Algebra and Trigonometry 2e
Algebra and Trigonometry 2e provides a comprehensive exploration of mathematical principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensure that the book addresses the needs of a variety of...
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| Format: | Electronic eBook |
| Language: | English |
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[Place of publication not identified]
OpenStax
[2021]
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| Series: | Open textbook library.
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| Online Access: | Access online version |
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Table of Contents:
- Preface
- Chapter 1. Prerequisites
- 1.1. Real Numbers: Algebra Essentials
- 1.2. Exponents and Scientific Notation
- 1.3. Radicals and Rational Exponents
- 1.4. Polynomials
- 1.5. Factoring Polynomials
- 1.6. Rational Expressions
- Chapter Review
- Exercises
- Chapter 2. Equations and Inequalities
- 2.1. The Rectangular Coordinate Systems and Graphs
- 2.2. Linear Equations in One Variable
- 2.3. Models and Applications
- 2.4. Complex Numbers
- 2.5. Quadratic Equations
- 2.6. Other Types of Equations
- 2.7. Linear Inequalities and Absolute Value Inequalities
- Chapter Review
- Exercises
- Chapter 3. Functions
- Introduction to Functions
- 3.1. Functions and Function Notation
- 3.2. Domain and Range
- 3.3. Rates of Change and Behavior of Graphs
- 3.4. Composition of Functions
- 3.5. Transformation of Functions
- 3.6. Absolute Value Functions
- 3.7. Inverse Functions
- Chapter Review
- Exercises
- Chapter 4. Linear Functions
- Introduction to Linear Functions
- 4.1. Linear Functions
- 4.2. Modeling with Linear Functionos
- 4.3. Fitting Linear Models to Data
- Chapter Review
- Exercises
- Chapter 5. Polynomial and Rational Functions
- Introduction to Polynomial and Rational Functions
- 5.1. Quadratic Functions
- 5.2. Power Functions and Polynomial Functions
- 5.3. Graphs of Polynomial Functions
- 5.4. Dividing Polynomials
- 5.5. Zeros of Polynomial Functions
- 5.6. Rational Functions
- 5.7. Inverses and Radical Functions
- 5.8. Modeling Using Variation
- Chapter Review
- Exercises
- Chapter 6. Exponential and Logarithmic Functions
- Introduction to Exponential and Logarithmic Functions
- 6.1. Exponential Functions
- 6.2. Graphs of Exponential Functions
- 6.3. Logarithmic Functions
- 6.4. Graphs of Logarithmic Functions
- 6.5. Logarithmic Properties
- 6.6. Exponential and Logarithmic Equations
- 6.7. Exponential and Logarithmic Models
- 6.8. Fitting Exponential Models to Data
- Chapter Review
- Exercises
- Chapter 7. The Unit Circle: Sine and Cosine Functions
- Introduction to The Unit Circle: Sine and Cosine Functions
- 7.1. Angles
- 7.2. Right Triangle Trigonometry
- 7.3. Unit Circle
- 7.4. The Other Trigonometric Functions
- Chapter Review
- Exercises
- Chapter 8. Periodic Functions
- Introduction to Periodic Functions
- 8.1 Graphs of the Sine and Cosine Functions
- 8.2 Graphs of the Other Trigonometric Functions
- 8.3 Inverse Trigonometric Functions
- Chapter Review
- Exercises
- Chapter 9. Trigonometric Identities and Equations
- Introduction to Trigonometric Identities and Equations
- 9.1 Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions
- 9.2 Sum and Difference Identities
- 9.3 Double-Angle, Half-Angle, and Reduction Formulas
- 9.4 Sum-to-Product and Product-to-Sum Formulas
- 9.5 Solving Trigonometric Equations
- Chapter Review
- Exercises
- Chapter 10. Further Applications of Trigonometry
- Introduction to Further Applications of Trigonometry
- 10.1 Non-right Triangles: Law of Sines
- 10.2 Non-right Triangles: Law of Cosines
- 10.3 Polar Coordinates
- 10.4 Polar Coordinates: Graphs
- 10.5 Polar Form of Complex Numbers
- 10.6 Parametric Equations
- 10.7 Parametric Equations: Graphs
- 10.8 Vectors
- Chapter Review
- Exercises
- Chapter 11. Systems of Equations and Inequalities
- Introduction to Systems of Equations and Inequalities
- 11.1 Systems of Linear Equations: Two Variables
- 11.2 Systems of Linear Equations: Three Variables
- 11.3 Systems of Nonlinear Equations and Inequalities: Two Variables
- 11.4 Partial Fractions
- 11.5 Matrices and Matrix Operations
- 11.6 Solving Systems with Gaussian Elimination
- 11.7 Solving Systems with Inverses
- 11.8 Solving Systems with Cramer's Rule
- Chapter Review
- Exercises
- Chapter 12. Analytic Geometry
- Introduction to Analytic Geometry
- 12.1 The Ellipse
- 12.2 The Hyperbola
- 12.3 The Parabola
- 12.4 Rotation of Axes
- 12.5 Conic Sections in Polar Coordinates
- Chapter Review
- Exercises
- Chapter 13. Sequences, Probability, and Counting Theory
- Introduction to Sequences, Probability, and Counting Theory
- 13.1 Sequences and Their Notations
- 13.2 Arithmetic Sequences
- 13.3 Geometric Sequences
- 13.4 Series and Their Notations
- 13.5 Counting Principles
- 13.6 Binomial Theorem
- 13.7 Probability
- Chapter Review
- Exercises
- Appendix A. Proofs, Identities, and Toolkit Functions
- Answer Key
- Index