Algebra and Trigonometry, 12th edition

  • Michael Sullivan

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Overview

Wherever you are in math preparation, Algebra and Trigonometry supports you through your mathematics journey. It offers the high-quality exercises that distinguish Sullivan texts, with his proven “Prepare, practice, review” method: prepare for class, practice with homework, and review concepts.

The 12th Edition adds many new and revised exercises and examples, adds new learning tips in margin notes, updates all graphing utility content and images, and much more.

Published by Pearson (January 18th 2024) - Copyright © 2025

ISBN-13: 9780138251550

Subject: Precalculus, College Algebra & Trigonometry

Category: Algebra & Trigonometry

Overview

Applications Index

R. Review

  • R.1 Real Numbers
  • R.2 Algebra Essentials
  • R.3 Geometry Essentials
  • R.4 Polynomials
  • R.5 Factoring Polynomials
  • R.6 Synthetic Division
  • R.7 Rational Expressions
  • R.8 nth Roots; Rational Exponents

1. Equations and Inequalities

  • 1.1 Linear Equations
  • 1.2 Quadratic Equations
  • 1.3 Complex Numbers; Quadratic Equations in the Complex Number System
  • 1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations
  • 1.5 Solving Inequalities
  • 1.6 Equations and Inequalities Involving Absolute Value
  • 1.7 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications
  • Chapter 1 Review, Test, and Projects

2. Graphs

  • 2.1 The Distance and Midpoint Formulas
  • 2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry
  • 2.3 Lines
  • 2.4 Circles
  • 2.5 Variation
  • Chapter 2 Review, Test, Cumulative Review, and Project

3. Functions and Their Graphs

  • 3.1 Functions
  • 3.2 The Graph of a Function
  • 3.3 Properties of Functions
  • 3.4 Library of Functions; Piecewise-defined Functions
  • 3.5 Graphing Techniques: Transformations
  • 3.6 Mathematical Models: Building Functions
  • Chapter 3 Review, Test, Cumulative Review, and Projects

4. Linear and Quadratic Functions

  • 4.1 Properties of Linear Functions and Linear Models
  • 4.2 Building Linear Models from Data
  • 4.3 Quadratic Functions and Their Properties
  • 4.4 Build Quadratic Models from Verbal Descriptions and from Data
  • 4.5 Inequalities Involving Quadratic Functions
  • Chapter 4 Review, Test, Cumulative Review, and Projects

5. Polynomial and Rational Functions

  • 5.1 Polynomial Functions
  • 5.2 Graphing Polynomials Functions; Models
  • 5.3 Properties of Rational Functions
  • 5.4 The Graph of a Rational Function
  • 5.5 Polynomial and Rational Inequalities
  • 5.6 The Real Zeros of a Polynomial Function
  • 5.7 Complex Zeros; Fundamental Theorem of Algebra
  • Chapter 5 Review, Test, Cumulative Review, and Projects

6. Exponential and Logarithmic Functions

  • 6.1 Composite Functions
  • 6.2 One-to-One Functions; Inverse Functions
  • 6.3 Exponential Functions
  • 6.4 Logarithmic Functions
  • 6.5 Properties of Logarithms
  • 6.6 Logarithmic and Exponential Equations
  • 6.7 Financial Models
  • 6.8 Exponential Growth and Decay Models; Newton's Law; Logistic Growth and Decay Models
  • 6.9 Building Exponential, Logarithmic, and Logistic Models from Data
  • Chapter 6 Review, Test, Cumulative Review, and Projects

7. Trigonometric Functions

  • 7.1 Angles, Arc, Length, and Circular Motion
  • 7.2 Right Triangle Trigonometry
  • 7.3 Computing the Values of Trigonometric Functions of Acute Angles
  • 7.4 Trigonometric Functions of Any Angle
  • 7.5 Unit Circle Approach; Properties of the Trigonometric Functions
  • 7.6 Graphs of the Sine and Cosine Functions
  • 7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
  • 7.8 Phase Shift; Sinusoidal Curve Fitting
  • Chapter 7 Review, Test, Cumulative Review, and Projects

8. Analytic Trigonometry

  • 8.1 The Inverse Sine, Cosine, and Tangent Functions
  • 8.2 The Inverse Trigonometric Functions (Continued)
  • 8.3 Trigonometric Equations
  • 8.4 Trigonometric Identities
  • 8.5 Sum and Difference Formulas
  • 8.6 Double-angle and Half-angle Formulas
  • 8.7 Product-to-Sum and Sum-to-Product Formulas
  • Chapter 8 Review, Test, Cumulative Review, and Projects

9. Applications of Trigonometric Functions

  • 9.1 Applications Involving Right Triangles
  • 9.2 The Law of Sines
  • 9.3 The Law of Cosines
  • 9.4 Area of a Triangle
  • 9.5 Simple Harmonic Motion; Damped Motion; Combining Waves
  • Chapter 9 Review, Test, Cumulative Revivew, and Projects

10. Polar Coordinates; Vectors

  • 10.1 Polar Coordinates
  • 10.2 Polar Equations and Graphs
  • 10.3 The Complex Plane; De Moivre's Theorem
  • 10.4 Vectors
  • 10.5 The Dot Product
  • Chapter 10 Review, Test, Cumulative Review, and Projects

11. Analytic Geometry

  • 11.1 Conics
  • 11.2 The Parabola
  • 11.3 The Ellipse
  • 11.4 The Hyperbola
  • 11.5 Rotation of Axes; General Form of a Conic
  • 11.6 Polar Equations of Conics
  • 11.7 Plane Curves and Parametric Equations
  • Chapter 11 Review, Test, Cumulative Review, and Projects

12. Systems of Equations and Inequalities

  • 12.1 Systems of Linear Equations: Substitution and Elimination
  • 12.2 Systems of Linear Equations: Matrices
  • 12.3 Systems of Linear Equations: Determinants
  • 12.4 Matrix Algebra
  • 12.5 Partial Fraction Decomposition
  • 12.6 Systems of Nonlinear Equations
  • 12.7 Systems of Inequalities
  • 12.8 Linear Programming
  • Chapter 12 Review, Test, Cumulative Review, and Projects

13. Sequences; Induction; the Binomial Theorem

  • 13.1 Sequences
  • 13.2 Arithmetic Sequences
  • 13.3 Geometric Sequences; Geometric Series
  • 13.4 Mathematical Induction
  • 13.5 The Binomial Theorem
  • Chapter 13 Review, Test, Cumulative Review, and Projects

14. Counting and Probability

  • 14.1 Counting
  • 14.2 Permutations and Combinations
  • 14.3 Probability
  • Chapter 14 Review, Test, Cumulative Review, and Projects

Appendix: Graphing Utilities

  • A.1 The Viewing Rectangle
  • A.2 Using a Graphing Utility to Graph Equations
  • A.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry
  • A.4 Using a Graphing Utility to Solve Equations
  • A.5 Square Screens
  • A.6 Using a Graphing Utility to Graph Inequalities
  • A.7 Using a Graphing Utility to Solve Systems of Linear Equations
  • A.8 Using a Graphing Utility to Graph a Polar Equation
  • A.9 Using a Graphing Utility to Graph Parametric Equations

Answers

Credits

Index

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