# Algebra & Trigonometry, 4th edition

Published by Pearson (February 22, 2024) © 2025

**Kirk Trigsted**University of Idaho

## MyLab

- Reach every student with personalized support
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## eTextbook

- Anytime, anywhere learning with the Pearson+ app
- Easy-to-use search, navigation and notebook
- Simpler studying with flashcards

For courses in Algebra & Trigonometry.

### Methodical guidance helps students succeed

**Algebra & Trigonometry with Interactive Assignments** engages and holds students accountable for their learning beyond the classroom, using a unique customizable learning environment pioneered by the author. This purposeful blend of videos, text, interactive figures, interactive assignments and other resources carefully introduces concepts and skills to build students’ confidence and capability.

The completely digital **4th Edition **immerses students in new, MyLab**®**-based Interactive Assignments that encourage active learning and participation. Additional revision features include new GeoGebra Graphing Exercises, a new standalone eTextbook, new corequisite content and assessments, and much more.

### Hallmark features of this title

- The
**Guided Notebook**has been updated to engage the student in active learning of key definitions and examples for each section and follows the new version of the eTextbook (editable version included). **GeoGebra Graphing****Exercises**allow students to directly manipulate graphs as they would by hand, to better assess their understanding of graphical concepts.**Corequisite and Integrated Review Resources****:**Corequisite resources are now built in, with expanded review content in Chapter R and diagnostic assessments of prerequisite skills that can be personalized for student needs.

### New and updated features of this title

**New**I**nteractive Assignments:**Customizable for each chapter and section, this new learning environment within MyLab Math encourages students to “read a little, watch a little, do a little” to develop deeper conceptual connections, while giving instructors a means to hold them accountable for their learning.**Updated****Interactive****eTexbook**: This innovative and intuitive new eTextbook experience offers dynamic resources to help students make the most of their studying.**New GeoGebra Graphing Exercises****:**A new way to assess students' understanding of graphical concepts, these exercises are directly manipulatable, auto-graded, and simulate a pen-to-paper experience that goes beyond traditional sliders and multiple-choice questions to better prepare students for graphing by hand.**New Videos****:**800+ new accessible videos are included within the eTextbook, incorporating hundreds of worked-out examples and interactive figures.**New Concept Check Exercises****:**Paired with eTextbook or video resources, these exercises help instructors assess students’ understanding of previously covered content. Strategically placed after definitions and key concepts within the Interactive Assignments, these exercises can also be included on separate instructor-created assignments to ensure students grasp the concepts required to succeed.**New Integrated Corequisite and Integrated Review Resources:**Corequisite resources are now built in, with expanded review content in Chapter R and diagnostic assessments of prerequisite skills that can be personalized for student needs.

### Features of MyLab Math for the 4th Edition

**New**I**nteractive Assignments:**Customizable for each chapter and section, this new learning environment within MyLab Math encourages students to “read a little, watch a little, do a little” to develop deeper conceptual connections, while giving instructors a means to hold them accountable for their learning.**Updated Interactive eTexbook**: This innovative and intuitive new eTextbook experience offers dynamic resources to help students make the most of their studying.**New GeoGebra Graphing Exercises:**A new way to assess students' understanding of graphical concepts, these exercises are directly manipulatable, auto-graded, and simulate a pen-to-paper experience that goes beyond traditional sliders and multiple-choice questions to better prepare students for graphing by hand.**New Videos:**800+ new accessible videos are included within the eTextbook, incorporating hundreds of worked-out examples and interactive figures.**New Concept Check Exercises:**Paired with eTextbook or video resources, these exercises help instructors assess students’ understanding of content covered previously. Strategically placed after definitions and key concepts within the Interactive Assignments, these exercises can also be included on separate instructor created assignments to ensure students grasp the concepts required to succeed.**New Integrated Corequisite and Integrated Review Resources:**Corequisite resources are now built in, with expanded review content in Chapter R and diagnostic assessments of prerequisite skills that can be personalized for student needs. If not needed, all corequisite materials can be hidden or skipped.

### Features of Pearson+ eTextbook for the 4th Edition

**UPDATED: Reformatted, more student-friendly eTextbook:**- adapts to whatever device a student uses
- is easier to scroll and page through, and contains less information on screen at a time
- allows for highlights, notes and bookmarks
- almost all videos are now playable right from within the eTextbook.

**NEW: The Instructor eTextbook**makes it easy for instructors to peruse the book and use it for planning purposes. There is also a**Print Reference version**of the Instructor eTextbook for those who prefer to use a physical book to plan for classes.

### R. Review Chapter

- R.1 Real Numbers
- R.2 A Review of Fractions and the Order of Operations
- R.3 The Properties of Integer Exponents
- R.4 Radicals and Rational Exponents
- R.5 Polynomials
- R.6 Operations with Radicals
- R.7 Factoring Polynomials
- R.8 Rational Expressions
- R.9 The Addition and Multiplication Properties of Equality
- Chapter Summary

### 1. Equations, Inequalities, and Applications

- 1.1 Linear and Rational Equations
- 1.2 Applications of Linear Equations and Rational Equations
- 1.3 Complex Numbers
- 1.4 Quadratic Equations
- 1.5 Applications of Quadratic Equations
- 1.6 Other Types of Equations
- 1.7 Linear Inequalities in One Variable
- 1.8 Absolute Value Equations and Inequalities
- 1.9 Polynomial and Rational Inequalities
- Chapter Summary

### 2. The Rectangular Coordinate System, Lines, and Circles

- 2.1 The Rectangular Coordinate System
- 2.2 Circles
- 2.3 Lines
- 2.4 Parallel and Perpendicular Lines
- Chapter Summary

### 3. Functions

- 3.1 Relations and Functions
- 3.2 Properties of a Function's Graph
- 3.3 Graphs of Basic Functions; Piecewise Functions
- 3.4 Transformations of Functions
- 3.5 The Algebra of Functions; Composite Functions
- 3.6 One-to-One Functions; Inverse Functions
- Chapter Summary

### 4. Polynomial and Rational Functions

- 4.1 Quadratic Functions
- 4.2 Applications and Modeling of Quadratic Functions
- 4.3 The Graphs of Polynomial Functions
- 4.4 Synthetic Division; The Remainder and Factor Theorems
- 4.5 The Zeros of Polynomial Functions; The Fundamental Theorem of Algebra
- 4.6 Rational Functions and Their Graphs
- 4.7 Variation
- Chapter Summary

### 5. Exponential and Logarithmic Functions and Equations

- 5.1 Exponential Functions
- 5.2 Logarithmic Functions
- 5.3 Properties of Logarithms
- 5.4 Exponential and Logarithmic Equations
- 5.5 Applications of Exponential and Logarithmic Functions
- Chapter Summary

### 6. An Introduction to Trigonometric Functions

- 6.1 An Introduction to Angles: Degree and Radian Measure
- 6.2 Applications of Radian Measure
- 6.3 Triangles
- 6.4 Right Triangle Trigonometry
- 6.5 Trigonometric Functions of General Angles
- 6.6 The Unit Circle
- Chapter Summary

### 7. The Graphs of Trigonometric Functions

- 7.1 The Graphs of Sine and Cosine
- 7.2 More on Graphs of Sine and Cosine; Phase Shift
- 7.3 The Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
- 7.4 Inverse Trigonometric Functions I
- 7.5 Inverse Trigonometric Functions II
- Chapter Summary

### 8. Trigonometric Identities, Formulas, and Equations

- 8.1 Trigonometric Identities
- 8.2 The Sum and Difference Formulas
- 8.3 The Double-Angle and Half-Angle Formulas
- 8.4 The Product-to-Sum and Sum-to-Product Formulas
- 8.5 Trigonometric Equations
- Chapter Summary

### 9. Applications of Trigonometry

- 9.1 Right Triangle Applications
- 9.2 The Law of Sines
- 9.3 The Law of Cosines
- 9.4 Area of Triangles
- Chapter Summary

### 10. Polar Equations, Complex Numbers, and Vectors

- 10.1 Polar Coordinates and Polar Equations
- 10.2 Graphing Polar Equations
- 10.3 Complex Numbers in Polar Form; DeMoivre's Theorem
- 10.4 Vectors
- 10.5 The Dot Product
- Chapter Summary

### 11. Conic Sections and Parametric Equations

- Introduction to Conic Sections
- 11.1 The Parabola
- 11.2 The Ellipse
- 11.3 The Hyperbola
- 11.4 Conic Sections in Polar Form
- 11.5 Parametric Equations
- Chapter Summary

### 12. Systems of Equations and Inequalities

- 12.1 Solving Systems of Linear Equations in Two Variables
- 12.2 Solving Systems of Linear Equations in Three Variables Using the Elimination Method
- 12.3 Solving Systems of Linear Equations in Three Variables Using Gaussian Elimination and Gauss-Jordan Elimination
- 12.4 Partial Fraction Decomposition
- 12.5 Systems of Nonlinear Equations
- 12.6 Systems of Inequalities
- Chapter Summary

### 13. Matrices

- 13.1 Matrix Operations
- 13.2 Inverses of Matrices and Matrix Equations
- 13.3 Determinants and Cramer's Rule
- Chapter Summary

### 14. Sequences and Series; Counting and Probability

- 14.1 Introduction to Sequences and Series
- 14.2 Arithmetic Sequences and Series
- 14.3 Geometric Sequences and Series
- 14.4 The Binomial Theorem
- 14.5 Mathematical Induction
- 14.6 The Theory of Counting
- 14.7 An Introduction to Probability
- Chapter Summary

### Appendices

- A: Degree, Minute, A Second Form and Degree Decimal Form
- B: Conic Section Proofs
- B.1 Parabola Proofs
- B.2 Ellipse Proofs
- B.3 Hyperbola Proofs

### About our author

**Kirk Trigsted** taught mathematics at the University of Idaho from 1996 to 2020 and is now emeritus faculty. Kirk was the director of one the first Emporium model math labs in the United States for 20 years. He was inspired by his students to develop the first digital-first Algebra & Trigonometry product ever developed in MyLab Math; the first edition was launched in 2008. Now, 16 years later, there are Trigsted titles ranging from Pre-Algebra to Precalculus. Kirk has been married for 27 years and has 4 children.

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