This book, intended for a graphing calculator optional college algebra and trigonometry course, offers students the content and tools they will need to successfully master college algebra and trigonometry. The authors have addressed the needs of students who will continue their study of mathematics, as well as those who are taking college algebra and trigonometry as their final mathematics course. Emphasis is placed on exploring mathematical concepts by using real data, current applications and optional technology.
1. Algebraic Expressions.
Real Numbers and Their Properties. 2. Equations and Inequalities.
Order and Absolute Value.
Polynomials; The Binomial Theorem.
Linear Equations. 3. Relations, Functions, and Graphs.
Linear Applications and Modeling.
Quadratic Applications and Modeling.
Other Types of Equations.
Absolute Value Equations and Inequalities.
Relations and the Rectangular Coordinate System; Circles. 4. Polynomial and Rational Functions.
Equations of Lines; Curve Fitting.
Graphs of Relations and Functions.
General Graphing Techniques.
Operations and Composition.
Quadratic Functions; Curve Fitting. 5. Exponential and Logarithmic Functions.
Zeros of Polynomial Functions.
Polynomials Functions: Graphs, Applications, and Models.
Rational Functions: Graphs, Applications, and Models.
Inverse Functions. 6. Trigonometric Functions.
Evaluating Logarithms and the Change-of-Base Theorem.
Exponential and Logarithmic Equations.
Applications and Models of Exponential Growth and Decay.
Angles. 7. Trigonometric Identities and Equations.
Trigonometric Functions and Fundamental Identities.
Finding Trigonometric Function Values.
Solving Right Triangles.
Circular Functions and Their Applications.
Graphs of the Sine and Cosine Functions.
Graphs of the Other Circular Functions.
Fundamental Identities. 8. Applications of Trigonometry.
Verifying Trigonometric Identities.
Sum and Difference Identities.
Double-Angle Identities and Half-Angle Identities.
Inverse Trigonometric Functions.
Equations with Inverse Trigonometric Functions.
Oblique Triangles and the Law of Sines. 9. Systems of Equations and Inequalities.
The Law of Cosines.
Vectors and Their Applications.
Products and Quotients of Complex Numbers.
Powers and Roots of Complex Numbers.
Linear Systems of Equations. 10. Analytic Geometry.
Matrix Solution of Linear Systems.
Determinant Solution of Linear Systems.
Systems of Inequalities and Linear Programming.
Properties of Matrices.
Parabolas. 11. Further Topics in Algebra.
Summary of the Conic Sections.
Sequences and Series.
Arithmetic Sequences and Series.
Geometric Sequences and Series.
The Binomial Theorem Revisited.
Basics of Probability.