# Algebra and Trigonometry

by Paul Sisson

Algebra and Trigonometry is thoughtfully written with an emphasis on connecting mathematics to the real-world. The content of each chapter is introduced using historical context as a hook, and strategically embedded technology notes ensure students become confident in the use of modern technologies. Expansive exercise sets provide ample opportunity to develop fluency through practice while building conceptual understanding using a variety of tasks from skill- and application-based assessments to critical thinking challenges. Chapter tests and projects ensure students can demonstrate a comprehensive understanding of the curriculum.

This title begins by introducing the student to the concepts of elementary functions and their properties, and then gradually builds the foundation of exponential, logarithmic, and trigonometric functions, the latter of which are developed using both right triangles and the unit circle. Additional topics include polar and parametric equations, vectors in the plane, hyperbolic functions, conic sections, systems of equations, sequences, and series. This title is suitable for college algebra, trigonometry, and precalculus courses.

**Formats:** Software, Textbook, eBook

Product | ISBN |
---|---|

Software + eBook | 978-1-64277-527-3 |

## Table of Contents

- Chapter 1: Fundamental Concepts of Algebra
- 1.1 Real Numbers
- 1.2 The Arithmetic of Algebraic Expressions
- 1.3 Properties of Exponents
- 1.4 Properties of Radicals
- 1.5 Polynomials
- 1.6 Factoring Polynomials
- 1.7 Rational Expressions
- 1.8 Complex Numbers
- Chapter 1 Review

- Chapter 2: Equations and Inequalities in One Variable
- 2.1 Linear Equations in One Variable
- 2.2 Linear Inequalities in One Variable
- 2.3 Quadratic Equations in One Variable
- 2.4 Polynomial and Polynomial-Like Equations in One Variable
- 2.5 Rational Equations in One Variable
- 2.6 Radical Equations in One Variable
- Chapter 2 Review

- Chapter 3: Equations and Inequalities in Two Variables
- 3.1 The Cartesian Coordinate System
- 3.2 Circles
- 3.3 Linear Equations in Two Variables
- 3.4 Slope and Forms of Linear Equations
- 3.5 Parallel and Perpendicular Lines
- 3.6 Linear Inequalities in Two Variables
- Chapter 3 Review

- Chapter 4: Relations, Functions, and Their Graphs
- 4.1 Relations and Functions
- 4.2 Linear Functions
- 4.3 Quadratic Functions
- 4.4 Other Common Functions
- 4.5 Variation and Multivariable Functions
- 4.6 Mathematical Models
- Chapter 4 Review

- Chapter 5: Working with Functions
- 5.1 Transformations of Functions
- 5.2 Properties of Functions
- 5.3 Combining Functions
- 5.4 Inverses of Functions
- Chapter 5 Review

- Chapter 6: Polynomial and Rational Functions
- 6.1 Polynomial Functions and Polynomial Inequalities
- 6.2 Polynomial Division and the Division Algorithm
- 6.3 Locating Real Zeros of Polynomial Functions
- 6.4 The Fundamental Theorem of Algebra
- 6.5 Rational Functions and Rational Inequalities
- Chapter 6 Review

- Chapter 7: Exponential and Logarithmic Functions
- 7.1 Exponential Functions and Their Graphs
- 7.2 Exponential Models
- 7.3 Logarithmic Functions and Their Graphs
- 7.4 Logarithmic Properties and Models
- 7.5 Exponential and Logarithmic Equations
- Chapter 7 Review

- Chapter 8: Trigonometric Functions
- 8.1 Radian and Degree Measure
- 8.2 Trigonometric Functions and Right Triangles
- 8.3 Trigonometric Functions and the Unit Circle
- 8.4 Graphs of Sine and Cosine Functions
- 8.5 Graphs of Other Trigonometric Functions
- 8.6 Inverse Trigonometric Functions
- Chapter 8 Review

- Chapter 9: Trigonometric Identities and Equations
- 9.1 Fundamental Trigonometric Identities
- 9.2 Sum and Difference Identities
- 9.3 Product-Sum Identities
- 9.4 Trigonometric Equations
- Chapter 9 Review

- Chapter 10: Additional Topics in Trigonometry
- 10.1 The Law of Sines
- 10.2 The Law of Cosines
- 10.3 Polar Coordinates and Polar Equations
- 10.4 Parametric Equations
- 10.5 Trigonometric Form of Complex Numbers
- 10.6 Vectors in the Cartesian Plane
- 10.7 The Dot Product
- 10.8 Hyperbolic Functions
- Chapter 10 Review

- Chapter 11: Conic Sections
- 11.1 Ellipses
- 11.2 Parabolas
- 11.3 Hyperbolas
- 11.4 Rotation of Conic Sections
- 11.5 Polar Equations of Conic Sections
- Chapter 11 Review

- Chapter 12: Systems of Equations and Inequalities
- 12.1 Solving Systems of Linear Equations by Substitution and Elimination
- 12.2 Matrix Notation and Gauss-Jordan Elimination
- 12.3 Determinants and Cramer's Rule
- 12.4 Basic Matrix Operations
- 12.5 Inverses of Matrices
- 12.6 Partial Fraction Decomposition
- 12.7 Systems of Linear Inequalities and Linear Programming
- 12.8 Systems of Nonlinear Equations and Inequalities
- Chapter 12 Review

- Chapter 13: Sequences, Series, Combinatorics, and Probability
- 13.1 Sequences and Series
- 13.2 Arithmetic Sequences and Series
- 13.3 Geometric Sequences and Series
- 13.4 Mathematical Induction
- 13.5 Combinatorics
- 13.6 Probability
- Chapter 13 Review