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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.
Table of Contents
1. Algebraic Expressions.
Real Numbers and Their Properties. Order and Absolute Value. Polynomials; The Binomial Theorem. Factoring Polynomials. Rational Expressions. Rational Exponents. Radical Expressions.
2. Equations and Inequalities.
Linear Equations. Linear Applications and Modeling. Complex Numbers. Quadratic Equations. Quadratic Applications and Modeling. Other Types of Equations. Inequalities. Absolute Value Equations and Inequalities.
3. Relations, Functions, and Graphs.
Relations and the Rectangular Coordinate System; Circles. Functions. Linear Functions. Equations of Lines; Curve Fitting. Graphs of Relations and Functions. General Graphing Techniques. Operations and Composition.
4. Polynomial and Rational Functions.
Quadratic Functions; Curve Fitting. Synthetic Division. Zeros of Polynomial Functions. Polynomials Functions: Graphs, Applications, and Models. Rational Functions: Graphs, Applications, and Models. Variation.
5. Exponential and Logarithmic Functions.
Inverse Functions. Exponential Functions. Logarithmic Functions. Evaluating Logarithms and the Change-of-Base Theorem. Exponential and Logarithmic Equations. Applications and Models of Exponential Growth and Decay.
6. Trigonometric Functions.
Angles. Trigonometric Functions and Fundamental Identities. Finding Trigonometric Function Values. Solving Right Triangles. Radian Measure. Circular Functions and Their Applications. Graphs of the Sine and Cosine Functions. Graphs of the Other Circular Functions.
7. Trigonometric Identities and Equations.
Fundamental Identities. Verifying Trigonometric Identities. Sum and Difference Identities. Double-Angle Identities and Half-Angle Identities. Inverse Trigonometric Functions. Trigonometric Equations. Equations with Inverse Trigonometric Functions.
8. Applications of Trigonometry.
Oblique Triangles and the Law of Sines. The Law of Cosines. Vectors and Their Applications. Products and Quotients of Complex Numbers. Powers and Roots of Complex Numbers. Polar Equations. Parametric Equations.
9. Systems of Equations and Inequalities.
Linear Systems of Equations. Matrix Solution of Linear Systems. Determinant Solution of Linear Systems. Partial Fractions. Nonlinear Systems. Systems of Inequalities and Linear Programming. Properties of Matrices. Matrix Inverses.
10. Analytic Geometry.
Parabolas. Ellipses. Hyperbolas. Summary of the Conic Sections.
11. Further Topics in Algebra.
Sequences and Series. Arithmetic Sequences and Series. Geometric Sequences and Series. The Binomial Theorem Revisited. Mathematical Induction. Counting Theory. Basics of Probability.