College Algebra and Trigonometry
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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
Acknowledgments
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
Index
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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