Algeba & Trigonometry Enhanced With Graphing Utilities

by Sullivan, Michael; Sullivan, Michael III

• ISBN13: 9780130833341
• ISBN10: 0130833347
• Edition: 2nd
• Format: Hardcover
• Copyright: 1999-09-01
• Publisher: Prentice Hall

Summary

Changes to this edition have significantly improved the text's accessibility. Graphing Calculator usage is used to promote mathematical modeling, problem solving and motivating concepts. The trigonometry is first developed through the right angle and then through unit circle. Features a full range of supplements including MathPak.

Table of Contents

Preface to the Instructor	ix
Preface to the Student	xiii
List of Application	xxiii
Photo Credits	xxvii
Graphs	1	(96)
Rectangular Coordinates; Graphing Utilities; Scatter Diagrams	2	(13)
Graphs of Equations	15	(14)
Solving Equations	29	(11)
Setting Up Equations; Applications	40	(13)
Solving Inequalities	53	(13)
Lines	66	(17)
Circles	83	(14)
Chapter Review	90	(5)
Chapter Projects	95	(2)
Linear and Quadratic Functions	97	(58)
Functions	98	(17)
Linear Functions and Models	115	(9)
Quadratic Equations and Functions	124	(15)
Quadratic Functions and Models	139	(16)
Chapter Review	150	(4)
Chapter Projects	154	(1)
Functions and Their Graphs	155	(58)
Characteristics of Functions; Library of Functions	156	(22)
Graphing Techniques: Transformations	178	(13)
Operations on Functions; Composite Functions	191	(9)
Mathematical Models: Constructing Functions	200	(13)
Chapter Review	208	(4)
Chapter Projects	212	(1)
Polynomial and Rational Functions	213	(96)
Power Functions and Models	214	(7)
Polynomial Functions and Models	221	(13)
Polynomial Division	234	(6)
The Real Zeros of a Polynomial Function	240	(14)
Complex Numbers; Quadratic Equations with a Negative Discriminant	254	(9)
Complex Zeros; Fundamental Theorem of Algebra	263	(7)
Rational Functions	270	(23)
Polynomial and Rational Inequalities	293	(16)
Chapter Review	302	(5)
Chapter Projects	307	(2)
Exponential and Logarithmic Functions	309	(92)
One-to-One Functions; Inverse Functions	310	(13)
Exponential Functions	323	(14)
Logarithmic Functions	337	(10)
Properties of Logarithms	347	(8)
Logarithmic and Exponential Equations	355	(7)
Compound Interest	362	(10)
Growth and Decay	372	(10)
Exponential, Logarithmic, and Logistic Curve Fitting	382	(19)
Chapter Review	393	(5)
Chapter Projects	398	(3)
Systems of Equations and Inequalities	401	(94)
Systems of Linear Equations: Two Equations Containing Two Variables	402	(11)
Systems of Linear Equations: Three Equations Containing Three Variables	413	(6)
Systems of Linear Equations: Matrices	419	(15)
Systems of Linear Equations: Determinants	434	(11)
Matrix Algebra	445	(19)
Systems of Linear Inequalities; Linear Programming	464	(17)
Partial Fraction Decomposition	481	(14)
Chapter Review	488	(5)
Chapter Projects	493	(2)
Trigonometric Functions	495	(92)
Angles and Their Measure	496	(12)
Right Triangle Trigonometry	508	(11)
Computing the Values of Trigonometric Functions of Given Angles	519	(7)
Trigonometric Functions of General Angles	526	(11)
Properties of the Trigonometric Functions; Unit Circle Approach	537	(11)
Graphs of the Trigonometric Functions	548	(12)
Sinusoidal Graphs; Sinusoidal Curve Fitting	560	(27)
Chapter Review	579	(6)
Chapter Projects	585	(2)
Analytic Trigonometry	587	(64)
Trigonometric Identities	589	(5)
Sum and Difference Formulas	594	(9)
Double-Angle and Half-Angle Formulas	603	(10)
Product-to-Sum and Sum-to-Product Formulas	613	(3)
The Inverse Trigonometric Functions	616	(16)
Trigonometric Equations (I)	632	(5)
Trigonometric Equations (II)	637	(14)
Chapter Review	644	(4)
Chapter Projects	648	(3)
Applications of Trigonometric Functions	651	(48)
Solving Right Triangles	652	(9)
The Law of Sines	661	(12)
The Law of Cosines	673	(6)
The Area of a Triangle	679	(6)
Simple Harmonic Motion; Damped Motion	685	(14)
Chapter Review	692	(5)
Chapter Projects	697	(2)
Polar Coordinates; Vectors	699	(64)
Polar Coordinates	700	(8)
Polar Equations and Graphs	708	(20)
The Complex Plane; DeMoivre's Theorem	728	(8)
Vectors	736	(11)
The Dot Product	747	(16)
Chapter Review	757	(4)
Chapter Projects	761	(2)
Analytic Geometry	763	(88)
Conics	764	(1)
The Parabola	765	(12)
The Ellipse	777	(13)
The Hyperbola	790	(14)
Rotation of Axes; General Form of a Conic	804	(9)
Polar Equations of Conics	813	(6)
Plane Curves and Parametric Equations	819	(15)
Systems of Nonlinear Equations	834	(17)
Chapter Review	845	(4)
Chapter Projects	849	(2)
Sequences; Induction; the Binomial Theorem	851	(54)
Sequences	852	(12)
Arithmetic Sequences	864	(7)
Geometric Sequences; Geometric Series	871	(16)
Mathematical Induction	887	(4)
The Binomial Theorem	891	(14)
Chapter Review	898	(4)
Chapter Projects	902	(3)
Counting and Probability	905	(54)
Sets and Counting	906	(6)
Permutations and Combinations	912	(10)
Probability of Equally Likely Outcomes	922	(16)
Analyzing Univariate Data; Obtaining Probabilities from Data	938	(21)
Chapter Review	952	(5)
Chapter Projects	957	(2)
APPENDIX REVIEW	959
1. Real Numbers	959	(14)
2. Algebra Review	973	(11)
3. Geometry Review	984	(6)
4. Integer Exponents	990	(8)
5. Polynomials	998	(8)
6. Factoring Polynomials	1006	(9)
7. Rational Expressions	1015	(12)
8. Square Roots; Radicals	1027	(8)
9. Rational Exponents	1035
Answers	AN1	(1)
Index	I1