Algebra and trigonometry / Cynthia Y. Young.

PREREQUISITES AND REVIEW 2
0.1 Real Numbers 4
0.2 Exponents and Radicals 12
0.3 Polynomials: Basic Operations 21
0.4 Factoring Polynomials 28
0.5 Rational Expressions 33
0.6 Equations 42
0.7 Complex Numbers 47
Oopsl 52 I Tying It All Together 53 I Review 54
Review Exercises 56 1 Practice Test 57
Chapter 1
EQUATIONS AND INEQUALITIES 58
1.1 Linear Equations 60
1.2 Applications involving Linear Equations 69
1.3 Quadratic Equations 83
1.4 Radical Equations; Equations Quadratic in Form 96
1.5 Linear Inequalities 103
1.6 Polynomial and Rational Inequalities 113
1.7 Absolute Value Equations and Inequalities 121
Oopsl 129 1 Tying It All Together 129 I Review 130 )
Review Exercises 131 I Practice Test 134
Chapter 2
GRAPHS 136
2.1 Basic Tools: Cartesian Plane, Distance, and Midpoint 138
2.2 Graphing Equations: Point Plotting and Symmetry 145
2.3 Straight Lines 156
2.4 Circles 172
Oopsl 181 I Tying It All Together 181 I Review 182 I
Review Exercises 183 I Practice Test 185
Chapter 3
FUNCTIONS AND THEIR GRAPHS 186
3.1 Functions 188
3.2 Graphs of Functions: Library of Common Functions and Piecewise-Defined
Functions 203
3.3 Graphing Techniques: Transformations 220
3.4 Operations on Functions and Composition of Functions 234
3.5 One-to-One Functions and Inverse Functions 244
Oopsl 258 I Tying It All Together 259 I Review 260
Review Exercises 262 I Practice Test 265
SrNOMIAL AND RAT-ONAL FUNCTIONS 266
4.1 Quadratic Functions 268
4.2 Polynomial Functions of Higher Degree 285
4.3 Dividing Polynomials: Long Division and Synthetic Division 303
4.4 Properties and Tests of Zeros of Polynomial Functions 312
4.5 Rational Functions 331
4.6 Modeling Using Variation 348
Oopsl 359 I Tying It All Together 359 ) Review 360 I
Review Exercises 362 I Practice Test 367
tx -'4h -;. n0 LO�GA&nrIT-&C4M F,iCsti OtS 368
5.1 Exponential Functions and Their Graphs 370
5.2 Exponential Functions with Base e 379
5.3 Logarithmic Functions and Their Graphs 386
5.4 Properties of Logarithms 398
5.5 Exponential and Logarithmic Equations 407
Oopsl 416 I Tying It All Together 416 I Review 417 I
Review Exercises 418 1 Practice Test 421
TG NOM EW TRaC FUNCTIONS 422
6.1 Angles, Degrees, and Triangles 424
6.2 Definition 1 of Trigonometric Functions: Right Triangle Ratios 441
6.3 Applications of Right Triangle Trigonometry: Solving Right Triangles 456
6.4 Definition 2 of Trigonometric Functions: Cartesian Plane 470
6.5 Trigonometric Functions of Nonacute Angles 486
6.6 Radian Measure and Applications 503
6.7 Definition 3 of Trigonometric Functions: Unit Circle Approach 522
6.8 Graphs of Sine and Cosine Functions 532
6.9 Graphs of Other Trigonometric Functions 559
Oopsl 579 j Tying It All Together 579 1 Review 580 I
Review Exercises 588 I Practice Test 591
:a,_- 'B4O i 592
7.1 Basic Trigonometric Identities 594
7.2 Verifying Trigonometric Identities 606
7.3 Sum and Difference Identities 615
7.4 Double-Angle Identities 628
7.5 Half-Angle Identities 636
7.6 Product-to-Sum and Sum-to-Product Identities 645
7.7 Inverse Trigonometric Functions 653
7.8 Trigonometric Equations 674
Oopsl 690 I Tying It All Together 690 I Review 691 I
Review Exercises 697 1 Practice Test 701
Chapter 8
ADITIONAL TOPICS IN TRIGONOMETRY 702
8.1 Oblique Triangles and the Law of Sines 704
8.2 Law of Cosines 719
8.3 Area of a Triangle 730
8.4 Vectors 737
8.5 Dot Product 752
8.6 Polar (Trigonometric) Form of Complex Numbers 760
8.7 Products, Quotients, Powers, and Roots of Complex Numbers 769
8.8 Polar Equations and Graphs 780
Oopsl 797 Tying It All Together 797 j Review 798
Review Exercises 802 J Practice Test 805
Chapter 9
SYSTEMS OF EQUATIONS AND INEQUALITIES 806
9.1 Systems of Linear Equations in Two Variables 808
9.2 Systems of Multivariable Linear Equations 822
9.3 Partial Fractions 833
9.4 Systems of Nonlinear Equations 845
9.5 Systems of Inequalities 855
9.6 Linear Programming 871
Oopsl 880 I Tying It All Together 880 I Review 881
Review Exercises 882 I Practice Test 885
Chapter 10
MATRICES 886
10.1 Matrices and Systems of Linear Equations 888
10.2 Systems of Linear Equations: Augmented Matrices 892
10.3 Systems of Linear Equations: Determinants 912
10.4 Matrix Algebra 923
OopsI 943 j Tying It All Together 944 I Review 945 I
Review Exercises 947 I Practice Test 949
Chapter 11
ANALYTIC GEOMETRY 950
11.1 Conic Basics 952
11.2 The Parabola 955
11.3 The Ellipse 969
11.4 The Hyperbola 982
11.5 Rotation of Axes 994
11.6 Polar Equations of Conics 1005
11.7 Parametric Equations and Graphs 1015
Oopsl 1024 I Tying It All Together 1025 I Review 1026 I
Review Exercises 1028 I Practice Test 1030
SEQUENCES, SERIES, AND PROBABILITY 1032
12.1 Sequences and Series 1034
12.2 Arithmetic Sequences and Series 1046
12.3 Geometric Sequences and Series 1055
12.4 Mathematical Induction 1067
12.5 The Binomial Theorem 1072
12.6 Counting, Permutations, and Combinations 1081
12.7 Probability 1092