College Algebra With Trigonometry

by Barnett, Raymond A.; Byleen, Karl E.

• ISBN13: 9780072368697
• ISBN10: 0072368691
• Edition: 7th
• Format: Hardcover
• Copyright: 2000-06-30
• Publisher: McGraw-Hill Science/Engineering/Math

Author Biography

Raymond A. Barnett received his B.A. in mathematical statistics from the University of California at Berkeley and his M.A. in mathematics from the University of Southern California Michael R. Ziegler received his B.S. from Shippensburg State College and his M.S. and Ph.D. from the University of Delaware. After completing postdoctoral work at the University of Kentucky, he was appointed to the faculty of Marquette University where he currently holds the rank of Professor in the Department of Mathematics, Statistics, and Computer Science Karl E. Byleen received his B.S., M.A., and Ph.D. degrees in mathematics from the University of Nebraska. He is currently an Associate Professor in the Department of Mathematics, Statistics, and Computer Science of Marquette University

Table of Contents

Preface	ix
Chapter Dependencies	xx
To the Student	xxiv
Basic Algebraic Operations	1	(72)
Algebra and Real Numbers	2	(10)
Polynomials: Basic Operations	12	(11)
Polynomials: Factoring	23	(10)
Rational Expressions: Basic Operations	33	(9)
Integer Exponents	42	(9)
Rational Exponents	51	(6)
Radicals	57	(16)
Rational Number Representations	67	(1)
Review	67	(6)
Equations and Inequalities	73	(100)
Linear Equations and Applications	74	(15)
Systems of Linear Equations and Applications	89	(9)
Linear Inequalities	98	(11)
Absolute Value in Equations and Inequalities	109	(10)
Complex Numbers	119	(11)
Quadratic Equations and Applications	130	(15)
Equations Reducible to Quadratic Form	145	(8)
Polynomial and Rational Inequalities	153	(20)
Rates of Change	162	(1)
Review	163	(5)
Cumulative Review Exercise	168	(5)
Graphs and Functions	173	(110)
Basic Tools; Circles	174	(17)
Straight Lines	191	(16)
Functions	207	(16)
Graphing Functions	223	(18)
Combining Functions	241	(17)
Inverse Functions	258	(25)
Mathematical Modeling in Business	274	(2)
Review	276	(7)
Polynomial and Rational Functions	283	(70)
Polynomial Functions and Graphs	285	(12)
Finding Rational Zeros of Polynomials	297	(13)
Approximating Real Zeros of Polynomials	310	(12)
Rational Functions	322	(15)
Partial Fractions	337	(16)
Interpolating Polynomials	345	(2)
Review	347	(6)
Exponential and Logarithmic Functions	353	(60)
Exponential Functions	354	(11)
The Exponential Function with Base e	365	(11)
Logarithmic Functions	376	(9)
Common and Natural Logarithms	385	(10)
Exponential and Logarithmic Equations	395	(18)
Growth of Increasing Functions	405	(1)
Review	405	(3)
Cumulative Review Exercise	408	(5)
Trigonometric Functions	413	(110)
Angles and Their Measure	414	(9)
Acute Angle Domains	423	(12)
General Angle and Real Number Domains	435	(9)
Exact Values for Special Angles and Real Numbers	444	(10)
Circular Functions	454	(12)
Graphing Basic Trigonometric Functions	466	(11)
Graphing y = k + A sin (Bx + C) and y = k + A cos (Bx + C)	477	(16)
Graphing More General Tangent, Cotangent, Secant, and Cosecant Functions	493	(8)
Inverse Trigonometric Functions	501	(22)
A Predator-Prey Analysis Involving Mountain Lions and Deer	514	(1)
Review	515	(8)
Trigonometric Identities and Conditional Equations	523	(54)
Basic Identities and Their Use	524	(9)
Sum, Difference, and Cofunction Identities	533	(10)
Double-Angle and Half-Angle Identities	543	(9)
Product-Sum and Sum-Product Identities	552	(5)
Trigonometric Equations	557	(20)
From M sin Bt + N cos Bt to A sin (Bt + C)---A Harmonic Analysis Tool	569	(2)
Review	571	(6)
Additional Topics in Trigonometry	577	(80)
Law of Sines	578	(10)
Law of Cosines	588	(8)
Geometric Vectors	596	(7)
Algebraic Vectors	603	(10)
Polar Coordinates and Graphs	613	(14)
Complex Numbers in Rectangular and Polar Forms	627	(8)
De Moivre's Theorem	635	(22)
Conic Sections and Planetary Orbits	641	(3)
Review	644	(7)
Cumulative Review Exercise	651	(6)
Systems of Equations and Inequalities	657	(74)
Systems of Linear Equations and Augmented Matrices	658	(18)
Gauss-Jordan Elimination	676	(14)
Systems Involving Second-Degree Equations	690	(9)
Systems of Linear Inequalities in Two Variables	699	(13)
Linear Programming	712	(19)
Modeling with Systems of Linear Equations	723	(2)
Review	725	(6)
Matrices and Determinants	731	(64)
Matrices: Basic Operations	732	(14)
Inverse of a Square Matrix	746	(10)
Matrix Equations and Systems of Linear Equations	756	(10)
Determinants	766	(8)
Properties of Determinants	774	(7)
Cramer's Rule	781	(14)
Using Matrices to Find Cost, Revenue and Profit	786	(1)
Review	787	(5)
Cumulative Review Exercise	792	(3)
Sequences and Series	795	(54)
Sequences and Series	796	(8)
Mathematical Induction	804	(8)
Arithmetic and Geometric Sequences	812	(13)
Binomial Formula	825	(8)
Multiplication Principle, Permutations, and Combinations	833	(16)
Sequences Specified by Recursion Formulas	845	(1)
Review	845	(4)
Additional Topics in Analytic Geometry	849
Conic Sections; Parabola	850
Ellipse	860
Hyperbola	871
Translation of Axes	883
Parametric Equations	893
Focal Chords	900
Review	901
Cumulative Review Exercise	907
Appendices
Appendix A Significant Digits	A-1
Appendix B Geometric Formulas	A-4
Answers	A-7
Applications Index	I-1
Subject Index	I-3