College Algebra and Trigonometry with Applications 2e

mathematics college algebra Table of Contents 3 Preface 6 Computer-Aided Mathematics 14 1 - Fundamentals of Algebra 18 1-1 Basic properties of the real number system 1 18 Exercises 1-1 26 1-2 Integer exponents and polynomials 11 28 Exercises 1-2 36 1-3 Factoring 23 40 Exercises 1-3 46 1-4 Rational expressions 31 48 Exercises 1-4 55 1-5 Radicals 40 57 Exercises 1-5 64 1-6 Rational exponents 49 66 Exercise 1-6 70 1-7 Complex numbers 55 72 Exercise 1-7 76 Chapter 1 Summary 61 78 Chapter 1 Review 62 79 Chapter 1 Test 65 1 2 - Equations and Inequalities 84 2-1 Linear equations 67 84 Exercises 2-1 1 2-2 Quadratic equations 77 94 Exercises 2-2 1 2-3 Equations involving radicals 89 106 Exercises 2-3 108 2-4 Inequalities in one variable 93 110 Exercises 2-4 118 2-5 Equations and Inequalities with absolute value 103 120 Exercises 2-5 123 Chapter 2 Summary 107 124 Chapter 2 Review 108 125 Chapter 2 Test 110 127 3 - Relations, Functions and Analytic Geometry 129 3-1 Points and lines 112 129 Exercises 3-1 137 3-2 Equations of Straight lines 123 140 Exercises 3-2 150 3-3 Functions 136 1 Exercises 3-3 159 3-4 The graphs of some common functions and transformations of graphs 144 161 Exercises 3-4 169 3-5 Circles and more properties of graphs 153 170 Exercises 3-5 179 Chapter 3 Summary 164 181 Chapter 3 Review 165 182 Chapter 3 Test 167 184 4 - Polynomial and Rational Functions, Algebra of Functions 186 4-1 Quadratic functions and functions defined on intervals 169 186 Exercises 4-1 191 4-2 Polynomial functions and synthetic division 176 193 Exercises 4-2 205 4-3 The graphs of polynomial functions, and finding zeros of functions by graphical methods 189 206 Exercises 4-3 215 4-4 Rational functions 199 216 Exercises 4-4 224 4-5 Composition and inverse of functions 209 226 Exercises 4-5 232 4-6 Decomposition of rational functions 217 234 Exercises 4-6 238 Chapter 4 Summary 222 239 Chapter 4 Review 223 240 Chapter 4 Test 224 241 5 - Trigonometric Functions 243 5-1 The trigonometric ratios 226 243 Exercises 5-1 249 5-2 Angle measure and the values of the trigonometric ratios 235 252 Exercises 5-2 257 5-3 The trigonometric functions-definitions 243 260 Exercises 5-3 264 5-4 Values for any angle-the reference angle/ASTC procedure 249 266 Exercises 5-4 271 5-5 Finding values from other values-reference triangles 255 272 Exercise 5-5 277 5-6 Introduction to trigonometric equations 262 279 Exercises 5-6 284 Chapter 5 Summary 268 285 Chapter 5 Review 269 286 Chapter 5 Test 271 288 6 - Radian Measure, Properties of Trigonometric Functions 290 6-1 Radian measure 273 290 Exercises 6-1 298 6-2 Properties of the sine, cosine, and tangent functions 301 Exercises 6-2 314 6-3 The tangent, cotangent, secant, and cosecant functions 299 316 Exercises 6-3 321 6-4 The inverse sine, cosine, and tangent functions 306 323 Exercises 6-4 331 6-5 The inverse cotangent, secant, and cosecant functions 316 333 Exercises 6-5 338 Chapter 6 Summary 322 1 Chapter 6 Review 323 1 Chapter 6 Test 324 341 7 - Trigonometric Equations 343 7-1 Basic trigonometric identities 326 343 Exercises 7-1 1 7-2 Sum and difference identities 331 348 Exercises 7-2 352 7-3 The double-angle and half-angle identities 338 355 Exercises 7-3 360 7-4 Conditional trigonometric equations 345 362 Exercises 7-4 368 Chapter 7 Summary 352 369 Chapter 7 Review 353 370 Chapter 7 Test 355 372 8 - Additional Topics in Trigonometry 373 8-1 The law of sines 356 373 Exercises 8-1 377 8-2 The law of cosines 363 380 Exercises 8-2 383 8-3 Vectors 368 385 Exercises 8-3 392 8-4 Complex numbers in polar form 377 394 Exercise 8-4 400 8-5 Polar coordinates 385 402 Exercises 8-5 408 Chapter 8 Summary 393 410 Chapter 8 Review 394 411 Chapter 8 Test 412 9 - Exponential and Logarithmic Functions 413 9-1 Exponential functions and thier properties 396 413 Exercises 9-1 418 9-2 Logarithmic functions-introduction 403 420 Exercises 9-2 1 9-3 Properties of logarithmic functions 408 425 Exercises 9-3 429 9-4 Values and graphs of logarithmic 413 430 Exercises 9-4 439 Solving logarithmic and exponential equations/applications 424 441 Exercises 9-5 448 Chapter 9 Summary 434 451 Chapter 9 Review 434 451 Chapter 9 Test 436 453 10 - Systems of Linear Equations and Inequalities 455 10-1 Solving systems of linear equations-the addition method 438 455 Exercises 10-1 1 10-2 Systems of linear equations-matrix elimination 448 465 Exercises 10-2 474 10-3 Systems of linear equations-Cramer's rule 459 476 Exercises 10-3 482 10-4 Systems of linear inequalities 469 486 Exercises 10-4 492 10-5 Systems of linear equations-matrix algebra 477 494 Exercises 10-5 505 Chapter 10 Summary 492 509 Chapter 10 Review 492 509 Chapter 10 Test 494 511 11 - The Conic Sections 513 11-1 The parabola 497 514 Exercises 11-1 521 11-2 The ellipse 505 522 Exercises 11-2 529 11-3 The hyperbola 514 531 Exercises 11-3 538 11-4 Systems of nonlinear equations and inequalities 523 540 Exercise 11-4 545 Chapter 11 Summary 531 548 Chapter 11 Review 531 548 Chapter 11 Test 532 549 12 - Topics in Discrete Mathematics 551 Exercises 12-1 556 12-2 Series 543 1 Exercises 12-2 565 12-3 The binomial expansion and more on sigma notation 552 569 Exercises 12-3 575 12-4 Finite Induction 559 576 Exercise 12-4 582 12-5 Introduction to combinatorics 567 584 Exercise 12-5 592 12-6 Introduction to probability 579 596 Exercises 12-6 602 12-7 Recursive definitions and recurrennce relations-optional 588 605 Exercises 12-7 611 Chapter 12 Summary 596 613 Chapter 12 Review 597 614 Chapter 12 Test 599 616 Appendix A - Development of Several Formulas 619 Appendix B - Answers and Solutions 621 Index of Applications 780 Index 783 Student's Solutions Manual 788 chapter 1 1 exercise 1-1 795 exercise 1-2 795 exercise 1-3 796 exercise 1-4 797 exercise 1-5 798 exercise 1-6 799 exercise 1-7 799 chapter 1 review 800 chapter one test 802 chapter 2 1 exercise 2-1 803 exercise 2-2 803 exercise 2-3 804 exercise 2-4 805 exercise 2-5 806 chapter 2 review 806 chapter 2 test 809 chapter 3 1 exercise 3-1 811 exercise 3-2 812 exercise 3-3 813 exercise 3-4 814 exercise 3-5 816 chapter 3 review 817 chapter 3 test 822 chapter 4 1 section 4-1 824 exercise 4-2 825 exercise 4-3 827 exercise 4-4 828 exercise 4-5 831 exercise 4-6 832 chapter 4 review 834 chapter 4 test 839 chapter 5 1 exercise 5-1 842 exercise 5-2 842 exercise 5-3 843 exercise 5-4 844 exercise 5-5 844 exercise 5-6 846 chapter 5 review 846 chapter 5 test 848 chapter 6 1 exercise 6-1 849 exercise 6-2 849 exercise 6-3 852 exercise 6-4 853 exercise 6-5 855 chapter 6 review 855 chapter 6 test 857 chapter 7 1 exercise 7-1 859 exercise 7-2 859 exercise 7-3 860 exercise 7-4 862 chapter 7 review 864 chapter 7 test 867 chapter 8 1 exercise 8-1 868 exercise 8-2 869 exercise 8-3 870 exercise 8-4 871 exercise 8-5 872 chapter 8 review 873 chapter 8 test 875 chapter 9 1 exercise 9-1 876 exercise 9-2 877 exercise 9-3 877 exercise 9-4 877 exercise 9-5 878 chapter 9 review 879 chapter 9 test 881 chapter 10 1 exercise 10-1 883 exercise 10-2 884 exercise 10-3 886 exercise 10-4 887 exercise 10-5 890 chapter 10 review 891 chapter 10 test 894 chapter 11 1 exercise 11-1 896 exercise 11-2 898 exercise 11-3 900 exercise 11-4 903 chapter 11 review 906 chapter 11 test 909 chapter 12 1 exercise 12-1 911 exercise 12-2 912 exercise 12-3 913 exercise 12-4 914 exercise 12-5 915 exercise 12-6 915 exercise 12-7 916 chapter 12 review 917 chapter 12 test 919 mathematics,college,algebra,textbook mathematics college algebra textbook