Algebra and Trigonometry

Preface

Acknowledgments

To the Student

About the Author

Applications Index



P. Prerequisites: Fundamental Concepts of Algebra

P.1 Algebraic Expressions, Mathematical Models, and Real Numbers

P.2 Exponents and Scientific Notation

P.3 Radicals and Rational Exponents

P.4 Polynomials

P.5 Factoring Polynomials

P.6 Rational Expressions



1. Equations and Inequalities

1.1 Graphs and Graphing Utilities

1.2 Linear Equations and Rational Equations

1.3 Models and Applications

1.4 Complex Numbers

1.5 Quadratic Equations

1.6 Other Types of Equations

1.7 Linear Inequalities and Absolute Value Inequalities



2. Functions and Graphs

2.1 Basics of Functions and Their Graphs

2.2 More on Functions and Their Graphs

2.3 Linear Functions and Slope

2.4 More on Slope

2.5 Transformations of Functions

2.6 Combinations of Functions; Composite Functions

2.7 Inverse Functions

2.8 Distance and Midpoint Formulas; Circles



3. Polynomial and Rational Functions

3.1 Quadratic Functions

3.2 Polynomial Functions and Their Graphs

3.3 Dividing Polynomials; Remainder and Factor Theorems

3.4 Zeros of Polynomial Functions

3.5 Rational Functions and Their Graphs

3.6 Polynomial and Rational Inequalities

3.7 Modeling Using Variation



4. Exponential and Logarithmic Functions

4.1 Exponential Functions

4.2 Logarithmic Functions

4.3 Properties of Logarithms

4.4 Exponential and Logarithmic Equations

4.5 Exponential Growth and Decay; Modeling Data



5. Trigonometric Functions

5.1 Angles and Radian Measure

5.2 Right Triangle Trigonometry

5.3 Trigonometric Functions of Any Angle

5.4 Trigonometric Functions of Real Numbers; Periodic Functions

5.5 Graphs of Sine and Cosine Functions

5.6 Graphs of Other Trigonometric Functions

5.7 Inverse Trigonometric Functions

5.8 Applications of Trigonometric Functions



6. Analytic Trigonometry

6.1 Verifying Trigonometric Identities

6.2 Sum and Difference Formulas

6.3 Double-Angle, Power-Reducing, and Half-Angle Formulas

6.4 Product-to-Sum and Sum-to-Product Formulas

6.5 Trigonometric Equations



7. Additional Topics in Trigonometry

7.1 The Law of Sines

7.2 The Law of Cosines

7.3 Polar Coordinates

7.4 Graphs of Polar Equations

7.5 Complex Numbers in Polar Form; DeMoivre's Theorem

7.6 Vectors

7.7 The Dot Product



8. Systems of Equations and Inequalities

8.1 Systems of Linear Equations in Two Variables

8.2 Systems of Linear Equations in Three Variables

8.3 Partial Fractions

8.4 Systems of Nonlinear Equations in Two Variables

8.5 Systems of Inequalities

8.6 Linear Programming



9. Matrices and Determinants

9.1 Matrix Solutions to Linear Systems

9.2 Inconsistent and Dependent Systems and Their Applications

9.3 Matrix Operations and Their Applications

9.4 Multiplicative Inverses of Matrices and Matrix Equations

9.5 Determinants and Cramer's Rule



10. Conic Sections and Analytic Geometry

10.1 The Ellipse

10.2 The Hyperbola

10.3 The Parabola

10.4 Rotation of Axes

10.5 Parametric Equations

10.6 Conic Sections in Polar Coordinates



11. Sequences, Induction, and Probability

11.1 Sequences and Summation Notation

11.2 Arithmetic Sequences

11.3 Geometric Sequences and Series

11.4 Mathematical Induction

11.5 The Binomial Theorem

11.6 Counting Principles, Permutations, and Combinations

11.7 Probability



Appendix

Where Did That Come From? Selected Proofs

Answers to Selected Exercises

Subject Index

Photo Credits