# Algebra & Trigonometry

2^{nd}Edition

ISBN10: 0077276515

ISBN13: 9780077276515

Copyright: 2010

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ISBN10: 0077276515 | ISBN13: 9780077276515

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The estimated amount of time this product will be on the market is based on a number of factors, including faculty input to instructional design and the prior revision cycle and updates to academic research-which typically results in a revision cycle ranging from every two to four years for this product. Pricing subject to change at any time.

The estimated amount of time this product will be on the market is based on a number of factors, including faculty input to instructional design and the prior revision cycle and updates to academic research-which typically results in a revision cycle ranging from every two to four years for this product. Pricing subject to change at any time.

### Program Details

### Chapter R: A Review of Basic Concepts and Skills

#### R-1 The Language, Notation, and Numbers of Mathematics

#### R-2 Algebraic Expressions and the Properties of Real Numbers

#### R-3 Exponents, Scientific Notation, and a Review of Polynomials

#### R-4 Factoring Polynomials

#### R-5 Rational Expressions

#### R-6 Radicals and Rational Exponents

### Chapter 1: Equations and Inequalities

#### 1-1 Linear Equations, Formulas, and Problem Solving

#### 1-2 Linear Inequalities in One Variable

#### 1-3 Absolute Value Equations and Inequalities

#### 1-4 Complex Numbers

#### 1-5 Solving Quadratic Equations

#### 1-6 Solving Other Types of Equations

### Chapter 2: Relations, Functions and Graphs

#### 2-1 Rectangular Coordinates; Graphing Circles and Relations

#### 2-2 Graphs of Linear Equations

#### 2-3 Linear Equations and Rates of Change

#### 2-4 Functions, Notation, and Graphs of Functions

#### 2-5 Analyzing the Graph of a Function

#### 2-6 Toolbox Functions and Transformations

#### 2-7 Piecewise-Defined Functions

#### 2-8 The Algebra and Composition of Functions

### Chapter 3: Polynomial and Rational Functions

#### 3-1 Quadratic Functions and Applications

#### 3-2 Synthetic Division; The Remainder and Factor Theorems

#### 3-3 The Zeroes of Polynomial Functions

#### 3-4 Graphing Polynomial Functions

#### 3-5 Graphing Rational Functions

#### 3-6 Additional Insights into Rational Functions

#### 3-7 Polynomial and Rational Inequalities

#### 3-8 Variation: Function Models in Action

### Chapter 4: Exponential and Logarithmic Functions

#### 4-1 One-to-One and Inverse Functions

#### 4-2 Exponential Functions

#### 4-3 Logarithms and Logarithmic Functions

#### 4-4 Properties of Logarithms; Solving Exponential and Logarithmic Equations

#### 4-5 Applications from Business, Finance, and Science

### Chapter 5: Introduction to Trigonometric Functions

#### 5-1 Angle Measure, Special Triangles, and Special Angles

#### 5-2 The Trigonometry of Right Triangles

#### 5-3 Trigonometry and the Coordinate Plane

#### 5-4 Unit Circles and the Trigonometric of Real Numbers

#### 5-5 Graphs of Sine and Cosine Functions; Cosecant and Secant Functions

#### 5-6 Graphs of Tangent and Cotangent Functions

#### 5-7 Transformations and Applications of Trigonometric Graphs

### Chapter 6: Trigonometric Identities, Inverses, and Equations

#### 6-1 Fundamental Identities and Families of Identities

#### 6-2 Constructing and Verifying Identities

#### 6-3 The Sum and Difference Identities

#### 6-4 Double Angle, Half Angle & Product-to-Sum Identities

#### 6-5 The Inverse Trigonometric Functions and Their Applications

#### 6-6 Solving Basic Trigonometric Equations

#### 6-7 General Trigonometric Equations and Applications

### Chapter 7: Applications of Trigonometry

#### 7-1 Oblique Triangles and the Law of Sines

#### 7-2 The Law of Cosines; Area of a Triangle

#### 7-3 Vectors and Vector Diagrams

#### 7-4 Vector Applications and the Dot Product

#### 7-5 Complex Numbers in Trigonometric Form

#### 7-6 Demoivre’s Theorem and the Theorem on nth Roots

### Chapter 8: Systems of Equations and Inequalities

#### 8-1 Linear Systems in Two Variables with Applications

#### 8-2 Linear Systems in Three Variables with Applications

#### 8-3 Nonlinear Systems of Equations and Inequalities

#### 8-4 Systems of Inequalities and Linear Programming

### Chapter 9: Matrices and Matrix Applications

#### 9-1 Solving Systems Using Matrices and Row Operations

#### 9-2 The Algebra of Matrices

#### 9-3 Solving Linear Systems Using Matrix Equations

#### 9-4 Applications of Matrices and Determinants: Cramer's Rule, Partial Fractions, and More

### Chapter 10: Analytical Geometry and Conic Sections

#### 10-1 Introduction to Analytic Geometry

#### 10-2 The Circle and the Ellipse

#### 10-3 The Hyperbola

#### 10-4 The Analytic Parabola

#### 10-5 Polar Coordinates, Equations, and Graphs

#### 10-6 More on Conic Sections: Rotation of Axes and Polar Form

#### 10-7 Parametric Equations and Graphs

### Chapter 11: Additional Topics in Algebra

#### 11-1 Sequences and Series

#### 11-2 Arithmetic Sequences

#### 11-3 Geometric Sequences

#### 11-4 Mathematical Induction

#### 11-5 Counting Techniques

#### 11-6 Introduction to Probability

#### 11-7 The Binomial Theorem Summary and Concept Review

#### APPENDICES

##### A-1 More on Synthetic Division

##### A-2 More on Matrices

##### A-3 Deriving the Equation of a Conic

##### A-4 Proof Positive - A Selection of Proofs from Algebra and Trigonometry

# About the Author

**John Coburn**

John Coburn grew up in the Hawaiian Islands, the seventh of sixteen children. He received his Associate of Arts degree in 1977 from Windward Community College, where he graduated with honors. In 1979 he received a Bachelor’s Degree in Education from the University of Hawaii. After being lured into the business world for five years, he returned to his first love, accepting a teaching position in high school mathematics where he was recognized as Teacher of the Year in 1987. Soon afterward, the decision was made to seek a Masters Degree, which he received two years later from the University of Oklahoma. For the last fifteen years, he has been teaching mathematics at the Florissant Valley campus of St. Louis Community College, where he is now a full professor. During his tenure there he has received numerous nominations as an outstanding teacher by the local chapter of Phi Theta Kappa, two nominations to Who’s Who Among America’s Teachers and was recognized as Teacher of the year in 2004 by the Mathematics Educators of Greater St. Louis (MEGSL). He has made numerous presentations and local, state and national conferences on a wide variety of topics. His other loves include his family, music, athletics, games and all things beautiful, and hopes this love of life comes through in his writing, and serves to make the learning experience an interesting and engaging one for all students.

### Chapter R: A Review of Basic Concepts and Skills

#### R-1 The Language, Notation, and Numbers of Mathematics

#### R-2 Algebraic Expressions and the Properties of Real Numbers

#### R-3 Exponents, Scientific Notation, and a Review of Polynomials

#### R-4 Factoring Polynomials

#### R-5 Rational Expressions

#### R-6 Radicals and Rational Exponents

### Chapter 1: Equations and Inequalities

#### 1-1 Linear Equations, Formulas, and Problem Solving

#### 1-2 Linear Inequalities in One Variable

#### 1-3 Absolute Value Equations and Inequalities

#### 1-4 Complex Numbers

#### 1-5 Solving Quadratic Equations

#### 1-6 Solving Other Types of Equations

### Chapter 2: Relations, Functions and Graphs

#### 2-1 Rectangular Coordinates; Graphing Circles and Relations

#### 2-2 Graphs of Linear Equations

#### 2-3 Linear Equations and Rates of Change

#### 2-4 Functions, Notation, and Graphs of Functions

#### 2-5 Analyzing the Graph of a Function

#### 2-6 Toolbox Functions and Transformations

#### 2-7 Piecewise-Defined Functions

#### 2-8 The Algebra and Composition of Functions

### Chapter 3: Polynomial and Rational Functions

#### 3-1 Quadratic Functions and Applications

#### 3-2 Synthetic Division; The Remainder and Factor Theorems

#### 3-3 The Zeroes of Polynomial Functions

#### 3-4 Graphing Polynomial Functions

#### 3-5 Graphing Rational Functions

#### 3-6 Additional Insights into Rational Functions

#### 3-7 Polynomial and Rational Inequalities

#### 3-8 Variation: Function Models in Action

### Chapter 4: Exponential and Logarithmic Functions

#### 4-1 One-to-One and Inverse Functions

#### 4-2 Exponential Functions

#### 4-3 Logarithms and Logarithmic Functions

#### 4-4 Properties of Logarithms; Solving Exponential and Logarithmic Equations

#### 4-5 Applications from Business, Finance, and Science

### Chapter 5: Introduction to Trigonometric Functions

#### 5-1 Angle Measure, Special Triangles, and Special Angles

#### 5-2 The Trigonometry of Right Triangles

#### 5-3 Trigonometry and the Coordinate Plane

#### 5-4 Unit Circles and the Trigonometric of Real Numbers

#### 5-5 Graphs of Sine and Cosine Functions; Cosecant and Secant Functions

#### 5-6 Graphs of Tangent and Cotangent Functions

#### 5-7 Transformations and Applications of Trigonometric Graphs

### Chapter 6: Trigonometric Identities, Inverses, and Equations

#### 6-1 Fundamental Identities and Families of Identities

#### 6-2 Constructing and Verifying Identities

#### 6-3 The Sum and Difference Identities

#### 6-4 Double Angle, Half Angle & Product-to-Sum Identities

#### 6-5 The Inverse Trigonometric Functions and Their Applications

#### 6-6 Solving Basic Trigonometric Equations

#### 6-7 General Trigonometric Equations and Applications

### Chapter 7: Applications of Trigonometry

#### 7-1 Oblique Triangles and the Law of Sines

#### 7-2 The Law of Cosines; Area of a Triangle

#### 7-3 Vectors and Vector Diagrams

#### 7-4 Vector Applications and the Dot Product

#### 7-5 Complex Numbers in Trigonometric Form

#### 7-6 Demoivre’s Theorem and the Theorem on nth Roots

### Chapter 8: Systems of Equations and Inequalities

#### 8-1 Linear Systems in Two Variables with Applications

#### 8-2 Linear Systems in Three Variables with Applications

#### 8-3 Nonlinear Systems of Equations and Inequalities

#### 8-4 Systems of Inequalities and Linear Programming

### Chapter 9: Matrices and Matrix Applications

#### 9-1 Solving Systems Using Matrices and Row Operations

#### 9-2 The Algebra of Matrices

#### 9-3 Solving Linear Systems Using Matrix Equations

#### 9-4 Applications of Matrices and Determinants: Cramer's Rule, Partial Fractions, and More

### Chapter 10: Analytical Geometry and Conic Sections

#### 10-1 Introduction to Analytic Geometry

#### 10-2 The Circle and the Ellipse

#### 10-3 The Hyperbola

#### 10-4 The Analytic Parabola

#### 10-5 Polar Coordinates, Equations, and Graphs

#### 10-6 More on Conic Sections: Rotation of Axes and Polar Form

#### 10-7 Parametric Equations and Graphs

### Chapter 11: Additional Topics in Algebra

#### 11-1 Sequences and Series

#### 11-2 Arithmetic Sequences

#### 11-3 Geometric Sequences

#### 11-4 Mathematical Induction

#### 11-5 Counting Techniques

#### 11-6 Introduction to Probability

#### 11-7 The Binomial Theorem Summary and Concept Review

#### APPENDICES

##### A-1 More on Synthetic Division

##### A-2 More on Matrices

##### A-3 Deriving the Equation of a Conic

##### A-4 Proof Positive - A Selection of Proofs from Algebra and Trigonometry

# About the Author

**John Coburn**

John Coburn grew up in the Hawaiian Islands, the seventh of sixteen children. He received his Associate of Arts degree in 1977 from Windward Community College, where he graduated with honors. In 1979 he received a Bachelor’s Degree in Education from the University of Hawaii. After being lured into the business world for five years, he returned to his first love, accepting a teaching position in high school mathematics where he was recognized as Teacher of the Year in 1987. Soon afterward, the decision was made to seek a Masters Degree, which he received two years later from the University of Oklahoma. For the last fifteen years, he has been teaching mathematics at the Florissant Valley campus of St. Louis Community College, where he is now a full professor. During his tenure there he has received numerous nominations as an outstanding teacher by the local chapter of Phi Theta Kappa, two nominations to Who’s Who Among America’s Teachers and was recognized as Teacher of the year in 2004 by the Mathematics Educators of Greater St. Louis (MEGSL). He has made numerous presentations and local, state and national conferences on a wide variety of topics. His other loves include his family, music, athletics, games and all things beautiful, and hopes this love of life comes through in his writing, and serves to make the learning experience an interesting and engaging one for all students.

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