Algebra and Trigonometry

by Stewart, James; Redlin, Lothar; Watson, Saleem

• ISBN13: 9780534380298
• ISBN10: 0534380298
• Format: Hardcover
• Copyright: 2000-12-20
• Publisher: Cengage High School

Summary

James Stewart, the author of the worldwide best-selling calculus texts, along with two of his former Ph.D. students, Lothar Redlin and Saleem Watson, collaborated in writing this book to address a problem they frequently saw in their calculus courses. Many students were not prepared to "think mathematically" but attempted to memorize facts and mimic examples. ALGEBRA AND TRIGONOMETRY was designed specifically to help readers learn to think mathematically and to develop true problem-solving skills. Patient, clear, and accurate, the text consistently illustrates how useful and applicable mathematics is to real life. The new book follows the successful approach taken in the authors' previous books, COLLEGE ALGEBRA, Third Edition, and PRECALCULUS, Third Edition.

Table of Contents

Basic Algebra	2	(72)
What Is Algebra?	3	(6)
Real Numbers	9	(11)
Exponents and Radicals	20	(12)
Algebraic Expressions	32	(12)
Discovery Project Visualizing a Formula	43	(1)
Fractional Expressions	44	(9)
Basic Equations	53	(21)
Review	63	(3)
Test	66	(1)
Principles of Problem Solving	67	(7)
Coordinates and Graphs	74	(56)
The Coordinate Plane	75	(9)
Discovery Project Visualizing Data	82	(2)
Graphs of Equations	84	(10)
Graphing Calculators and Computers	94	(6)
Lines	100	(30)
Review	115	(3)
Test	118	(1)
Principles of Modeling	119	(11)
Equations and Inequalities	130	(78)
Algebraic and Graphical Solutions of Equations	131	(5)
Modeling with Equations	136	(15)
Writing Project Equations Through the Ages	150	(1)
Quadratic Equations	151	(13)
Complex Numbers	164	(7)
Other Equations	171	(10)
Linear Inequalities	181	(6)
Nonlinear Inequalities	187	(9)
Absolute Value	196	(12)
Review	199	(3)
Test	202	(1)
Focus on Problem Solving	203	(5)
Functions	208	(102)
What Is a Function?	209	(11)
Graphs of Functions	220	(11)
Applied Functions: Variation	231	(5)
Average Rate of Change: Increasing and Decreasing Functions	236	(11)
Transformations of Functions	247	(11)
Extreme Values of Functions	258	(10)
Combining Functions	268	(12)
Laboratory Project Iteration and Chaos	278	(2)
One-to-One Functions and Their Inverses	280	(30)
Review	289	(5)
Test	294	(2)
Focus on Modeling	296	(14)
Polynomial and Rational Functions	310	(68)
Polynomial Functions and Their Graphs	311	(15)
Dividing Polynomials	326	(7)
Real Zeros of Polynomials	333	(13)
Discovery Project Zeroing in on a Zero	345	(1)
The Fundamental Theorem of Algebra	346	(8)
Rational Functions	354	(24)
Review	370	(2)
Test	372	(1)
Focus on Problem Solving	373	(5)
Exponential and Logarithmic Functions	378	(68)
Exponential Functions	379	(8)
Discovery Project Exponential Explosion	386	(1)
The Natural Exponential Function	387	(10)
Logarithmic Functions	397	(10)
Laws of Logarithms	407	(5)
Exponential and Logarithmic Equations	412	(7)
Applications of Exponential and Logarithmic Functions	419	(27)
Review	434	(3)
Test	437	(1)
Focus on Modeling	438	(8)
Trigonometric Functions of Angles	446	(60)
Angle Measure	447	(8)
Trigonometry of Right Triangles	455	(11)
Trigonometric Functions of Angles	466	(12)
Discovery Project Similarity	476	(2)
The Law of Sines	478	(8)
The Law of Cosines	486	(20)
Review	494	(4)
Test	498	(2)
Focus on Problem Solving	500	(6)
Trigonometric Functions of Real Numbers	506	(60)
The Unit Circle	507	(9)
Trigonometric Functions of Real Numbers	516	(10)
Trigonometric Graphs	526	(16)
Discovery Project Predator/Prey Models	540	(2)
More Trigonometric Graphs	542	(24)
Review	550	(3)
Test	553	(1)
Focus on Modeling	554	(12)
Analytic Trigonometry	566	(82)
Trigonometric Identities	567	(8)
Addition and Subtraction Formulas	575	(7)
Double-Angle, Half-Angle, and Product-Sum Formulas	582	(10)
Inverse Trigonometric Functions	592	(10)
Discovery Project Where to Sit at the Movies	600	(2)
Trigonometric Equations	602	(8)
Trigonometric Form of Complex Numbers; DeMoivre's Theorem	610	(9)
Vectors	619	(11)
The Dot Product	630	(18)
Review	638	(4)
Test	642	(2)
Focus on Problem Solving	644	(4)
Systems of Equations and Inequalities	648	(86)
Systems of Equations	649	(9)
Pairs of Lines	658	(8)
Systems of Linear Equations	666	(14)
The Algebra of Matrices	680	(9)
Laboratory Project Will the Species Survive?	688	(1)
Inverses of Matrices and Matrix Equations	689	(10)
Determinants and Cramer's Rule	699	(10)
Systems of Inequalities	709	(5)
Partial Fractions	714	(20)
Review	720	(3)
Test	723	(2)
Focus on Modeling	725	(9)
Topics in Analytic Geometry	734	(82)
Parabolas	736	(9)
Laboratory Project Rolling Down a Ramp	744	(1)
Ellipses	745	(10)
Hyperbolas	755	(9)
Shifted Conics	764	(8)
Rotation of Axes	772	(8)
Polar Coordinates	780	(12)
Polar Equations of Conics	792	(6)
Parametric Equations	798	(18)
Review	806	(4)
Test	810	(2)
Focus on Modeling	812	(4)
Sequences and Series	816	(60)
Sequences and Summation Notation	817	(10)
Arithmetic Sequences	827	(6)
Geometric Sequences	833	(10)
Discovery Project Finding Patterns	842	(1)
Annuities and Installment Buying	843	(7)
Mathematical Induction	850	(7)
The Binomial Theorem	857	(19)
Review	867	(3)
Test	870	(1)
Focus on Problem Solving	871	(5)
Counting and Probability	876
Counting Principles	877
Permutations and Combinations	882
Probability	891
Laboratory Project Small Samples, Big Results	903
Expected Value	904
Review	907
Test	910
Focus on Modeling	911
Answers to Odd-Numbered Exercises and Chapter Tests	A1
Index	A65