Cover

RESULTS FROM GEOMETRY

GRAPHS

GRAPHS OF THE TRIGONOMETRIC FUNCTIONS

Precalculus

Copyright

Contents

List of Projects

Preface

CHAPTER 1 Fundamentals

1.1 SETS OF REAL NUMBERS

1.2 ABSOLUTE VALUE

1.3 SOLVING EQUATIONS（REVIEW AND PREVIEW）

1.4 RECTANGULAR COORDINATES.VISUALIZING DATA

1.5 GRAPHS AND GRAPHING UTILITIES

1.6 EQUATIONS OF LINES

1.7 SYMMETRY AND GRAPHS.CIRCLES

CHAPTER 2 Equations and Inequalities

2.1 QUADRATIC EQUATIONS:THEORY AND EXAMPLES

2.2 OTHER TYPES OF EQUATIONS

2.3 INEQUALITIES

2.4 MORE ON INEQUALITIES

CHAPTER 3 Functions

3.1 THE DEFINITION OF A FUNCTION

3.2 THE GRAPH OF A FUNCTION

3.3 SHAPES OF GRAPHS.AVERAGE RATE OF CHANGE

3.4 TECHNIQUES IN GRAPHING

3.5 METHODS OF COMBINING FUNCTIONS.ITERATION

3.6 INVERSE FUNCTIONS

CHAPTER 4 Polynomial and Rational Functions.Applications to Optimization

4.1 LINEAR FUNCTIONS

4.2 QUADRATIC FUNCTIONS

4.3 USING ITERATION TO MODEL POPULATION GROWTH（Optional Section,Online）

4.4 SETTING UP EQUATIONS THAT DEFINE FUNCTIONS

4.5 MAXIMUM AND MINIMUM PROBLEMS

4.6 POLYNOMIAL FUNCTIONS

4.7 RATIONAL FUNCTIONS

CHAPTER 5 Exponential and Logarithmic Functions

5.1 EXPONENTIAL FUNCTIONS

5.2 THE EXPONENTIAL FUNCTION y=e^x

5.3 LOGARITHMIC FUNCTIONS

5.4 PROPERTIES OF LOGARITHMS

5.5 EQUATIONS AND INEQUALITIES WITH LOGS AND EXPONENTS

5.6 COMPOUND INTEREST

5.7 EXPONENTIAL GROWTH AND DECAY

CHAPTER 6 An Introduction to Trigonometry via Right Triangles

6.1 TRIGONOMETRIC FUNCTIONS OF ACUTE ANGLES

6.2 RIGHT-TRIANGLE APPLICATIONS

6.3 TRIGONOMETRIC FUNCTIONS OF ANGLES

6.4 TRIGONOMETRIC IDENTITIES

CHAPTER 7 The Trigonometric Functions

7.1 RADIAN MEASURE

7.2 TRIGONOMETRIC FUNCTIONS OF ANGLES

7.3 EVALUATING THE TRIGONOMETRIC FUNCTIONS

7.4 ALGEBRA AND THE TRIGONOMETRIC FUNCTIONS

7.5 RIGHT TRIANGLE TRIGONOMETRY

CHAPTER 8 Graphs of the Trigonometric Functions

8.1 TRIGONOMETRIC FUNCTIONS OF REAL NUMBERS

8.2 GRAPHS OF THE SINE AND COSINE FUNCTIONS

8.3 GRAPHS OF y=A sin（Bx-C） AND y=A cos（Bx-C）

8.4 SIMPLE HARMONIC MOTION

8.5 GRAPHS OF THE TANGENT AND THE RECIPROCAL FUNCTIONS

CHAPTER 9 Analytical Trigonometry

9.1 THE ADDITION FORMULAS

9.2 THE DOUBLE-ANGLE FORMULAS

9.3 THE PRODUCT-TO-SUM AND SUM-TO-PRODUCT FORMULAS

9.4 TRIGONOMETRIC EQUATIONS

9.5 THE INVERSE TRIGONOMETRIC FUNCTIONS

CHAPTER 10 Additional Topics in Trigonometry

10.1 RIGHT-TRIANGLE APPLICATIONS

10.2 THE LAW OF SINES AND THE LAW OF COSINES

10.3 VECTORS IN THE PLANE:A GEOMETRIC APPROACH

10.4 VECTORS IN THE PLANE:AN ALGEBRAIC APPROACH

10.5 PARAMETRIC EQUATIONS

10.6 INTRODUCTION TO POLAR COORDINATES

10.7 CURVES IN POLAR COORDINATES

10.8 DEMOIVRE'S THEOREM

CHAPTER 11 Systems of Equations

11.1 SYSTEMS OF TWO LINEAR EQUATIONS IN TWO UNKNOWNS

11.2 GAUSSIAN ELIMINATION

11.3 MATRICES

11.4 THE INVERSE OF A SQUARE MATRIX

11.5 DETERMINANTS AND CRAMER'S RULE

11.6 NONLINEAR SYSTEMS OF EQUATIONS

11.7 SYSTEMS OF INEQUALITIES

CHAPTER 12 The Conic Sections

12.1 THE BASIC EQUATIONS

12.2 THE PARABOLA

12.3 TANGENTS TO PARABOLAS（OPTIONAL SECTION）

12.4 THE ELLIPSE

12.5 THE HYPERBOLA

12.6 THE FOCUS-DIRECTRIX PROPERTY OF CONICS

12.7 THE CONICS IN POLAR COORDINATES

12.8 ROTATION OF AXES

CHAPTER 13 Roots of Polynomial Equations

13.1 DIVISION OF POLYNOMIALS

13.2 THE REMAINDER THEOREM AND THE FACTOR THEOREM

13.3 THE FUNDAMENTAL THEOREM OF ALGEBRA

13.4 RATIONAL AND IRRATIONAL ROOTS

13.5 CONJUGATE ROOTS AND DESCARTES'RULE OF SIGNS

13.6 INTRODUCTION TO PARTIAL FRACTIONS

13.7 MORE ABOUT PARTIAL FRACTIONS

CHAPTER 14 Additional Topics in Algebra

14.1 MATHEMATICAL INDUCTION

14.2 THE BINOMIAL THEOREM

14.3 INTRODUCTION TO SEQUENCES AND SERIES

14.4 ARITHMETIC SEQUENCES AND SERIES

14.5 GEOMETRIC SEQUENCES AND SERIES

14.6 AN INTRODUCTION TO LIMITS

APPENDIX

Index

FACTORING TECHNIQUES

PRINCIPAL TRIGONOMETRIC IDENTITIES