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Algebra & Trigonometry for K-12 Textbooks

by Ron Larson and Robert P. Hostetler

Edition: 6TH 04Copyright: 2004

Publisher: Houghton Mifflin Harcourt

Published: 2004

International: No

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Ideal for instructors who teach a precalculus level course and wish to include a comprehensive review of algebra at the beginning, this text introduces trigonometry first with a right triangle approach and then with the unit circle. As the best-selling text in the field, Algebra and Trigonometry provides unparalleled exercises, motivating real-life applications, a supportive pedagogical design, and innovative ancillaries and resources, making it a complete solution for both students and instructors.

- New! Model It real-life applications in nearly every text section are multi-part exercises that require students to generate and analyze mathematical models. First referenced in the Why You Should Learn It at the beginning of each section, these interesting applications illustrate why it is important to learn the concepts in each section.
- New! Enlarged printable graphs in many exercise sets contain problems asking students to draw on the graph provided. Because this is not feasible in the actual text, printable enlargements of these graphs are available on the web site www.mathgraphs.com.
- New! Proofs in Mathematics shows the proofs of selected theorems and demonstrates different proof techniques. For added convenience, in the Sixth Edition these proofs have been moved from an appendix to the end of relevant chapters.
- New! P.S. Problem Solving, at the conclusion of each chapter, features a collection of thought-provoking and challenging exercises that further explore and expand upon the concepts of the chapter. These exercises have unique characteristics that set them apart from traditional algebra and trigonometry exercises.
- New! A wealth of student success tools includes How to Study This Chapter, a chapter-opening study guide that includes What you should learn (section-opening objectives), Important Vocabulary, a list of Study Tools, and a list of Additional Resources to help the student prepare for the chapter; Why you should learn it, a section-opening, real-life application or a reference to other branches of mathematics, illustrating the relevance of the section's content; and What did you learn?, a concise chapter summary organized by section. These objectives are correlated to the chapter Review Exercises to help students prepare for exams.
- Abundant, up-to-date Real-Life Applications are integrated throughout the examples and exercises and identified by a globe icon to reinforce the relevance of the concepts being learned.
- A wide variety of Exercises, including computational, conceptual, and applied problems are carefully graded in difficulty to allow students to gain confidence as they progress. Each exercise set includes Synthesis Exercises that promote further exploration of mathematical concepts, critical-thinking skills, and writing about mathematics, and Review Exercises that reinforce previously learned skills and concepts.
- Special Algebra of Calculus examples and exercises highlight the algebraic techniques used in calculus to show students how the mathematics they are learning now will be used in future courses.
- Optional graphing technology support is provided in marginal point-of-use instructions that encourage the use of graphing technology as a tool to visualize mathematical concepts, to verify other solution methods, and to facilitate computation. In addition, the section An Introduction to Graphing Utilities helps the student become familiar with the basic functionality of a graphing utility. The use of technology is optional in this text; all exercises that require the use of a graphing utility are clearly identified by an icon.
- Explorations preceding the introduction of selected topics provide the opportunity to engage students in active discovery of mathematical concepts and relationships, often through the power of technology. Explorations strengthen students' critical- thinking skills and help develop an intuitive understanding of theoretical concepts.
- All Examples have been carefully chosen to illustrate a particular mathematical concept or problem-solving skill. Every example contains step-by-step solutions, most with line-by-line explanations that lead students through the solution process, making it easy for students to understand the concepts being explained.
- Additional carefully crafted learning tools designed to create a rich learning environment include Study Tips, Historical Notes, Writing about Mathematics, Chapter Review Exercises, Chapter Tests, and Cumulative Tests.
- A clear, predictable layout, in which solutions and explanations begin and end on the same page, allows students to see concepts and solutions as a whole, without page-turning distractions.

**P. Prerequisites**

P.1 Review of Real Numbers and Their Properties

P.2 Exponents and Radicals

P.3 Polynomials and Special Products

P.4 Factoring

P.5 Rational Expressions

P.6 Errors and the Algebra of Calculus

P.7 Graphical Representation of Data

**1. Equations and Inequalities**

1.1 Graphs of Equations

1.2 Linear Equations in One Variable

1.3 Modeling with Linear Equations

1.4 Quadratic Equations

1.5 Complex Numbers

1.6 Other Types of Equations

1.7 Linear Inequalities in One Variable

1.8 Other Types of Inequalities

**2. Functions and Their Graphs**

2.1 Linear Equations in Two Variables

2.2 Functions

2.3 Analyzing Graphs of Functions

2.4 A Library of Functions

2.5 Shifting, Reflecting, and Stretching Graphs

2.6 Combinations of Functions

2.7 Inverse Functions

**3. Polynomial Functions**

3.1 Quadratic Functions

3.2 Polynomial Functions of Higher Degree

3.3 Polynomial and Synthetic Division

3.4 Zeros of Polynomial Functions

3.5 Mathematical Modeling

**4. Rational Functions and Conics**

4.1 Rational Functions and Asymptotes

4.2 Graphs of Rational Functions

4.3 Partial Fractions

4.4 Conics

4.5 Translations of Conics

**5. Exponential and Logarithmic Functions**

5.1 Exponential Functions and Their Graphs

5.2 Logarithmic Functions and Their Graphs

5.3 Properties of Logarithms

5.4 Exponential and Logarithmic Equations

5.5 Exponential and Logarithmic Models

**6. Trigonometry**

6.1 Angles and Their Measures

6.2 Right Triangle Trigonometry

6.3 Trigonometric Functions of Any Angle

6.4 Graphs of Sine and Cosine Functions

6.5 Graphs of Other Trigonometric Functions

6.6 Inverse Trigonometric Functions

6.7 Applications and Models

**7. Analytic Trigonometry**

7.1 Using Fundamental Identities

7.2 Verifying Trigonometric Identities

7.3 Solving Trigonometric Equations

7.4 Sum and Difference Formulas

7.5 Multiple-Angle and Product-to-Sum Formulas

**8. Additional Topics in Trigonometry**

8.1 Law of Sines

8.2 Law of Cosines

8.3 Vectors in the Plane

8.4 Vectors and Dot Products

8.5 Trigonometric Form of a Complex Number

**9. Systems of Equations and Inequalities**

9.1 Solving Systems of Equations

9.2 Two-Variable linear Systems

9.3 Multivariable Linear Systems

9.4 Systems of Inequalities

9.5 Linear Programming

**10. Matrices and Determinants**

10.1 Matrices and Systems of Equations

10.2 Operations with Matrices

10.3 The Inverse of a Square Matrix

10.4 The Determinant of a Square Matrix

10.5 Applications of Matrices and Determinants

**11. Sequences, Series, and Probability**

11.1 Sequences and Series

11.2 Arithmetic Sequences and Partial Sums

11.3 Geometric Sequences and Series

11.4 Mathematical Induction

11.5 The Binomial Theorem

11.6 Counting Principles

11.7 Probability

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Summary

Ideal for instructors who teach a precalculus level course and wish to include a comprehensive review of algebra at the beginning, this text introduces trigonometry first with a right triangle approach and then with the unit circle. As the best-selling text in the field, Algebra and Trigonometry provides unparalleled exercises, motivating real-life applications, a supportive pedagogical design, and innovative ancillaries and resources, making it a complete solution for both students and instructors.

- New! Model It real-life applications in nearly every text section are multi-part exercises that require students to generate and analyze mathematical models. First referenced in the Why You Should Learn It at the beginning of each section, these interesting applications illustrate why it is important to learn the concepts in each section.
- New! Enlarged printable graphs in many exercise sets contain problems asking students to draw on the graph provided. Because this is not feasible in the actual text, printable enlargements of these graphs are available on the web site www.mathgraphs.com.
- New! Proofs in Mathematics shows the proofs of selected theorems and demonstrates different proof techniques. For added convenience, in the Sixth Edition these proofs have been moved from an appendix to the end of relevant chapters.
- New! P.S. Problem Solving, at the conclusion of each chapter, features a collection of thought-provoking and challenging exercises that further explore and expand upon the concepts of the chapter. These exercises have unique characteristics that set them apart from traditional algebra and trigonometry exercises.
- New! A wealth of student success tools includes How to Study This Chapter, a chapter-opening study guide that includes What you should learn (section-opening objectives), Important Vocabulary, a list of Study Tools, and a list of Additional Resources to help the student prepare for the chapter; Why you should learn it, a section-opening, real-life application or a reference to other branches of mathematics, illustrating the relevance of the section's content; and What did you learn?, a concise chapter summary organized by section. These objectives are correlated to the chapter Review Exercises to help students prepare for exams.
- Abundant, up-to-date Real-Life Applications are integrated throughout the examples and exercises and identified by a globe icon to reinforce the relevance of the concepts being learned.
- A wide variety of Exercises, including computational, conceptual, and applied problems are carefully graded in difficulty to allow students to gain confidence as they progress. Each exercise set includes Synthesis Exercises that promote further exploration of mathematical concepts, critical-thinking skills, and writing about mathematics, and Review Exercises that reinforce previously learned skills and concepts.
- Special Algebra of Calculus examples and exercises highlight the algebraic techniques used in calculus to show students how the mathematics they are learning now will be used in future courses.
- Optional graphing technology support is provided in marginal point-of-use instructions that encourage the use of graphing technology as a tool to visualize mathematical concepts, to verify other solution methods, and to facilitate computation. In addition, the section An Introduction to Graphing Utilities helps the student become familiar with the basic functionality of a graphing utility. The use of technology is optional in this text; all exercises that require the use of a graphing utility are clearly identified by an icon.
- Explorations preceding the introduction of selected topics provide the opportunity to engage students in active discovery of mathematical concepts and relationships, often through the power of technology. Explorations strengthen students' critical- thinking skills and help develop an intuitive understanding of theoretical concepts.
- All Examples have been carefully chosen to illustrate a particular mathematical concept or problem-solving skill. Every example contains step-by-step solutions, most with line-by-line explanations that lead students through the solution process, making it easy for students to understand the concepts being explained.
- Additional carefully crafted learning tools designed to create a rich learning environment include Study Tips, Historical Notes, Writing about Mathematics, Chapter Review Exercises, Chapter Tests, and Cumulative Tests.
- A clear, predictable layout, in which solutions and explanations begin and end on the same page, allows students to see concepts and solutions as a whole, without page-turning distractions.

Table of Contents

**P. Prerequisites**

P.1 Review of Real Numbers and Their Properties

P.2 Exponents and Radicals

P.3 Polynomials and Special Products

P.4 Factoring

P.5 Rational Expressions

P.6 Errors and the Algebra of Calculus

P.7 Graphical Representation of Data

**1. Equations and Inequalities**

1.1 Graphs of Equations

1.2 Linear Equations in One Variable

1.3 Modeling with Linear Equations

1.4 Quadratic Equations

1.5 Complex Numbers

1.6 Other Types of Equations

1.7 Linear Inequalities in One Variable

1.8 Other Types of Inequalities

**2. Functions and Their Graphs**

2.1 Linear Equations in Two Variables

2.2 Functions

2.3 Analyzing Graphs of Functions

2.4 A Library of Functions

2.5 Shifting, Reflecting, and Stretching Graphs

2.6 Combinations of Functions

2.7 Inverse Functions

**3. Polynomial Functions**

3.1 Quadratic Functions

3.2 Polynomial Functions of Higher Degree

3.3 Polynomial and Synthetic Division

3.4 Zeros of Polynomial Functions

3.5 Mathematical Modeling

**4. Rational Functions and Conics**

4.1 Rational Functions and Asymptotes

4.2 Graphs of Rational Functions

4.3 Partial Fractions

4.4 Conics

4.5 Translations of Conics

**5. Exponential and Logarithmic Functions**

5.1 Exponential Functions and Their Graphs

5.2 Logarithmic Functions and Their Graphs

5.3 Properties of Logarithms

5.4 Exponential and Logarithmic Equations

5.5 Exponential and Logarithmic Models

**6. Trigonometry**

6.1 Angles and Their Measures

6.2 Right Triangle Trigonometry

6.3 Trigonometric Functions of Any Angle

6.4 Graphs of Sine and Cosine Functions

6.5 Graphs of Other Trigonometric Functions

6.6 Inverse Trigonometric Functions

6.7 Applications and Models

**7. Analytic Trigonometry**

7.1 Using Fundamental Identities

7.2 Verifying Trigonometric Identities

7.3 Solving Trigonometric Equations

7.4 Sum and Difference Formulas

7.5 Multiple-Angle and Product-to-Sum Formulas

**8. Additional Topics in Trigonometry**

8.1 Law of Sines

8.2 Law of Cosines

8.3 Vectors in the Plane

8.4 Vectors and Dot Products

8.5 Trigonometric Form of a Complex Number

**9. Systems of Equations and Inequalities**

9.1 Solving Systems of Equations

9.2 Two-Variable linear Systems

9.3 Multivariable Linear Systems

9.4 Systems of Inequalities

9.5 Linear Programming

**10. Matrices and Determinants**

10.1 Matrices and Systems of Equations

10.2 Operations with Matrices

10.3 The Inverse of a Square Matrix

10.4 The Determinant of a Square Matrix

10.5 Applications of Matrices and Determinants

**11. Sequences, Series, and Probability**

11.1 Sequences and Series

11.2 Arithmetic Sequences and Partial Sums

11.3 Geometric Sequences and Series

11.4 Mathematical Induction

11.5 The Binomial Theorem

11.6 Counting Principles

11.7 Probability

Publisher Info

Publisher: Houghton Mifflin Harcourt

Published: 2004

International: No

Published: 2004

International: No

Ideal for instructors who teach a precalculus level course and wish to include a comprehensive review of algebra at the beginning, this text introduces trigonometry first with a right triangle approach and then with the unit circle. As the best-selling text in the field, Algebra and Trigonometry provides unparalleled exercises, motivating real-life applications, a supportive pedagogical design, and innovative ancillaries and resources, making it a complete solution for both students and instructors.

- New! Model It real-life applications in nearly every text section are multi-part exercises that require students to generate and analyze mathematical models. First referenced in the Why You Should Learn It at the beginning of each section, these interesting applications illustrate why it is important to learn the concepts in each section.
- New! Enlarged printable graphs in many exercise sets contain problems asking students to draw on the graph provided. Because this is not feasible in the actual text, printable enlargements of these graphs are available on the web site www.mathgraphs.com.
- New! Proofs in Mathematics shows the proofs of selected theorems and demonstrates different proof techniques. For added convenience, in the Sixth Edition these proofs have been moved from an appendix to the end of relevant chapters.
- New! P.S. Problem Solving, at the conclusion of each chapter, features a collection of thought-provoking and challenging exercises that further explore and expand upon the concepts of the chapter. These exercises have unique characteristics that set them apart from traditional algebra and trigonometry exercises.
- New! A wealth of student success tools includes How to Study This Chapter, a chapter-opening study guide that includes What you should learn (section-opening objectives), Important Vocabulary, a list of Study Tools, and a list of Additional Resources to help the student prepare for the chapter; Why you should learn it, a section-opening, real-life application or a reference to other branches of mathematics, illustrating the relevance of the section's content; and What did you learn?, a concise chapter summary organized by section. These objectives are correlated to the chapter Review Exercises to help students prepare for exams.
- Abundant, up-to-date Real-Life Applications are integrated throughout the examples and exercises and identified by a globe icon to reinforce the relevance of the concepts being learned.
- A wide variety of Exercises, including computational, conceptual, and applied problems are carefully graded in difficulty to allow students to gain confidence as they progress. Each exercise set includes Synthesis Exercises that promote further exploration of mathematical concepts, critical-thinking skills, and writing about mathematics, and Review Exercises that reinforce previously learned skills and concepts.
- Special Algebra of Calculus examples and exercises highlight the algebraic techniques used in calculus to show students how the mathematics they are learning now will be used in future courses.
- Optional graphing technology support is provided in marginal point-of-use instructions that encourage the use of graphing technology as a tool to visualize mathematical concepts, to verify other solution methods, and to facilitate computation. In addition, the section An Introduction to Graphing Utilities helps the student become familiar with the basic functionality of a graphing utility. The use of technology is optional in this text; all exercises that require the use of a graphing utility are clearly identified by an icon.
- Explorations preceding the introduction of selected topics provide the opportunity to engage students in active discovery of mathematical concepts and relationships, often through the power of technology. Explorations strengthen students' critical- thinking skills and help develop an intuitive understanding of theoretical concepts.
- All Examples have been carefully chosen to illustrate a particular mathematical concept or problem-solving skill. Every example contains step-by-step solutions, most with line-by-line explanations that lead students through the solution process, making it easy for students to understand the concepts being explained.
- Additional carefully crafted learning tools designed to create a rich learning environment include Study Tips, Historical Notes, Writing about Mathematics, Chapter Review Exercises, Chapter Tests, and Cumulative Tests.
- A clear, predictable layout, in which solutions and explanations begin and end on the same page, allows students to see concepts and solutions as a whole, without page-turning distractions.

**P. Prerequisites**

P.1 Review of Real Numbers and Their Properties

P.2 Exponents and Radicals

P.3 Polynomials and Special Products

P.4 Factoring

P.5 Rational Expressions

P.6 Errors and the Algebra of Calculus

P.7 Graphical Representation of Data

**1. Equations and Inequalities**

1.1 Graphs of Equations

1.2 Linear Equations in One Variable

1.3 Modeling with Linear Equations

1.4 Quadratic Equations

1.5 Complex Numbers

1.6 Other Types of Equations

1.7 Linear Inequalities in One Variable

1.8 Other Types of Inequalities

**2. Functions and Their Graphs**

2.1 Linear Equations in Two Variables

2.2 Functions

2.3 Analyzing Graphs of Functions

2.4 A Library of Functions

2.5 Shifting, Reflecting, and Stretching Graphs

2.6 Combinations of Functions

2.7 Inverse Functions

**3. Polynomial Functions**

3.1 Quadratic Functions

3.2 Polynomial Functions of Higher Degree

3.3 Polynomial and Synthetic Division

3.4 Zeros of Polynomial Functions

3.5 Mathematical Modeling

**4. Rational Functions and Conics**

4.1 Rational Functions and Asymptotes

4.2 Graphs of Rational Functions

4.3 Partial Fractions

4.4 Conics

4.5 Translations of Conics

**5. Exponential and Logarithmic Functions**

5.1 Exponential Functions and Their Graphs

5.2 Logarithmic Functions and Their Graphs

5.3 Properties of Logarithms

5.4 Exponential and Logarithmic Equations

5.5 Exponential and Logarithmic Models

**6. Trigonometry**

6.1 Angles and Their Measures

6.2 Right Triangle Trigonometry

6.3 Trigonometric Functions of Any Angle

6.4 Graphs of Sine and Cosine Functions

6.5 Graphs of Other Trigonometric Functions

6.6 Inverse Trigonometric Functions

6.7 Applications and Models

**7. Analytic Trigonometry**

7.1 Using Fundamental Identities

7.2 Verifying Trigonometric Identities

7.3 Solving Trigonometric Equations

7.4 Sum and Difference Formulas

7.5 Multiple-Angle and Product-to-Sum Formulas

**8. Additional Topics in Trigonometry**

8.1 Law of Sines

8.2 Law of Cosines

8.3 Vectors in the Plane

8.4 Vectors and Dot Products

8.5 Trigonometric Form of a Complex Number

**9. Systems of Equations and Inequalities**

9.1 Solving Systems of Equations

9.2 Two-Variable linear Systems

9.3 Multivariable Linear Systems

9.4 Systems of Inequalities

9.5 Linear Programming

**10. Matrices and Determinants**

10.1 Matrices and Systems of Equations

10.2 Operations with Matrices

10.3 The Inverse of a Square Matrix

10.4 The Determinant of a Square Matrix

10.5 Applications of Matrices and Determinants

**11. Sequences, Series, and Probability**

11.1 Sequences and Series

11.2 Arithmetic Sequences and Partial Sums

11.3 Geometric Sequences and Series

11.4 Mathematical Induction

11.5 The Binomial Theorem

11.6 Counting Principles

11.7 Probability