College Algebra and Trigonometry

College Algebra and Trigonometry

2nd Edition - January 1, 1986

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  • Authors: Bernard Kolman, Arnold Shapiro
  • eBook ISBN: 9781483277134

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College Algebra and Trigonometry, Second Edition provides a comprehensive approach to the fundamental concepts and techniques of college algebra and trigonometry. The book incorporates improvements from the previous edition to provide a better learning experience. It contains chapters that are devoted to various mathematical concepts, such as the real number system, the theory of polynomial equations, trigonometric functions, and the geometric definition of each conic section. Progress checks, warnings, and features are inserted. Every chapter contains a summary, including terms and symbols with appropriate page references; key ideas for review to stress the concepts; review exercises to provide additional practice; and progress tests to provide self-evaluation and reinforcement. The answers to all Review Exercises and Progress Tests appear in the back of the book. College students will find the book very useful and invaluable.

Table of Contents

  • Preface


    To the Student

    Chapter 1 The Foundations of Algebra

    1.1 The Real Number System

    1.2 The Real Number Line

    1.3 Algebraic Expressions; Polynomials

    1.4 Factoring

    1.5 Rational Expressions

    1.6 Integer Exponents

    1.7 Rational Exponents and Radicals

    1.8 Complex Numbers

    Chapter 2 Equations and Inequalities

    2.1 Linear Equations in One Unknown

    2.2 Applications

    2.3 Linear Inequalities

    2.4 Absolute Value in Equations and Inequalities

    2.5 The Quadratic Equation

    2.6 Applications of Quadratic Equations

    2.7 Second-Degree Inequalities

    Chapter 3 Functions

    3.1 The Rectangular Coordinate System

    3.2 Functions and Function Notation

    3.3 Graphs of Functions

    3.4 Linear Functions

    3.5 Direct and Inverse Variation (Optional)

    3.6 Combining Functions; Inverse Functions

    Chapter 4 Exponential and Logarithmic Functions

    4.1 Exponential Functions

    4.2 Logarithmic Functions

    4.3 Fundamental Properties of Logarithms

    4.4 Computing with Logarithms (Optional)

    4.5 Exponential and Logarithmic Equations

    Chapter 5 The Trigonometric Functions

    5.0 Review of Geometry

    5.1 Angles and Their Measurement

    5.2 The Sine, Cosine, and Tangent Functions

    5.3 Values of Sine, Cosine, and Tangent

    5.4 Graphs of Sine, Cosine, and Tangent

    5.5 Secant, Cosecant, and Cotangent

    5.6 The Inverse Trigonometric Functions

    Chapter 6 Trigonometry: Measuring Triangles

    6.1 Right Triangle Trigonometry

    6.2 Applications of Right Triangle Trigonometry

    6.3 Law of Cosines

    6.4 Law of Sines

    Chapter 7 Analytic Trigonometry

    7.1 Trigonometric Identities

    7.2 The Addition Formulas

    7.3 Double- and Half-Angle Formulas

    7.4 The Product-Sum Formulas

    7.5 Trigonometric Equations

    7.6 Trigonometry and Complex Numbers

    Chapter 8 Analytic Geometry: The Conic Sections

    8.1 Analytic Geometry

    8.2 The Circle

    8.3 The Parabola

    8.4 The Ellipse and Hyperbola

    8.5 Identifying the Conic Sections

    Chapter 9 Systems of Equations and Inequalities

    9.1 Systems of Equations

    9.2 Solving by Elimination

    9.3 Applications

    9.4 Systems of Linear Equations in Three Unknowns

    9.5 Systems of Linear Inequalities

    9.6 Linear Programming (Optional)

    Chapter 10 Matrices and Determinants

    10.1 Matrices and Linear Systems

    10.2 Matrix Operations and Applications (Optional)

    10.3 Inverses of Matrices (Optional)

    10.4 Determinants and Cramer's Rule

    Chapter 11 Theory of Polynomials

    11.1 Polynomial Division and Synthetic Division

    11.2 The Remainder and Factor Theorems

    11.3 Factors and Zeros

    11.4 Real and Rational Zeros

    11.5 Rational Functions and Their Graphs

    Chapter 12 Topics in Algebra

    12.1 Sequences and Sigma Notation

    12.2 Arithmetic Sequences

    12.3 Geometric Sequences

    12.4 Mathematical Induction

    12.5 The Binomial Theorem

    12.6 Counting: Permutations and Combinations

    12.7 Probability

    Tables Appendix

    Answers to Odd-Numbered Exercises, and to Review Exercises and Progress Tests

    Solutions to Selected Review Exercises


Product details

  • No. of pages: 672
  • Language: English
  • Copyright: © Academic Press 1986
  • Published: January 1, 1986
  • Imprint: Academic Press
  • eBook ISBN: 9781483277134

About the Authors

Bernard Kolman

Affiliations and Expertise

Drexel University

Arnold Shapiro

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