College Algebra and Trigonometry

Marge Lial has always been interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, is now affiliated with American River College. Marge is an avid reader and traveler. Her travel experiences often find their way into her books as applications, exercise sets, and feature sets. She is particularly interested in archeology. Trips to various digs and ruin sites have produced some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.

When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics education or journalism. His ultimate decision was to become a teacher, but after twenty-five years of teaching at the high school and university levels and fifteen years of writing mathematics textbooks, both of his goals have been realized. His love for both teaching and for mathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum. John's personal life is busy as he devotes time to his family (wife Gwen, and sons Chris, Jack, and Josh). He has been a rabid baseball fan all of his life. John's other hobbies include numismatics (the study of coins) and record collecting. He loves the music of the 1960s and has an extensive collection of the recorded works of Frankie Valli and the Four Seasons.

David Schneider has taught mathematics at universities for over 34 years and has authored 36 books. He has an undergraduate degree in mathematics from Oberlin College and a PhD in mathematics from MIT. During most of his professional career, he was on the faculty of the University of Maryland--College Park. His hobbies include travel, dancing, bicycling, and hiking.

R. Review of Basic Concepts

R.1 Sets

R.2 Real Numbers and Their Properties

R.3 Polynomials

R.4 Factoring Polynomials

R.5 Rational Expressions

R.6 Rational Exponents

R.7 Radical Expressions

1. Equations and Inequalities

1.1 Linear Equations

1.2 Applications and Modeling with Linear Equations

1.3 Complex Numbers

1.4 Quadratic Equations

1.5 Applications and Modeling with Quadratic Equations

1.6 Other Types of Equations and Applications

1.7 Inequalities

1.8 Absolute Value Equations and Inequalities

2. Graphs and Functions

2.1 Rectangular Coordinates and Graphs

2.2 Circles

2.3 Functions

2.4 Linear Functions

2.5 Equations of Lines and Linear Models

2.6 Graphs of Basic Functions

2.7 Graphing Techniques

2.8 Function Operations and Composition

3. Polynomial and Rational Functions

3.1 Quadratic Functions and Models

3.2 Synthetic Division

3.3 Zeros of Polynomial Functions

3.4 Polynomial Functions: Graphs, Applications, and Models

3.5 Rational Functions: Graphs, Applications, and Models

3.6 Variation

4. Inverse, Exponential, and Logarithmic Functions

4.1 Inverse Functions

4.2 Exponential Functions

4.3 Logarithmic Functions

4.4 Evaluating Logarithms and the Change-of-Base Theorem

4.5 Exponential and Logarithmic Equations

4.6 Applications and Models of Exponential Growth and Decay

5. Trigonometric Functions

5.1 Angles

5.2 Trigonometric Functions

5.3 Evaluating Trigonometric Functions

5.4 Solving Right Triangles

6. The Circular Functions and Their Graphs

6.1 Radian Measure

6.2 The Unit Circle and Circular Functions

6.3 Graphs of the Sine and Cosine Functions

6.4 Translations of the Graphs of the Sine and Cosine Functions

6.5 Graphs of the Tangent, Cotangent, Secant, and Cosecant

6.6 Harmonic Motion

7. Trigonometric Identities and Equations

7.1 Fundamental Identities

7.2 Verifying Trigonometric Identities

7.3 Sum and Difference Identities

7.4 Double-Angle and Half-Angle Identities

7.5 Inverse Circular Functions

7.6 Trigonometric Equations

7.7 Equations Involving Inverse Trigonometric Functions

8. Applications of Trigonometry

8.1 The Law of Sines

8.2 The Law of Cosines

8.3 Vectors, Operation, and the Dot Product

8.4 Applications of Vectors

8.5 Trigonometric (Polar) Form of Complex Numbers; Products and Quotients

8.6 De Moivre's Theorem; Powers and Roots of Complex Numbers

8.7 Polar Equations and Graphs

8.8 Parametic Equations, Graphs, and Applications

9. Systems and Matrices

9.1 Systems of Linear Equations

9.2 Matrix Solution of Linear Systems

9.3 Determinant Solution of Linear Systems

9.4 Partial Fractions

9.5 Nonlinear Systems of Equations

9.6 Systems of Inequalities and Linear Programming

9.7 Properties of Matrices

9.8 Matrix Inverses

10. Analytic Geometry

10.1 Parabolas

10.2 Ellipses

10.3 Hyperbolas

10.4 Summary of the Conic Sections

11. Further Topics in Algebra

11.1 Sequences and Series

11.2 Arithmetic Sequences and Series

11.3 Geometric Sequences and Series

11.4 The Binomial Theorem

11.5 Mathematical Induction

11.6 Counting Theory

11.7 Basics of Probability

Appendices

Appendix A. Polar Form of Conic Sections

Appendix B. Rotation of Axes

Appendix C. Geometry Formulas

Glossary

Solutions to Selected Exercises

Answers to Selected Exercises

Index of Applications

Index

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