Algebra and Trigonometry with Analytic Geometry

Every chapter ends with Review Exercises, Discussion Exercises, and a Chapter Test. 1. FUNDAMENTAL CONCEPTS OF ALGEBRA. Real Numbers. Exponents and Radicals. Algebraic Expressions. Fractional Expressions. 2. EQUATIONS AND INEQUALITIES. Equations. Applied Problems. Quadratic Equations. Complex Numbers. Other Types of Equations. Inequalities. More on Inequalities. 3. FUNCTIONS AND GRAPHS. Rectangular Coordinate Systems. Graphs of Equations. Lines. Definition of Function. Graphs of Functions. Quadratic Functions. Operations on Functions. 4. POLYNOMIAL AND RATIONAL FUNCTIONS. Polynomial Functions of Degree Greater than 2. Properties of Division. Zeros of Polynomials. Complex and Rational Zeros of Polynomials. Rational Functions. Variation. 5. INVERSE, EXPONENTIAL, AND LOGARITHMIC FUNCTIONS. Inverse Functions. Exponential Functions. The Natural Exponential Function. Logarithmic Functions. Properties of Logarithms. Exponential and Logarithmic Equations. 6. THE TRIGONOMETRIC FUNCTIONS. Angles. Trigonometric Functions of Angles. Trigonometric Functions of Real Numbers. Values of Trigonometric Functions. Trigonometric Graphs. Additional Trigonometric Graphs. Applied Problems. 7. ANALYTIC TRIGONOMETRY. Verifying Trigonometric Identities. Trigonometric Equations. The Addition and Subtraction Formulas. Multiple-Angle Formulas. Product-to-Sum and Sum-to-Product Formulas. The Inverse Trigonometric Functions. 8. APPLICATIONS OF TRIGONOMETRY. The Law of Sines. The Law of Cosines. Vectors. The Dot Product. Trigonometric Form for Complex Numbers. De Moivre's Theorem and nth Roots of Complex Numbers. 9. SYSTEMS OF EQUATIONS AND INEQUALITIES. Systems of Equations. Systems of Linear Equations in Two Variables. Systems of Inequalities. Linear Programming. Systems of Linear Equations in More than Two Variables. The Algebra of Matrices. The Inverse of a Matrix. Determinants. Properties of Determinants. Partial Fractions. 10. SEQUENCES, SERIES AND PROBABILITY. Infinite Sequences and Summation Notation. Arithmetic Sequences. Geometric Sequences. Mathematical Induction. The Binomial Theorem. Permutations. Distinguishable Permutations and Combinations. Probability. 11. TOPICS FROM ANALYTIC GEOMETRY. Parabolas. Ellipses. Hyperbolas. Plane Curves and Parametric Equations. Polar Coordinates. Polar Equations of Conics. Appendix I: Common Graphs and Their Equations. Appendix II: A Summary of Graph Transformations. Appendix III: Graphs of the Trigonometric Functions and Their Inverses. Appendix IV: Values of the Trigonometric Functions of Special Angles on a Unit Circle.