Algebra and Trigonometry

by Blitzer, Robert F.

• ISBN13: 9780130893321
• ISBN10: 0130893323
• Format: Hardcover
• Copyright: 2001-01-01
• Publisher: Pearson College Div

Summary

Gets Them Engaged. Keeps Them Engaged & Blitzer's philosophy: present the full scope of mathematics, while always (1) engaging the student by opening their minds to learning (2) keeping the student engaged on every page (3) explaining ideas directly, simply, and clearly so they don't get "lost" when studying and reviewing.

Table of Contents

Preface	vii
To the Student	xi
Applications Index	xviii
Prerequisites: Fundamental Concepts of Algebra	1	(84)
Real Numbers and Algebraic Expressions	2	(11)
Exponents and Scientific Notation	13	(10)
Radicals and Rational Exponents	23	(12)
Polynomials	35	(11)
Factoring Polynomials	46	(8)
Rational Expressions	54	(11)
Complex Numbers	65	(6)
Graphs and Graphing Utilities	71	(14)
Summary	81	(1)
Review Exercises or Algebra Skills Diagnostic Test	82	(2)
Test	84	(1)
Equations, Inequalities, and Mathematical Models	85	(82)
Linear Equations	86	(11)
Formulas and Applications	97	(12)
Quadratic Equations	109	(18)
Other Types of Equations	127	(12)
Linear Inequalities	139	(12)
Quadratic and Rational Inequalities	151	(16)
Summary	162	(1)
Review Exercises	163	(2)
Test	165	(2)
Functions and Graphs	167	(91)
Lines and Slope	168	(12)
Parallel and Perpendicular Lines and Circles	180	(10)
Introduction to Functions	190	(13)
Graphs of Functions	203	(18)
Transformations and Combinations of Functions	221	(17)
Composite and Inverse Functions	238	(20)
Summary	250	(1)
Review Exercises	251	(4)
Test	255	(1)
Cumulative Review Exercises	256	(2)
Polynomial and Rational Functions	258	(92)
Quadratic Functions	259	(13)
Polynomial Functions and Their Graphs	272	(1)
Dividing Polynomials: Remainder and Factor Theorems	273	(21)
Zeros of Polynomial Functions	294	(10)
More on Zeros of Polynomial Functions	304	(10)
Rational Functions and Their Graphs	314	(18)
Modeling Using Variation	332	(18)
Summary	344	(1)
Review Exercises	345	(3)
Test	348	(1)
Cumulative Review Exercises	349	(1)
Exponential and Logarithmic Functions	350	(65)
Exponential Functions	351	(11)
Logarithmic Functions	362	(13)
Properties of Logarithms	375	(9)
Exponential and Logarithmic Equations	384	(11)
Modeling with Exponential and Logarithmic Functions	395	(20)
Summary	408	(1)
Review Exercises	409	(4)
Test	413	(1)
Cumulative Review Exercises	414	(1)
Trigonometric Functions	415	(117)
Angles and Their Measure	416	(14)
Right Triangle Trigonometry	430	(16)
Trigonometric Functions of Any Angle	446	(10)
Trigonometric Functions of Real Numbers; Periodic Functions	456	(8)
Graphs of Sine and Cosine Functions	464	(22)
Graphs of Other Trigonometric Functions	486	(12)
Inverse Trigonometric Functions	498	(16)
Applications of Trigonometric Functions	514	(18)
Summary	525	(2)
Review Exercises	527	(3)
Test	530	(1)
Cumulative Review Exercises	531	(1)
Analytic Trigonometry	532	(54)
Verifying Trigonometric Identities	533	(10)
Sum and Difference Formulas	543	(10)
Double-Angle and Half-Angle Formulas	553	(11)
Product-to-Sum and Sum-to-Product Formulas	564	(8)
Trigonometric Equations	572	(14)
Summary	582	(1)
Review Exercises	583	(2)
Test	585	(1)
Cumulative Review Exercises	585	(1)
Additional Topics in Trigonometry	586	(85)
The Law of Sines	587	(12)
The Law of Cosines	599	(8)
Polar Coordinates	607	(11)
Graphs of Polar Equations	618	(12)
Complex Numbers in Polar Form; DeMoivre's Theorem	630	(13)
Vectors	643	(13)
The Dot Product	656	(15)
Summary	665	(2)
Review Exercises	667	(2)
Test	669	(1)
Cumulative Review Exercises	670	(1)
Systems of Equations and Inequalities	671	(66)
Systems of Linear Equations in Two Variables	672	(14)
Systems of Linear Equations in Three Variables	686	(9)
Partial Fractions	695	(9)
Systems of Nonlinear Equations in Two Variables	704	(9)
Systems of Inequalities	713	(10)
Linear Programming	723	(14)
Summary	732	(1)
Review Exercises	733	(3)
Test	736	(1)
Cumulative Review Exercises	736	(1)
Matrices and Determinants	737	(71)
Matrix Solutions to Linear Systems	738	(14)
Inconsistent and Dependent Systems and Their Applications	752	(9)
Matrix Operations and Their Applications	761
Multiplicative Inverses of Matrices and Matrix Equations	755	(35)
Determinants and Cramer's Rule	790	(18)
Summary	803	(1)
Review Exercises	804	(2)
Test	806	(1)
Cumulative Review Exercises	807	(1)
Conic Sections and Analytic Geometry	808	(83)
The Ellipse	809	(13)
The Hyperbola	822	(16)
The Parabola	838	(12)
Rotation of Axes	850	(13)
Parametric Equations	863	(11)
Conic Sections in Polar Coordinates	874	(17)
Summary	885	(1)
Review Exercises	886	(2)
Test	888	(1)
Cumulative Review Exercises	889	(2)
Sequences, Induction, and Probability	891	(1)
Sequences and Summation Notation	892	(11)
Arithmetic Sequences	903	(9)
Geometric Sequences	911	(14)
Mathematical Induction	925	(9)
The Binomial Theorem	934	(8)
Counting Principles, Permutations, and Combinations	942	(11)
Probability	953	(13)
Summary	966	(1)
Review Exercises	967	(2)
Test	969	(1)
Cumulative Review Exercises	970
Appendix Where Did That Come From? Selected Proofs	A1
Answers to Selected Exercises	AA1
Subject Index	I-1
Photo Credits	P-1