Introduction to Algebra and Trigonometry

Introduction to Algebra and Trigonometry

1st Edition - January 1, 1981

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  • Authors: Bernard Kolman, Arnold Shapiro
  • eBook ISBN: 9781483263915

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Introduction to Algebra and Trigonometry provides a complete and self-contained presentation of the fundamentals of algebra and trigonometry. This book describes an axiomatic development of the foundations of algebra, defining complex numbers that are used to find the roots of any quadratic equation. Advanced concepts involving complex numbers are also elaborated, including the roots of polynomials, functions and function notation, and computations with logarithms. This text also discusses trigonometry from a functional standpoint. The angles, triangles, and applications involving triangles are likewise treated. Other topics include analytic geometry, conic sections, and use of a coordinate system to prove theorems from plane, and matrix operations and inverses. This publication is valuable to students aiming to gain more knowledge of the fundamentals of mathematics.

Table of Contents

  • Preface


    To the Student

    Chapter One 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 Review Material

    Chapter Two 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—Quadratic Equations

    2.7 Second-Degree Inequalities

    Chapter Review Material

    Chapter Three Functions

    3.1 Rectangular Coordinate Systems

    3.2 Functions and Function Notation

    3.3 Graphs of Functions

    3.4 Linear Functions

    3.5 Direct and Inverse Variation

    3.6 Combining Functions; Inverse Functions

    Chapter Review Material

    Chapter Four Exponential And Logarithmic Functions

    4.1 Exponential Functions

    4.2 Logarithmic Functions

    4.3 Properties of Logarithms

    4.4 Computing with Logarithms (Optional)

    4.5 Exponential and Logarithmic Equations

    Chapter Review Material

    Chapter Five Trigonometry: The Circular Functions

    5.1 The Wrapping Function

    5.2 The Sine, Cosine, and Tangent Functions

    5.3 Graphs of Sine, Cosine, and Tangent

    5.4 Variation of Sine, Cosine, and Tangent

    5.5 Graphs: Amplitude, Variation, and Phase Shift

    5.6 Secant, Cosecant, and Cotangent

    5.7 The Inverse Trigonometric Functions

    Chapter Review Material

    Chapter Six Angles And Triangles

    6.1 Angles and Their Measurement

    6.2 Trigonometric Functions of Angles

    6.3 Right Angle Trigonometry

    6.4 Law of Cosines

    6.5 Law of Sines

    Chapter Review Material

    Chapter Seven 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 Review Material

    Chapter Eight 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 Review Material

    Chapter Nine Systems Of Equations And Inequalities

    9.1 Systems of Linear Equations

    9.2 Solving by Elimination

    9.3 Applications

    9.4 Systems of Linear Equations in Three Unknowns

    9.5 Systems Involving Nonlinear Equations

    9.6 Systems of Linear Inequalities in Two Variables

    Chapter Review Material

    Chapter Ten 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 Review Material

    Chapter Eleven Roots Of Polynomials

    11.1 Polynomial Division and Synthetic Division

    11.2 The Remainder and Factor Theorems

    11.3 Factors and Roots

    11.4 Real and Rational Roots

    11.5 Rational Functions and Their Graphs

    Chapter Review Material

    Chapter Twelve Topics In Algebra

    12.1 Arithmetic Progressions

    12.2 Geometric Progressions

    12.3 Mathematical Induction

    12.4 The Binomial Theorem

    12.5 Counting: Permutations and Combinations

    12.6 Probability

    Chapter Review Material


    Answers To Odd-Numbered Exercises, Review Exercises, And Progress Tests


Product details

  • No. of pages: 620
  • Language: English
  • Copyright: © Academic Press 1981
  • Published: January 1, 1981
  • Imprint: Academic Press
  • eBook ISBN: 9781483263915

About the Authors

Bernard Kolman

Affiliations and Expertise

Drexel University

Arnold Shapiro

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