College Algebra and Trigonometry, 5th Edition

College Algebra and Trigonometry, Fifth Edition, by Lial, Hornsby, Schneider, and Daniels, engages and supports students in the learning process by developing both the conceptual understanding and the analytical skills necessary for success in mathematics. With the Fifth Edition, the authors adapt to the new ways in which students are learning, as well as the ever-changing classroom environment.

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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