Algebra and Trigonometry

(NOTE: Each chapter concludes with Chapter Review and Project at Motorola.) R. Review. Real Numbers. Algebra Review. Geometry Review. Integer Exponents. Polynomials. Factoring Polynomials. Rational Expressions. Square Roots; Radicals. Rational Exponents. 1. Equations and Inequalities. Equations. Setting Up Equations: Applications. Quadratice Equations. Radical Equations; Equations Quadratic in Form. Solving Inequalities. Equations and Inequalities Involving Absolute Value. 2. Graphs. Rectangular Coordinates. Graphs of Equations. Lines. Parallel and Perpendicular Lines; Circles. Scatter Diagrams; Linear Curve Fitting. Variation. 3. Functions and Their Graphs. Functions. Properties of Functions. Library of Functions; Piecewise-Defined Functions. Graphing Techniques: Transformations. Operations on Functions; Composite Functions. Mathematical Models: Constructing Functions. 4. Polynomial and Rational Functions. Quadratice Functions and Models. Polynomial Functions. Rational Functions I. Rational Functions II: Analyzing Graphs. Polynomial and Rational Inequalities. 5. The Zeros of a Polynomial Function. Synthetic Division. The Real Zeros of a Polynomial Function. Complex Numbers; Quadratic Equations with a Negative Discriminant. Complex Zeros; Fundamental Theorem of Algebra. 6. Exponential and Logarithmic Functions. One-to-One Functions; Inverse Functions. Exponential Functions. Logarithmic Functions. Properties of Logarithms; Exponential and Logarithmic Models. Logarithmic and Exponential Equations. Compound Interest. Growth and Decay; Newtons Law; Logistic Models. Logarithmic Scales. 7. Trigonometric Functions. Angles and Their Measure. Right Triangle Trigonometry. Computing the Values of Trigonometric Functions of Given Angles. Trigonometric Functions of General Angles. Properties of the Trigonometric Functions; Unit Circle Approach. Graphs of the Sine and Cosine Functions. Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions. Phase Shift; Sinusoidal Curve Fitting. 8. Analytic Trigonometry. The Inverse Sine, Cosine, and Tangent Functions. The Inverse Trigonometric Functions (Continues). Trigonometric Identities. Sum and Difference Formulas. Double-angle and Half-angle Formulas. Product-to-Sum and Sum-to-Product Formulas. Trigonometric Equations I. Trigonometric Equations II. 9. Applications of Trigonometric Functions. Applications Involving Right Triangles. The Law of Sines. The Law of Cosines. The Area of a Triangle. Simple Harmonic Motion; Damped Motion; Combining Waves. 10. Polar Coordinates; Vectors. Polar Coordinates. Polar Equations and Graphs. The Complex Plane; De Moivres Theorem. Vectors. The Dot Product. 11. Analytic Geometry. Conics. The Parabola. The Ellipse. The Hyperbola. Rotation of Axes; General Form of a Conic. Polar Equations of Conics. Plane Curves and Parametric Equations. 12. Systems of Equations and Inequalities. Systems of Linear Equations: Two Equations Containing Two Variables. Systems of Linear Equations: Three Equations Containing Three Variables. Systems of Linear Equations: Matrices. Systems of Linear Equations: Determinants. Matrix Algebra. Partial Fraction Decomposition. Systems of Nonlinear Equations. Systems of Inequalities. Linear Programming. 13. Sequences; Induction; The Binomial Theorem. Sequences. Arithmetic Sequences. Geometric Sequences; Geometric Series. Mathematical Induction. The Binomial Theorem. 14. Counting and Probability Sets and Counting. Permutations and Combinations. Probability. Appendix: Graphing Utilities. The Viewing Rectangle. Using a Graphing Utility to Graph Equations. Using a Graphing Utility to Locate Intercepts and Check for Symmetry. Using a Graphing Utility to Solve Equations. Square Screens. Using a Graphing Utility to Graph Inequalities. Using a Graphing Utility to Solve Systems of Linear Equations. Using a Graphing Utility to Graph a Polar Equation. Using a Graphing Utility to Graph Parametric Equations. Answers. Index.