Algebra and Trigonometry

Description

Algebra and Trigonometry provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensures that the book meets the needs of a variety of courses. Algebra and Trigonometry offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned. Preface 1. About OpenStax 2. About OpenStax's Resources 3. About Algebra and Trigonometry 4. Pedagogical Foundations and Features 5. Additional Resources Chapter 1. Prerequisites 1.1. Real Numbers: Algebra Essentials 1.2. Exponents and Scientific Notation 1.3. Radicals and Rational Expressions 1.4. Polynomials 1.5. Factoring Polynomials 1.6. Rational Expressions Glossary 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 Equations and Absolute Value Inequalities Glossary Chapter 3. 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 Glossary Chapter 4. Linear Functions 4.1. Linear Functions 4.2. Modeling with Linear Functions 4.3. Fitting Linear Models to Data Glossary Chapter 5. 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 Glossary Chapter 6. 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 Glossary Chapter 7. 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 Glossary Chapter 8. Periodic Functions 8.1. Graphs of the Sine and Cosine Functions 8.2. Graphs of the Other Trigonometric Functions 8.3. Inverse Trigonometric Functions Glossary Chapter 9. Trigonometric Identities and Equations 9.1. Solving Trigonometric Equations with Identities 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. Solviong Trigonometric Equations Glossary Chapter 10. 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 Glossary Chapter 11. 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 Glossary Chapter 12. Analytic Geometry 12.1. The Ellipse 12.2. The Hyperbola 12.3. The Parabola 12.4. Rotation of Axis Glossary Chapter 13. 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 Glossary Appendix A. Proofs, Identities, and Toolkit Functions Try It Answers Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Odd Answers Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Index