  # Algebra and Trigonometry Enhanced with Graphing Utilities, 8th edition

• Michael Sullivan

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## Overview

The proven approach of Michael Sullivan and Michael Sullivan III focuses you on the fundamental skills needed for the algebra and trigonometry course: prepare for class, practice with homework, and review the concepts. Part of the Enhanced with Graphing Utilities Series, Algebra and Trigonometry Enhanced with Graphing Utilities fully integrates graphing utilities into topics, allowing you to explore mathematical concepts and encounter ideas usually studied in later courses. Many examples show solutions using algebra side by side with graphing techniques. In the 8th Edition, all exercises and examples in the text have been reviewed and updated as needed, and the authors have added new problem-solving and review features.

ISBN-13: 9780136872795

Subject: Precalculus, College Algebra & Trigonometry

Category: Algebra & Trigonometry

## Overview

1. 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 n th Roots; Rational Exponents
1. Graphs, Equations, and Inequalities
• 1.1 Graphing Utilities; Introduction to Graphing Equations
• 1.2 Solving Equations Using a Graphing Utility; Linear and Rational Equations
• 1.4 Complex Numbers; Quadratic Equations in the Complex Number System
• 1.5 Radical Equations; Equations Quadratic in Form; Absolute Value Equations; Factorable Equations
• 1.6 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications
• 1.7 Solving Inequalities
2. Graphs
• 2.1 The Distance and Midpoint Formulas
• 2.2 Intercepts: Symmetry; Graphing Key Equations
• 2.3 Lines
• 2.4 Circles
• 2.5 Variation
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
• 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
5. Polynomial and Rational Functions
• 5.1 Polynomial Functions
• 5.2 The Graph of a Polynomial Function; Models
• 5.3 The Real Zeroes of a Polynomial Function
• 5.4 Complex Zeroes: Fundamental Theorem of Algebra
• 5.5 Properties of Rational Functions
• 5.6 The Graph of a Rational Function
• 5.7 Polynomial and Rational Inequalities
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
7. Trigonometric Functions
• 7.1 Angles and Their Measure
• 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
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
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
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
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
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
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
14. Counting and Probability
• 14.1 Counting
• 14.2 Permutations and Combinations
• 14.3 Probability

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