Algebra and Trigonometry With Analytic Geometry

by Swokowski, Earl W.; Cole, Jeffrey A.

• ISBN13: 9780534953089
• ISBN10: 0534953085
• Format: Paperback
• Copyright: 1997-01-11
• Publisher: Brooks Cole

Summary

This latest edition in the highly respected Swokowski/Cole precalculus series retains the elements that have made it so popular with instructors and students alike: its exposition is clear, the time-tested exercise sets feature a variety of applications, its uncluttered layout is appealing, and the difficulty level of problems is appropriate and consistent. The goal of this text is to prepare students for further courses in mathematics. Mathematically sound, ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY (CLASSIC EDITION), Eleventh Edition, effectively prepares students for further courses in mathematics through its excellent, time-tested problem sets.

Table of Contents

PREFACE	x
CHAPTER 1 FUNDAMENTAL CONCEPTS OF ALGEBRA	1	(52)
1.1 Real Numbers	2	(13)
1.2 Exponents and Radicals	15	(12)
1.3 Algebraic Expressions	27	(13)
1.4 Fractional Expressions	40	(9)
CHAPTER 1 REVIEW EXERCISES	49	(2)
CHAPTER 1 DISCUSSION EXERCISES	51	(2)
CHAPTER 2 EQUATIONS AND INEQUALITIES	53	(70)
2.1 Equations	54	(8)
2.2 Applied Problems	62	(12)
2.3 Quadratic Equations	74	(12)
2.4 Complex Numbers	86	(6)
2.5 Other Types of Equations	92	(9)
2.6 Inequalities	101	(9)
2.7 More on Inequalities	110	(7)
CHAPTER 2 REVIEW EXERCISES	117	(3)
CHAPTER 2 DISCUSSION EXERCISES	120	(3)
CHAPTER 3 FUNCTIONS AND GRAPHS	123	(114)
3.1 Rectangular Coordinate Systems	124	(7)
3.2 Graphs of Equations	131	(13)
3.3 Lines	144	(17)
3.4 Definition of Function	161	(15)
3.5 Graphs of Functions	176	(13)
3.6 Quadratic Functions	189	(14)
3.7 Operations on Functions	203	(10)
3.8 Inverse Functions	213	(10)
3.9 Variation	223	(6)
CHAPTER 3 REVIEW EXERCISES	229	(5)
CHAPTER 3 DISCUSSION EXERCISES	234	(3)
CHAPTER 4 POLYNOMIAL AND RATIONAL FUNCTIONS	237	(56)
4.1 Polynomial Functions of Degree Greater Than 2	238	(8)
4.2 Properties of Division	246	(8)
4.3 Zeros of Polynomials	254	(13)
4.4 Complex and Rational Zeros of Polynomials	267	(8)
4.5 Rational Functions	275	(15)
CHAPTER 4 REVIEW EXERCISES	290	(2)
CHAPTER 4 DISCUSSION EXERCISES	292	(1)
CHAPTER 5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS	293	(60)
5.1 Exponential Functions	294	(11)
5.2 The Natural Exponential Function	305	(10)
5.3 Logarithmic Functions	315	(15)
5.4 Properties of Logarithms	330	(8)
5.5 Exponential and Logarithmic Equations	338	(10)
CHAPTER 5 REVIEW EXERCISES	348	(2)
CHAPTER 5 DISCUSSION EXERCISES	350	(3)
CHAPTER 6 THE TRIGONOMETRIC FUNCTIONS	353	(96)
6.1 Angles	354	(9)
6.2 Trigonometric Functions of Angles	363	(16)
6.2 Trigonometric Functions of Real Numbers	379	(19)
6.4 Values of the Trigonometric Functions	398	(7)
6.5 Trigonometric Graphs	405	(15)
6.6 Additional Trigonometric Graphs	420	(9)
6.7 Applied Problems	429	(13)
CHAPTER 6 REVIEW EXERCISES	442	(6)
CHAPTER 6 DISCUSSION EXERCISES	448	(1)
CHAPTER 7 ANALYTIC TRIGONOMETRY	449	(64)
7.1 Verifying Trigonometric Identities	450	(5)
7.2 Trigonometric Equations	455	(12)
7.3 The Addition and Subtraction Formulas	467	(11)
7.4 Multiple-Angle Formulas	478	(10)
7.5 Product-to-Sum and Sum-to-Product Formulas	488	(5)
7.6 The Inverse Trigonometric Functions	493	(15)
CHAPTER 7 REVIEW EXERCISES	508	(3)
CHAPTER 7 DISCUSSION EXERCISES	511	(2)
CHAPTER 8 APPLICATIONS OF TRIGONOMETRY	513	(60)
8.1 The Law of Sines	514	(10)
8.2 The Law of Cosines	524	(10)
8.3 Trigonometric Form for Complex Numbers	534	(5)
8.4 De Moivre's Theorem and nth Roots of Complex Numbers	539	(5)
8.5 Vectors	544	(14)
8.6 The Dot Product	558	(10)
CHAPTER 8 REVIEW EXERCISES	568	(3)
CHAPTER 8 DISCUSSION EXERCISES	571	(2)
CHAPTER 9 SYSTEMS OF EQUATIONS AND INEQUALITIES	573	(90)
9.1 Systems of Equations	574	(9)
9.2 Systems of Linear Equations in Two Variables	583	(8)
9.3 Systems of Linear Equations in More Than Two Variables	591	(15)
9.4 Partial Fractions	606	(6)
9.5 Systems of Inequalities	612	(7)
9.6 Linear Programming	619	(9)
9.7 The Algebra of Matrices	628	(9)
9.8 The Inverse of a Matrix	637	(6)
9.9 Determinants	643	(7)
9.10 Properties of Determinants	650	(8)
CHAPTER 9 REVIEW EXERCISES	658	(3)
CHAPTER 9 DISCUSSION EXERCISES	661	(2)
CHAPTER 10 SEQUENCES, SERIES, AND PROBABILITY	663	(72)
10.1 Infinite Sequences and Summation Notation	664	(9)
10.2 Arithmetic Sequences	673	(7)
10.3 Geometric Sequences	680	(9)
10.4 Mathematical Induction	689	(6)
10.5 The Binomial Theorem	695	(9)
10.6 Permutations	704	(7)
10.7 Distinguishable Permutations and Combinations	711	(7)
10.8 Probability	718	(12)
CHAPTER 10 REVIEW EXERCISES	730	(3)
CHAPTER 10 DISCUSSION EXERCISES	733	(2)
CHAPTER 11 TOPICS AND ANALYTIC GEOMETRY	735	(69)
11.1 Parabolas	736	(10)
11.2 Ellipses	746	(13)
11.3 Hyperbolas	759	(13)
11.4 Plane Curves and Parametric Equations	772	(10)
11.5 Polar Coordinates	782	(12)
11.6 Polar Equations of Conics	794	(7)
CHAPTER II REVIEW EXERCISES	801	(2)
CHAPTER II DISCUSSION EXERCISES	803	(1)
APPENDIXES	804
I Using a TI-82/83 Graphing Calculator	804	(38)
II Common Graphs and Their Equations	842	(2)
III A Summary of Graph Transformations	844	(2)
IV Graphs of Trigonometric Functions and Their Inverses	846
ANSWERS TO SELECTED EXERCISES	A1	(88)
INDEX OF APPLICATIONS	A89	(6)
INDEX	A95