Algebra and Trigonometry

Cynthia Y. Young (Autor)

Loseblattwerk

1296 Seiten

2017 | 4th edition
John Wiley & Sons Inc (Verlag)
978-1-119-44513-5 (ISBN)

Infos

Cynthis Young's Algebra & Trigonometry, Fourth Edition will allow students to take the guesswork out of studying by providing them with a clear roadmap: what to do, how to do it, and whether they did it right, while seamlessly integrating to Young's learning content. Algebra & Trigonometry, Fourth Edition is written in a clear, single voice that speaks to students and mirrors how instructors communicate in lecture. Young's hallmark pedagogy enables students to become independent, successful learners. Varied exercise types and modeling projects keep the learning fresh and motivating. Algebra & Trigonometry 4e continues Young's tradition of fostering a love for succeeding in mathematics.

Autor

Cynthia Young received her BA in Math Education from UNC in 1990, has two masters, one in Mathematical Sciences from UCF in 1993 and a second in Electrical Engineering from the University of Washington in 1997.  Finally, she received a PhD in Applied Mathematics from the University of Washington in 1996. She is already a tenured professor at UCF and is very actively involved in the supervision of UCF's graduate and undergraduate research assistants. Before becoming an award-winning Associate Professor at UCF, Cynthia taught High School. Cynthia received numerous grants and was named the principal investigator on six military and academic research projects. She has been an administrator/advisor to the Florida Space Institute at the Kennedy Space Center since 1998. Cynthia is a veteran presenter at conferences and conventions and has published over a dozen journal articles.  In addition, she has been a contributor to several texts, including a College Algebra workbook for McGraw-Hill. Lastly, she edited the Marcel Decker's Optical Engineering Encyclopedia.

Inhalt

[0] Prerequisites and Review 2

0.1 REAL NUMBERS 4

0.2 INTEGER EXPONENTS AND SCIENTIFIC NOTATION 17

0.3 POLYNOMIALS: BASIC OPERATIONS 27

0.4 FACTORING POLYNOMIALS 36

0.5 RATIONAL EXPRESSIONS 46

0.6 RATIONAL EXPONENTS AND RADICALS 60

0.7 COMPLEX NUMBERS 70

Review 77

Review Exercises 79

Practice Test 81

[1] Equations and Inequalities 82

1.1 LINEAR EQUATIONS 84

1.2 APPLICATIONS INVOLVING LINEAR EQUATIONS 93

1.3 QUADRATIC EQUATIONS 107

1.4 OTHER TYPES OF EQUATIONS 121

1.5 LINEAR INEQUALITIES 129

1.6 POLYNOMIAL AND RATIONAL INEQUALITIES 139

1.7 ABSOLUTE VALUE EQUATIONS AND INEQUALITIES 149

Review 157

Review Exercises 158

Practice Test 162

Cumulative Test 163

[2] Graphs 164

2.1 BASIC TOOLS: CARTESIAN PLANE, DISTANCE, AND MIDPOINT 166

2.2 GRAPHING EQUATIONS, POINT-PLOTTING, INTERCEPTS, AND SYMMETRY 173

2.3 LINES 186

2.4 CIRCLES 202

2.5 LINEAR REGRESSION: BEST FIT 209

Review 231

Review Exercises 232

Practice Test 234

Cumulative Test 235

[3] Functions and Their Graphs 236

3.1 FUNCTIONS 238

3.2 GRAPHS OF FUNCTIONS; PIECEWISE-DEFINED FUNCTIONS; INCREASING AND DECREASING FUNCTIONS; AVERAGE RATE OF CHANGE 255

3.3 GRAPHING TECHNIQUES: TRANSFORMATIONS 274

3.4 OPERATIONS ON FUNCTIONS AND COMPOSITION OF FUNCTIONS 287

3.5 ONE-TO-ONE FUNCTIONS AND INVERSE FUNCTIONS 298

3.6 MODELING FUNCTIONS USING VARIATION 312

Review 322

Review Exercises 324

Practice Test 328

Cumulative Test 329

[4] Polynomial and Rational Functions 330

4.1 QUADRATIC FUNCTIONS 332

4.2 POLYNOMIAL FUNCTIONS OF HIGHER DEGREE 349

4.3 DIVIDING POLYNOMIALS: LONG DIVISION AND SYNTHETIC DIVISION 363

4.4 THE REAL ZEROS OF A POLYNOMIAL FUNCTION 372

4.5 COMPLEX ZEROS: THE FUNDAMENTAL THEOREM OF ALGEBRA 388

4.6 RATIONAL FUNCTIONS 396

Review 416

Review Exercises 418

Practice Test 422

Cumulative Test 423

[5] Exponential and Logarithmic Functions 424

5.1 EXPONENTIAL FUNCTIONS AND THEIR GRAPHS 426

5.2 LOGARITHMIC FUNCTIONS AND THEIR GRAPHS 440

5.3 PROPERTIES OF LOGARITHMS 456

5.4 EXPONENTIAL AND LOGARITHMIC EQUATIONS 464

5.5 EXPONENTIAL AND LOGARITHMIC MODELS 474

Review 485

Review Exercises 487

Practice Test 490

Cumulative Test 491

[6] Trigonometric Functions 492

6.1 ANGLES, DEGREES, AND TRIANGLES 494

6.2 DEFINITION 1 OF TRIGONOMETRIC FUNCTIONS:RIGHT TRIANGLE RATIOS 511

6.3 APPLICATIONS OF RIGHT TRIANGLE TRIGONOMETRY:SOLVING RIGHT TRIANGLES 525

6.4 DEFINITION 2 OF TRIGONOMETRIC FUNCTIONS: CARTESIAN PLANE 538

6.5 TRIGONOMETRIC FUNCTIONS OF NONACUTE ANGLES 552

6.6 RADIAN MEASURE AND APPLICATIONS 567

6.7 DEFINITION 3 OF TRIGONOMETRIC FUNCTIONS: UNIT CIRCLE APPROACH 584

6.8 GRAPHS OF SINE AND COSINE FUNCTIONS 594

6.9 GRAPHS OF OTHER TRIGONOMETRIC FUNCTIONS 623

Review 641

Review Exercises 647

Practice Test 650

Cumulative Test 651

[7] Analytic Trigonometry 652

7.1 BASIC TRIGONOMETRIC IDENTITIES 654

7.2 VERIFYING TRIGONOMETRIC IDENTITIES 665

7.3 SUM AND DIFFERENCE IDENTITIES 675

7.4 DOUBLE-ANGLE IDENTITIES 689

7.5 HALF-ANGLE IDENTITIES 697

7.6 PRODUCT-TO-SUM AND SUM-TO-PRODUCT IDENTITIES 708

7.7 INVERSE TRIGONOMETRIC FUNCTIONS 716

7.8 TRIGONOMETRIC EQUATIONS 737

Review 754

Review Exercises 757

Practice Test 762

Cumulative Test 763

[8] Additional Topics in Trigonometry 764

8.1 OBLIQUE TRIANGLES AND THE LAW OF SINES 766

8.2 THE LAW OF COSINES 780

8.3 THE AREA OF A TRIANGLE 791

8.4 VECTORS 798

8.5 THE DOT PRODUCT 813

8.6 POLAR (TRIGONOMETRIC) FORM OF COMPLEX NUMBERS 821

8.7 PRODUCTS, QUOTIENTS, POWERS, AND ROOTS OF COMPLEX NUMBERS;DE MOIVRE’S THEOREM 829

8.8 POLAR EQUATIONS AND GRAPHS 841

Review 856

Review Exercises 859

Practice Test 862

Cumulative Test 863

[9] Systems of Linear Equations and Inequalities 864

9.1 SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES 866

9.2 SYSTEMS OF LINEAR EQUATIONS IN THREE VARIABLES 881

9.3 PARTIAL FRACTIONS 892

9.4 SYSTEMS OF LINEAR INEQUALITIES IN TWO VARIABLES 903

9.5 THE LINEAR PROGRAMMING MODEL 914

Review 921

Review Exercises 922

Practice Test 924

Cumulative Test 925

[10] Matrices 926

10.1 MATRICES AND SYSTEMS OF LINEAR EQUATIONS 928

10.2 MATRIX ALGEBRA 950

10.3 MATRIX EQUATIONS; THE INVERSE OF A SQUARE MATRIX 964

10.4 THE DETERMINANT OF A SQUARE MATRIX AND CRAMER’S RULE 976

Review 990

Review Exercises 993

Practice Test 996

Cumulative Test 997

[11] Analytic Geometry and Systems of Nonlinear Equations and Inequalities 998

11.1 CONIC BASICS 1000

11.2 THE PARABOLA 1003

11.3 THE ELLIPSE 1015

11.4 THE HYPERBOLA 1028

11.5 SYSTEMS OF NONLINEAR EQUATIONS 1039

11.6 SYSTEMS OF NONLINEAR INEQUALITIES 1049

11.7 ROTATION OF AXES 1057

11.8 POLAR EQUATIONS OF CONICS 1067

11.9 PARAMETRIC EQUATIONS AND GRAPHS 1078

Review 1086

Review Exercises 1089

Practice Test 1093

Cumulative Test 1095

[12] Sequences, Series, and Probability 1096

12.1 SEQUENCES AND SERIES 1098

12.2 ARITHMETIC SEQUENCES AND SERIES 1109

12.3 GEOMETRIC SEQUENCES AND SERIES 1117

12.4 MATHEMATICAL INDUCTION 1128

12.5 THE BINOMIAL THEOREM 1133

12.6 COUNTING, PERMUTATIONS, AND COMBINATIONS 1141

12.7 PROBABILITY 1151

Review 1160

Review Exercises 1162

Practice Test 1166

Cumulative Test 1167

Answers to Odd-Numbered Exercises 1169

Applications Index 1261

Subject Index 1265

Produkt-Details

• Erscheinungsdatum: 26.11.2021
• Verlagsort: New York
• Sprache: englisch
• Maße: 216 x 277 mm
• Gewicht: 2540 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• ISBN-10: 1-119-44513-2 / 1119445132
• ISBN-13: 978-1-119-44513-5 / 9781119445135
• Zustand: Neuware