 53

2.1 Recursively Defined Sequences 54

2.2 Modeling Growth and Decay 64

2.3 A First Look at Limits 71

2.4 Graphing and Sequences 77

2.5 Loans and Investments 86

Chapter 2 Review 99

Chapter 3: Linear Models and Systems 103

3.1 Linear Equations 104

3.2 Revisiting Slope 111

3.3 Fitting a Line to Data 119

3.4 Linear Systems 127

3.5 Substitution and Elimination 133

Chapter 3 Review 142

Chapter 4: Functions, Relations, and Transformations 148

4.1 Interpreting Graphs 149

4.2 Function Notation 155

4.3 Lines in Motion 163

4.4 Translations and the Quadratic Family 170

4.5 Reflections and the Square Root Family 177

4.6 Stretches and Shrinks and the Absolute Value Family 184

4.7 Transformations and the Circle Family 192

4.8 Compositions of Functions 200

Chapter 4 Review 211

Chapter 5: Exponential, Power, and Logarithmic Functions 215

5.1 The Exponential Function 216

5.2 Properties of Exponents 223

5.3 Fractional Exponents and Roots 229

5.4 Applications of Power Equations 239

5.5 Building Inverses of Functions 243

5.6 The Logarithmic Function 251

5.7 Properties of Logarithms 257

5.8 Applications of Logarithms 264

Chapter 5 Review 273

Chapter 6: Quadratic and Other Polynomial Functions 277

6.1 Polynomial Degree and Finite Differences 278

6.2 Equivalent Quadratic Forms 286

6.3 Completing the Square 294

6.4 The Quadratic Formula 301

6.5 Complex Numbers 307

6.6 Factoring Polynomials 314

6.7 Higher-Degree Polynomials 320

6.8 More about Finding Solutions 327

Chapter 6 Review 337

Chapter 7: Matrices and Linear Systems 341

7.1 Matrix Representations 342

7.2 Matrix Operations 349

7.3 The Row Reduction Method 360

7.4 Solving Systems with Inverse Matrices 368

7.5 Systems of Linear Inequalities 378

7.6 Linear Programming 385

Chapter 7 Review 395

Chapter 8: Parametric Equations and Trigonometry 401

8.1 Graphing Parametric Equations 402

8.2 Converting Parametric to Nonparametric Equations 411

8.3 Right Triangle Trigonometry 418

8.4 Using Trigonometry to Set a Course 431

8.5 Projectile Motion 438

8.6 The Law of Sines 445

8.7 The Law of Cosines 453

Chapter 8 Review 462

Chapter 9: Conic Sections and Rational Functions 466

9.1 Using the Distance Formula 467

9.2 Circles and Ellipses 474

9.3 Parabolas 486

9.4 The Hyperbola 494

9.5 Nonlinear Systems of Equations 503

9.6 Introduction to Rational Functions 508

9.7 Graphs of Rational Functions 516

9.8 Operations with Rational Expressions 524

Chapter 9 Review 533

Chapter 10: Series 539

10.1 Arithmetic Series 540

10.2 Infinite Geometric Series 547

10.3 Partial Sums of Geometric Series 554

Chapter 10 Review 562

Chapter 11: Probability 565

11.1 Randomness and Probability 566

11.2 Counting Outcomes and Tree Diagrams 577

11.3 Mutually Exclusive Events and Venn Diagrams 586

11.4 Random Variables and Expected Value 593

11.5 Permutations and Probability 600

11.6 Combinations and Probability 607

11.7 The Binomial Theorem and Pascal’s Triangle 613

Chapter 11 Review 623

Chapter 12: Trigonometric Functions (on the Student CD)

12.1 Defining the Circular Function

12.2 Radian Measure and Arc Length

12.3 Graphing Trigonometric Functions

12.4 Inverses of Trigonometric Functions

12.5 Polar Coordinates

Chapter 13: Trigonometric Identities (on the Student CD)

13.1 Fundamental Trigonometric Identities

13.2 Sum and Difference Identities

13.3 Double- and Half-Angle Identities

13.4 Modeling with Trigonometric Equations

13.5 Solving Trigonometric Equations

Chapter 13 Review

Selected Answers 627

Glossary 675

Photo Credits 687

Index 688

Resources on the Student CD

Prerequisite Review: Numbers and Figures • Operations on Numbers •

The Ideas that Motivate Algebra • Exponents • Radicals • Polynomials •

Factoring Polynomials • Rational Expressions

Chapter 12 Trigonometric Functions

Chapter 13 Trigonometric Identities

Calculator Notes

Microsoft® Excel Notes

Interactive Spreadsheets for Excel Explorations

Preface xix

To the Student xxvii

To the Instructor xxix

Acknowledgments xxxi

Chapter 1: Problem Solving 1

1.1 Pictures, Graphs, and Diagrams 2

1.2 Symbolic Representation 9

1.3 Organizing Information 16

1.4 Measures of Central Tendency and Box Plots 24

1.5 Measures of Spread 31

Chapter 1 Review 45

Chapter 2: Patterns and Recursion 53

2.1 Recursively Defined Sequences 54

2.2 Modeling Growth and Decay 64

2.3 A First Look at Limits 71

2.4 Graphing and Sequences 77

2.5 Loans and Investments 86

Chapter 2 Review 99

Chapter 3: Linear Models and Systems 103

3.1 Linear Equations 104

3.2 Revisiting Slope 111

3.3 Fitting a Line to Data 119

3.4 Linear Systems 127

3.5 Substitution and Elimination 133

Chapter 3 Review 142

Chapter 4: Functions, Relations, and Transformations 148

4.1 Interpreting Graphs 149

4.2 Function Notation 155

4.3 Lines in Motion 163

4.4 Translations and the Quadratic Family 170

4.5 Reflections and the Square Root Family 177

4.6 Stretches and Shrinks and the Absolute Value Family 184

4.7 Transformations and the Circle Family 192

4.8 Compositions of Functions 200

Chapter 4 Review 211

Chapter 5: Exponential, Power, and Logarithmic Functions 215

5.1 The Exponential Function 216

5.2 Properties of Exponents 223

5.3 Fractional Exponents and Roots 229

5.4 Applications of Power Equations 239

5.5 Building Inverses of Functions 243

5.6 The Logarithmic Function 251

5.7 Properties of Logarithms 257

5.8 Applications of Logarithms 264

Chapter 5 Review 273

Chapter 6: Quadratic and Other Polynomial Functions 277

6.1 Polynomial Degree and Finite Differences 278

6.2 Equivalent Quadratic Forms 286

6.3 Completing the Square 294

6.4 The Quadratic Formula 301

6.5 Complex Numbers 307

6.6 Factoring Polynomials 314

6.7 Higher-Degree Polynomials 320

6.8 More about Finding Solutions 327

Chapter 6 Review 337

Chapter 7: Matrices and Linear Systems 341

7.1 Matrix Representations 342

7.2 Matrix Operations 349

7.3 The Row Reduction Method 360

7.4 Solving Systems with Inverse Matrices 368

7.5 Systems of Linear Inequalities 378

7.6 Linear Programming 385

Chapter 7 Review 395

Chapter 8: Parametric Equations and Trigonometry 401

8.1 Graphing Parametric Equations 402

8.2 Converting Parametric to Nonparametric Equations 411

8.3 Right Triangle Trigonometry 418

8.4 Using Trigonometry to Set a Course 431

8.5 Projectile Motion 438

8.6 The Law of Sines 445

8.7 The Law of Cosines 453

Chapter 8 Review 462

Chapter 9: Conic Sections and Rational Functions 466

9.1 Using the Distance Formula 467

9.2 Circles and Ellipses 474

9.3 Parabolas 486

9.4 The Hyperbola 494

9.5 Nonlinear Systems of Equations 503

9.6 Introduction to Rational Functions 508

9.7 Graphs of Rational Functions 516

9.8 Operations with Rational Expressions 524

Chapter 9 Review 533

Chapter 10: Series 539

10.1 Arithmetic Series 540

10.2 Infinite Geometric Series 547

10.3 Partial Sums of Geometric Series 554

Chapter 10 Review 562

Chapter 11: Probability 565

11.1 Randomness and Probability 566

11.2 Counting Outcomes and Tree Diagrams 577

11.3 Mutually Exclusive Events and Venn Diagrams 586

11.4 Random Variables and Expected Value 593

11.5 Permutations and Probability 600

11.6 Combinations and Probability 607

11.7 The Binomial Theorem and Pascal’s Triangle 613

Chapter 11 Review 623

Chapter 12: Trigonometric Functions (on the Student CD)

12.1 Defining the Circular Function

12.2 Radian Measure and Arc Length

12.3 Graphing Trigonometric Functions

12.4 Inverses of Trigonometric Functions

12.5 Polar Coordinates

Chapter 13: Trigonometric Identities (on the Student CD)

13.1 Fundamental Trigonometric Identities

13.2 Sum and Difference Identities

13.3 Double- and Half-Angle Identities

13.4 Modeling with Trigonometric Equations

13.5 Solving Trigonometric Equations

Chapter 13 Review

Selected Answers 627

Glossary 675

Photo Credits 687

Index 688

Resources on the Student CD

Prerequisite Review: Numbers and Figures • Operations on Numbers •

The Ideas that Motivate Algebra • Exponents • Radicals • Polynomials •

Factoring Polynomials • Rational Expressions

Chapter 12 Trigonometric Functions

Chapter 13 Trigonometric Identities

Calculator Notes

Microsoft® Excel Notes

Interactive Spreadsheets for Excel Explorations

- Discovery-based Investigations provide in-depth contextual content, real-life data, and the integration of technology to let students explore a problem before solving it
- Students analyze data, which they are given or gather themselves, to make sense of the mathematical relationships they observe
- Examples are fully worked out and include reasons that justify the process
- Support the use of graphing calculators, which let students easily manipulate large amounts of data and see the “big picture” of the math being used
- Optional interactive Explorations, included on the Student CD, use Microsoft® Excel to build spreadsheets for Activities in which students investigate algebra concepts