# Precalculus, 3rd Edition

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# Precalculus, 3rd Edition

ISBN: ES8-1-119-33951-9

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WileyPLUS improves outcomes with robust practice problems and feedback, fosters engagement with course content and educational videos, and gives students the flexibility to increase confidence as they learn and prepare outside of class.

## Description

Precalculus was developed to create a program that seamlessly align with how teachers teach and fully supports student learning. Cynthia Young’s goal was to create an intuitive, supportive product for students without sacrificing the rigor needed for true conceptual understanding and preparation for Calculus. Precalculus helps bridge the gap between in-class work and homework by mirroring the instructor voice outside the classroom through pedagogical features.

## Related Resources

##### Instructor

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##### Student

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[0] Review: Equations and Inequalities 2

0.1 Linear Equations 4

0.3 Other Types of Equations 31

0.4 Inequalities 45

0.5 Graphing Equations 60

0.6 Lines 73

0.7 Modeling Variation 86

0.8 Linear Regression: Best Fit (Online Only)

Review 94

Review Exercises 96

Practice Test 99

[1] Functions and Their Graphs 100

1.1 Functions 102

1.2 Graphs of Functions 118

1.3 Graphing Techniques: Transformations 138

1.4 Combining Functions 151

1.5 One-To-One Functions and Inverse Functions 161

Review 177

Review Exercises 179

Practice Test 182

[2] Polynomial and Rational Functions 184

2.2 Polynomial Functions of Higher Degree 201

2.3 Dividing Polynomials 214

2.4 The Real Zeros of a Polynomial Function 222

2.5 Complex Zeros: The Fundamental Theorem of Algebra 238

2.6 Rational Functions 247

Review 266

Review Exercises 269

Practice Test 272

Cumulative Test 273

[3] Exponential and Logarithmic Functions 274

3.1 Exponential Functions and Their Graphs 276

3.2 Logarithmic Functions and Their Graphs 291

3.3 Properties of Logarithms 306

3.4 Exponential and Logarithmic Equations 315

3.5 Exponential and Logarithmic Models 326

Review 337

Review Exercises 339

Practice Test 342

Cumulative Test 343

[4] Trigonometric Functions of Angles 344

4.1 Angle Measure 346

4.2 Right Triangle Trigonometry 363

4.3 Trigonometric Functions of Angles 381

4.4 The Law of Sines 399

4.5 The Law of Cosines 413

Review 425

Review Exercises 428

Practice Test 430

Cumulative Test 431

[5] Trigonometric Functions of Real Numbers 432

5.1 Trigonometric Functions: The Unit Circle Approach 434

5.2 Graphs of Sine and Cosine Functions 443

5.3 Graphs of Other Trigonometric Functions 473

Review 490

Review Exercises 494

Practice Test 496

Cumulative Test 497

[6] Analytic Trigonometry 498

6.1 Verifying Trigonometric Identities 500

6.2 Sum and Difference Identities 510

6.3 Double-Angle and Half-Angle Identities 523

6.4 Product-To-Sum and Sum-To-Product Identities 539

6.5 Inverse Trigonometric Functions 547

6.6 Trigonometric Equations 568

Review 584

Review Exercises 588

Practice Test 592

Cumulative Test 593

[7] Vectors, The Complex Plane, and Polar Coordinates 594

7.1 Vectors 596

7.2 The Dot Product 610

7.3 Polar (Trigonometric) Form of Complex Numbers 618

7.4 Products, Quotients, Powers, and Roots of Complex Numbers 627

7.5 Polar Coordinates and Graphs of Polar Equations 638

Review 653

Review Exercises 656

Practice Test 658

Cumulative Test 659

[8] Systems of Linear Equations and Inequalities 660

8.1 Systems of Linear Equations In Two Variables 662

8.2 Systems of Linear Equations In Three Variables 678

8.3 Systems of Linear Equations and Matrices 691

8.4 Matrix Algebra 714

8.5 The Determinant of a Square Matrix and Cramer’s Rule 739

8.6 Partial Fractions 753

8.7 Systems of Linear Inequalities In Two Variables 765

Review 780

Review Exercises 784

Practice Test 788

Cumulative Test 789

[9] Conics, Systems of Nonlinear Equations and Inequalities, and Parametric Equations 790

9.1 Conic Basics 792

9.2 The Parabola 795

9.3 The Ellipse 808

9.4 The Hyperbola 821

9.5 Systems of Nonlinear Equations 834

9.6 Systems of Nonlinear Inequalities 846

9.7 Rotation of Axes 856

9.8 Polar Equations of Conics 866

9.9 Parametric Equations and Graphs 876

Review 884

Review Exercises 887

Practice Test 890

Cumulative Test 891

Applications Index 945

Subject Index 948

[10] Sequences and Series (Online Only)

10.1 Sequences and Series

10.2 Arithmetic Sequences and Series

10.3 Geometric Sequences and Series

10.4 Mathematical Induction

10.5 The Binomial Theorem

Review

Review Exercises

Practice Test

Cumulative Test

[11] Limits: A Preview to Calculus (Online Only)

11.1 Introduction to Limits: Estimating Limits Numerically and Graphically

11.2 Techniques for Finding Limits

11.3 Tangent Lines and Derivatives

11.4 Limits at Infinity; Limits of Sequences

11.5 Finding The Area Under a Curve

Review

Review Exercises

Practice Test

Cumulative Test

Appendix Prerequisites and Review (Online Only)

A.1 Real Numbers

A.2 Integer Exponents and Scientific Notation

A.3 Polynomials: Basic Operations

A.4 Factoring Polynomials

A.5 Rational Expressions

A.7 Complex Numbers

Review

Review Exercises

Practice Test

• New Interactive Animations: Based on Cynthia Young’s lectures the interactive animations were created to help students build a solid conceptual understanding of specific learning objectives by delivering learning content integrated with ed interactive questions to guide and solidify students’ foundational knowledge of the topic.
•  New Math Maple questions: These question types are HTML5 based and fully mobile to enable functionality demanded by the modern student.
•  ORION Algebra Refresher Module:  Every student comes to class with a different set of mastered prerequisite skills. The Algebra Refresher Module helps students and instructors identify prerequisite knowledge gaps and provides adaptive remediation to prepare all students for success.
• Clear, Concise, and Inviting Writing: This program provides material in a student centric, clear manner, presented in a layout designed to reduce math anxiety.
• Author Lecture Videos: Video lectures provides an opening overview for each chapter and section level worked example videos for the topics students find the most challenging.
• Parallel Words and Math: This course reverses the common presentation of examples by placing the explanation in words on the left and the mathematics problem on the right. This makes it easier for students to read through examples as the material flows more naturally and appears as information is commonly presented in lectures.
• Catch the Mistake exercises: “Catch the Mistake” exercises included in each course section put students in the role of the instructor grading homework, which increases the students’ depth of understanding and reinforces what they have learned.
•  Your Turn problems: Students are frequently asked to work a problem immediately following an example to reinforce and check their understanding. This feature helps students build confidence as they progress in the course. These problems are ideal in-class activities that prepare students for their homework assignments.
• Correct vs. Incorrect examples: In addition to standard examples, some problems are worked both correctly and incorrectly to highlight common errors students make. Counter examples like these are an effective learning approach for many students.
•  Modeling Our World projects: Found online for every course section, these projects engage students by using real world data to model mathematical applications found in everyday life.
•  Cumulative Section Tests: Cumulative tests are included at the end of each course section to assess and improve students' retention of material.