technical mathematics fourth edition pdf

www.EngineeringBooksPDF.com Triangle P5a1b1c A bh Circle C 2pr A pr2 Circular Cylinder L 2prh T 2pr (r h)) V pr2h © Cengage Learning 2013 Square P 4s A s2 © Cengage Learning 2013 © Cengage Learning 2013 Rectangle P 2(a b) A ab Rectangular Prism L 2h(l w) T 2(lw lh hw) V lwh © Cengage Learning 2013 Rhombus P 4s A sh © Cengage Learning 2013 Pyramid L ps T ps B V Bh Cube L 4s2 T 6s2 V s3 © Cengage Learning 2013 © Cengage Learning 2013 © Cengage Learning 2013 Parallelogram P 2(a b) A bh © Cengage Learning 2013 Circular Cone L prs T pr(r s) V pr2h Prism L ph T ph 2B V Bh (B area of base) © Cengage Learning 2013 © Cengage Learning 2013 Trapezoid P a b 1 c b2 A (b1 b2)h Sphere T 4pr2 V pr3 © Cengage Learning 2013 © Cengage Learning 2013 © Cengage Learning 2013 Copyright 2011 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part www.EngineeringBooksPDF.com Nonvertical line, slope m y x3 4p(y k) (x h)2, p © Cengage Learning 2013 © Cengage Learning 2013 Horizontal line, vertical line © Cengage Learning 2013 y !x © Cengage Learning 2013 y bx, b 0, b  © Cengage Learning 2013 1y k22 1x h22 1, a b a2 b2 © Cengage Learning 2013 1y k22 1x h22 51 a2 b2 Distance formula, slope m of a nonvertical line © Cengage Learning 2013 © Cengage Learning 2013 y logb x, b y sin x © Cengage Learning 2013 y cos x © Cengage Learning 2013 y x2 © Cengage Learning 2013 © Cengage Learning 2013 (x h)2 (y k)2 r2 y tan x © Cengage Learning 2013 © Cengage Learning 2013 © Cengage Learning 2013 Copyright 2011 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part www.EngineeringBooksPDF.com Technical MaTheMaTics 4th Edition Copyright 2011 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part www.EngineeringBooksPDF.com Copyright 2011 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part www.EngineeringBooksPDF.com T ec h n i c a l M aT h e M aT i cs 4th Edition John C PEtErson Chattanooga state technical Community College Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States Copyright 2011 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part www.EngineeringBooksPDF.com This is an electronic sample of the print textbook The publisher reserves the right to remove content from this title at any time if subsequent rights restrictions require it For valuable information on pricing, previous editions, changes to current editions and alternate formats, please visit www.cengage.com/highered to search by ISBN#, author, title, or keyword for materials in your areas of interest Copyright 2011 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part www.EngineeringBooksPDF.com Technical Mathematics, 4th Edition John C Peterson Vice President, Editorial: Dave Garza Director of Learning Solutions: Sandy Clark Acquisitions Editor: Stacy Masucci Managing Editor: Larry Main Product Manager: Mary Clyne Editorial Assistant: Andrea Timpano Vice President, Marketing: Jennifer Baker Marketing Director: Deborah Yarnell Marketing Manager: Erica Ropitzky Senior Production Director: Wendy Troeger © 2013, 2004, 1997, 1994 Delmar, Cengage Learning ALL RIGHTS RESERVED No part of this work covered by the copyright herein may be reproduced, transmitted, stored, or used in any form or by any means graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, Web distribution, information networks, or information storage and retrieval systems, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the publisher For product information and technology assistance, contact us at Cengage Learning Customer & Sales Support, 1-800-354-9706 For permission to use material from this text or product, submit all requests online at www.cengage.com/permissions Further permissions questions can be emailed to permissionrequest@cengage.com Senior Production Manager: Mark Bernard Content Project Manager: Barbara Lefleur Library of Congress Control Number: 2011927787 Production Editor: Sara Dovre Wudali, Buuji, Inc ISBN-13: 978-1-1115-4046-3 Senior Art Director: David Arsenault Endsheet images © Cengage Learning 2013 Cover image © Vincenzo Lombardo/ Photographer’s Choice/Getty Images ISBN-10: 1-1115-4046-2 Delmar Maxwell Drive Clifton Park, NY 12065-2919 USA Cengage Learning is a leading provider of customized learning solutions with office locations around the globe, including Singapore, the United Kingdom, Australia, Mexico, Brazil, and Japan Locate your local office at: international.cengage.com/region Cengage Learning products are represented in Canada by Nelson Education, Ltd To learn more about Delmar, visit www.cengage.com/delmar Purchase any of our products at your local college store or at our preferred online store www.cengagebrain.com Notice to the Reader Publisher does not warrant or guarantee any of the products described herein or perform any independent analysis in connection with any of the product information contained herein Publisher does not assume, and expressly disclaims, any obligation to obtain and include information other than that provided to it by the manufacturer The reader is expressly warned to consider and adopt all safety precautions that might be indicated by the activities described herein and to avoid all potential hazards By following the instructions contained herein, the reader willingly assumes all risks in connection with such instructions The publisher makes no representations or warranties of any kind, including but not limited to, the warranties of fitness for particular purpose or merchantability, nor are any such representations implied with respect to the material set forth herein, and the publisher takes no responsibility with respect to such material The publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or part, from the readers’ use of, or reliance upon, this material Printed in the United States of America 16 15 14 13 12 Copyright 2011 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part www.EngineeringBooksPDF.com cOnTenTs Preface xii chaPTeR The Real number system 1.1 1.2 1.3 1.4 1.5 some sets and Basic Laws of real numbers Basic operations with real numbers 21 Exponents and roots 38 significant Digits and rounding off 49 scientific and Engineering notation 57 ChaPtEr 1 rEviEw 67 ChaPtEr 1 tEst 69 chaPTeR algebraic concepts and Operations 2.1 2.2 2.3 2.4 2.5 2.6 70 addition and subtraction 71 Multiplication 77 Division 83 solving Equations 90 Dimensional analysis 99 applications of Equations 104 ChaPtEr 2 rEviEw 116 ChaPtEr 2 tEst 118 chaPTeR Geometry 3.1 3.2 3.3 3.4 3.5 3.6 120 Lines, angles, and triangles 121 other Polygons 134 Circles 141 the area of irregular shapes 148 Geometric solids 155 similar Geometric shapes 167 ChaPtEr 3 rEviEw 173 ChaPtEr 3 tEst 177 v Copyright 2011 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part www.EngineeringBooksPDF.com vi ContEnts chaPTeR Functions and Graphs 4.1 4.2 4.3 4.4 4.5 4.6 4.7 179 relations and Functions 180 operations on Functions; Composite Functions 194 rectangular Coordinates 203 Graphs 208 Calculator Graphs and solving Equations Graphically 217 Using a spreadsheet to Graph and solve Equations Graphically 227 introduction to Modeling 240 ChaPtEr 4 rEviEw 250 ChaPtEr 4 tEst 252 chaPTeR an introduction to Trigonometry and Variation 5.1 5.2 5.3 5.4 5.5 254 angles, angle Measure, and trigonometric Functions 255 values of the trigonometric Functions 261 the right triangle 268 trigonometric Functions of any angle 276 applications of trigonometry 286 ChaPtEr 5 rEviEw 293 ChaPtEr 5 tEst 297 chaPTeR systems of linear equations and Determinants 6.1 6.2 6.3 6.4 298 Linear Equations 299 Graphical and algebraic Methods for solving two Linear Equations in two variables 309 algebraic Methods for solving three Linear Equations in three variables 317 Determinants and Cramer’s rule 324 ChaPtEr 6 rEviEw 339 ChaPtEr 6 tEst 341 chaPTeR Factoring and algebraic Fractions 7.1 7.2 7.3 343 special Products 344 Factoring 352 Factoring trinomials 356 Copyright 2011 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part www.EngineeringBooksPDF.com Index of ApplIcAtIons This index categorizes the application problems in this book alphabetically After each topic, the index lists the text page number followed by the problem number in parentheses For example, if you are looking for a problem on accounting, you would turn to page 738 and look for problem number 74 Accounting, 738(74) Acoustical engineering, 290(11–12), 355(45), 609(41), 614(43), 1003–1004(32) Acoustics, 48(97), 437(53) Aerodynamics, 154(12) Aeronautical engineering, 82(64), 560(85), 769(23), 948(34) Aeronautics, 398(40), 407(39), 496(28), 637(36) Agricultural technology, 165(23), 871(12) Agriculture, 468(66–67), 484(51), 853(25), 1002(34), 1014–1015(24) Air traffic control, 275–276(40), 777(29–30) Architectural technology, 172(11, 14), 351(65–66) Architecture, 139(20, 22), 146–147(14–16), 550(60), 853(30), 889–890(43–44), 942(28) Astronomy, 66(62), 524(24), 628(53), 743(28–29), 754(28), 762(19, 23), 776–777(24, 26), 790(17, 20), 792(34), 878(33–34) Automotive engineering, 248(8), 436(44) Automotive technology, 18(87–88), 19(91, 93), 34(42, 46), 48(99), 49(102), 56(58), 82(67), 103(15, 19, 25), 113(8), 216(34), 226(69), 248(13), 296(79), 316(48), 339(54, 57), 419(26), 437(54), 515–516(28–30), 530(12), 540(31, 33), 619(32), 777(31), 878(35–36), 931(26, 29), 1002(35), 1003(31) Biology, 594(21), 602(15, 17), 604(28), 628(49, 54) Broadcasting, 173(21–22), 524(22), 754(27) Business, 19(97–98), 20(102–103), 35(56–58), 48(94), 68(59), 82(66), 113(4–6, 11–12), 118(82), 193(83), 201–202(59–62, 65), 203(68), 216(33), 247(6), 248(12), 323(22), 341(39–41), 364(57), 436(45), 467–468(55), 468(64–65), 540(32), 654(37), 662(21), 862(23–24), 872(23–24), 878–879(39, 43), 893(32–33), 899–900(21–25), 902(27), 912–913­ (31–36), 917(23), 931(24), 933(20), 942(27), 970(50), 1021(13), 1043–1045(46–47, 50, 52) Cartography, 918(29) Chemistry, 114(21, 23–24), 115(32), 118(85), 443(17), 567(64), 852(21), 893(31) Civil engineering, 114(25), 131(32), 133(49), 138–139(14, 17, 19, 21), 147(18), 164(9–10, 17), 176(31), 364(62), 385(61), 418(21–22, 24–25), 419(27, 30), 425(32–33), 427–428(28, 31), 567(66), 573(66), 580(29), 754(21), 762(20), 769(20, 22), 792(31–32) Communications, 596–597(30, 33) Communications technology, 754(23) Computer science, 56(49), 82(63), 290(15–16), 879(44) Computer technology, 296(72), 437(48), 457(50), 609(44), 803(41) Construction, 19(95–96), 34–35(44, 48–49, 53–54, 61), 37(69, 71, 73–74), 56(48), 56(60), 82(65), 103(11), 104(29–30), 114(18), 132(42–44, 47), 133(50–51, 53), 138(12), 139–140(23–24), 165(18, 25–26), 166(29, 31–32), 167(33–34), 172(15), 176(30), 227(71), 275(34), 276(43), 291(24, 27), 296(74, 77, 80), 308­ (54–55), 375(47), 397(33–34), 398(39, 42), 411(11), 412(23–24), 424(27), 449(26), 457(51–52), 468(58–60), 738(78), 917–918(24), 942(26), 956(31), 957(35) Construction technology, 339(55), 406(31–34), 931(27) Drafting, 292(30), 853(24) Dynamics, 193(82), 364(58), 457(45–48), 484(45), 567(47–49), 626(34), 890(45) Ecology, 216(31–32), 364(59), 595(24), 614(44), 1021(16) Economics, 117(80–81) Electrical engineering, 385(62–63), 436(39–40), 871–872(20) Electrical technician, 34(47) Electrical technology, 653(29–32), 661(16) Electricity, 20(104), 56–57(62–63), 103(17, 22), 117(79), 146(10), 147(23–24), 166(28), 177(33), 275(31), 276(44), 291(28), 437(49, 55), 468(56–57), 484­ (49–50), 566–567(63), 626(27), 744(34), 853(27) Electronics, 18–19(89–90, 92, 94), 34(43), 35(51–52), 48–49(91–93, 100–101), 56(59), 66(66–67), 82(68), 115(33–34), 131(33), 133(52), 147(19), 285(101–102, 107–108), 295(67, 69), 316(49–51), 322–323(15–16), 338(51), 351(61), 364(55), 375(48), 385(57, 59, 64), 398(36–38), 407(38), 411(12–19), 425(31), 428(30), 437(55), 443–444(19, 23–24), 448(18–22), 458(56), 468(68), 496(23–24), 504(21, 24), 515(27), 516(31), 530–531(13–19, 22–24), 550(61), 552(27–28), 573(63), 580(34), 595(26), 603–604((22–23, 27), 614(42), 620(37,39), 626(31–33), 687(89–92), 695(52–62), 702(41–46), 707–708(35–44), 1150 Copyright 2011 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part www.EngineeringBooksPDF.com 1151 Index of ApplIcAtIons 715(33–40), 721–722(29–34), 723(38–40), 737 (71–72), 754(25), 769(21, 24), 777(34), 784(14), 853(28), 871(13–14), 878(37), 879(41), 930–931 (21–23), 986(58, 60), 1002(33), 1021(15), 1033(45–46) Energy, 114(20), 164(12, 15), 248(11), 351(64), 356(47), 449(23), 484(48), 754(24) Energy science, 654(35) Energy technology, 247(7), 290(19), 582(58), 653(21–23), 661(14), 662(22), 738(76), 879(40) Environmental science, 113(15), 154(14), 202(63, 67), 203(69–70), 227(70, 72), 249(19–21), 339(56), 485(52), 597(34), 619–620(34, 36), 654(34, 40), 661(18–19), 662(24), 738(75, 77), 931(28), 942(25), 948(35–36), 1014(21), 1021(14), 1022(19) Environmental technology, 172(16), 356(49) Finance, 113(9–10), 202(66), 560(86), 594(17–20), 596(32), 602(16), 619(25–26, 31), 628(47), 629(55), 957 (32–34, 36), 970(45), 1044(48, 51), 1045(54) Fire science, 276(42), 364(60), 398(41) Food science, 629(56) Food technology, 654(38) Forestry, 276(41), 296(76), 458(57–58), 468(61–62), 609(43), 620(40), 890(46–47) Graphic design, 291–292(29) Health technology, 248(14), 249(22), 308(56) Industrial design, 146(12), 147(17), 364(61), 419(31), 425(34), 484(46), 743–744(30–31), 852(18), 853(29), 871(19) Industrial engineering, 146(11), 744(32–33) Industrial management, 738(73), 777(33), 900(27–28) Industrial technology, 290(4), 637(38–40), 653(24–28), 853(29) Information technology, 654(39), 662(23), 803–804 (42–50), 817(37–40), 832(41–43) Information technology HTML, 830(29) Insurance, 248(10), 637(37, 42), 654(36), 661(20) Interior decorating, 102(10) Interior design, 139(18), 146(9) Land management, 315–316(41–44), 425(35), 609(42) Landscape architecture, 131(37), 193(84), 285(105), 323(21) Landscaping, 82(69), 154(9), 177(37), 792(35) Lighting technology, 580(31–32), 595(25), 889(41) Machine design, 419(32) Machine technology, 114–115(17, 28–29), 138(15–16), 177(36), 247(5), 295(68, 70), 308(49), 419(28–29), 444(28), 524(21, 23), 661(13, 15), 675(18), 878(38), 961(33), 1013(15) Manufacturing, 36(62–68) Material science, 890(48) Mechanical engineering, 132(40), 138(13), 290(14, 17–18), 436(43), 762(22, 25), 777(27–28), 790(18–19), 852(20) Mechanical technology, 131(34) Mechanics, 103(13), 164(14), 530(5–6, 11), 552(25), 1004(33) Medical technology, 37(70, 76–77), 102(9), 103(12), 115(31), 118(88), 193(86), 398(35), 496(27), 531(25), 594(22–23), 595(27), 602–603(18, 25–26), 604(29), 620(41–42), 637(35, 41), 852(22), 862(21–22), 863(21–22), 879(42), 948(31), 1014(22), 1043(45), 1045(53) Metallurgy, 338(53), 351(67–68), 356(50), 931(25, 30) Metalworking, 56(61), 118(89), 131(35), 133(54), 176–177(32), 285(103–104, 106) Meteorology, 202(64), 308(50), 504–506(25–31), 552(29), 595–596(28), 619(35), 626(25–26), 986(59) Music, 515(25), 516(32), 566(61–62) Navigation, 275(32–33), 290(13), 291(21, 26), 308(53), 397(31–32), 398(39, 42), 406–407(35–36), 410–412(5–8, 20–22), 418(23), 424(26), 443(18), 541(36), 582(57), 769(18), 776(25), 792(33) Nuclear energy, 319(28–30) Nuclear engineering, 628(48) Nuclear physics, 68(60), 968(37–38) Nuclear technology, 560(84), 582(55–56), 602(13–14), 603(24), 852(19) Nutrition, 103(26), 173(23–24), 893(34), 900(26) Oceanography, 496(26), 504(22–23), 530(7–8), 552(26), 573(62) Optics, 103(18), 291(22–23), 295(65–66), 356(48), 385(58), 436(41–42), 437(56), 754(22), 933(23–24), 986(57), 1001–1002(31–32, 36) Package design, 467(54) Petroleum engineering, 114(22), 193(81), 852(17), 853(26) Petroleum technology, 316(45–46), 323(20) Physics, 66(61, 63–65, 68), 103(21, 24), 114(27), 115(30), 118(86–87), 132(48), 177(35), 249(16), 275(36), 290(2–3, 9, 20), 308(51–52), 316(47), 338(52), 351(62–63), 375(48–49), 410(1–3), 411(9–10), 424–425(28–30), 427(27), 428(29), 443–444(20–24), 449(25), 468(63), 484(47), 530(9–10), 560(81–82), 580(30, 33), 626(28), 723(37), 737(69–70), 743(27), 776(23), 784(13), 871(15, 17–18), 889(42), 918(25–27), 933(19), 948(32–33), 956(29–30), 961(31–32, 34), 968(39), 970(49), 980(44), 986(56), 1013(16), 1044(49) Police science, 248(9), 407(40), 653(33), 661(17), 777(32) Product design, 164(13), 173(20) Programming, 131(36), 695(63) Quality control, 672–674(9–22), 675(9–17) Copyright 2011 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part www.EngineeringBooksPDF.com 1152 Index of ApplIcAtIons Recreation, 34(41, 45), 154(10, 13), 166(30), 193(85), 249(17–18), 444(25), 457–458(53–54), 1022(20) Robotics, 550(62) Sports management, 595(29) Sports technology, 540–541(35), 1033–1034(47–48) Surveying, 428(32) Seismology, 609(40, 45–46), 628(50) Semiconductor technology, 35(60), 103(27–28), 148(25–28) Sheet metal manufacturing, 165(27) Sheet metal technology, 37(72, 75), 146(13), 164(16), 165(19–22), 172–173(17–19), 364(56), 467(53), 853(23) Solar energy, 437(52), 457(49), 496(25) Sound, 449(24), 573(64) Space technology, 118(84), 147(20), 290(10), 291(25), 296(73), 424(25), 444(25), 550(59), 762(24), 871(16), 872(22) Thermal science, 82(70) Thermodynamics, 355(42), 356(46), 603(19–21), 620(38), 754(26), 784(15) Transportation, 19(99–100), 113(13–14), 118(83), 164(11), 323(19), 385(60), 437(50), 871(11), 902(26), 1013–1014(19–20, 23), 1021–1022(17–18) Transportation engineering, 114(26), 132(41), 275(37–39), 290(1), 296(71), 426(36), 762(26), 872(21) Wastewater technology, 48(96), 172(12), 355(43), 436 (46–47), 437(51), 458(55), 769–770(25–26) Copyright 2011 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part www.EngineeringBooksPDF.com INDEX Absolute errors, 51 Absolute inequalities, 873 Absolute value signs, 12–15 Absolute values, 4–5 Acute angles, 124 Acute triangles, 125 Addition algebraic fractions, 377 binary number system, 804 complex numbers, 687 hexadecimal number system, 826 integers (Rules 1–2), 21–23 matrices, 907 multinomials, 73–74 octal number system, 817 radicals, 567–569 in solving linear equations, 311–314, 318–319 vectors, 399–407 vectors using components, 400 Adjacent angles, 124 Algebraic expressions, 72 Algebraic fractions, 365–385 addition and subtraction of, 375–385 complex fractions, 381 fundamental principle of, 365 least common denominator, 378 multiplication and division of, 369–375 Algebraic logic, Algebraic methods for solving three linear equations in three variables, 317–323 Algebraic methods for solving two linear equations in two variables, 309–317 Algebraic operating system, Algebraic terms, 72–73 Algebraic concepts and operations, 70–119 addition and subtraction, 71–77 algebraic expressions, 72 algebraic terms, 72–73 applications of equations, 104–116 binomials, 73 constants, 71–72 difference of squares, 80 dimensional analysis, 99–104 division, 83–90 equal rations, 95 equations, 90 equivalent equations, 90–93 FOIL (First/Outside/Inside/ Last) method for multiplying binomials, 79 monomials, 73 multinomials, 73 multiplication, 77–83 polynomials, 85 proportion, 94–95 ratio, 93–94 solving equations, 90–99 special products, 80 square of a binomial, 80 trinomials, 73 variables, 71 See also Word problems Alternating current, 526 complex numbers in, 716–722 Altitude, of triangles, 126 Amplitude, in sine and cosine curves, 489–490 Analytic geometry, 725–793 basic definitions and straight lines, 729–739 distance formula, 726–727 formulas for the equation of a line, 734 lengths of irregular curves, 728–729 midpoint formula, 727 slope of lines, 731–733 circles, 739–744 general equation of, 740 standard equation of, 739 conic sections in polar coordinates, 785–790 general definition of a conic section, 785–786 polar equations of conic sections, 786 ellipses, 755–763 reflective properties of, 758 standard equation for horizontal major axis, 756 standard equation for vertical major axis, 757 hyperbolas, 763–770 reflective properties of, 766 standard equation for horizontal major horizontal axis, 764 standard equation for vertical major horizontal axis, 764–765 parabolas, 745–755 reflective properties of, 747–748 standard equation for a horizontal parabola, 747 standard equation for a vertical parabola, 746 rotation of axes, 778–784 classifying the graph of a general quadratic equation, 781 discriminant, 781 general second-degree equation, 778 translation of axes, 770–778 See also Geometry Angle of the line in linear equations, 302–305 Angles, 121–134, 122–125 acute, 124 adjacent, 124 complementary, 124 congruent, 124 of elevation or depression, 273 obtuse, 124 perpendicular, 124 positive and negative angles, 235 1153 Copyright 2011 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part www.EngineeringBooksPDF.com 1154 INDEX Angles (Continued) right, 124 straight, 124 supplementary, 124 trigonometric function values of, 276–286 Approximate numbers, 52 Arc, 141 Arc length, 143 Area of circles, 141–142 of geometric solids, 162 of irregular shapes, 148–151 of polygons, 135 rectangular methods for approximating area, 1015–1016 of similar geometric shapes, 170 of triangles, 126, 422–423 Area question in calculus, 1015–1022 Arithmetic of rational numbers (Rules 6–8), 25–33 Arithmetic sequences, 942–943 Arithmetic series, 952 ASCII (application of binary and octal numbers), 815–816 ASCII table, 816 Associative property, Attribute charts (the p chart), 668 Augmented matrix, 906–907 Average slope, 1007 Axes rotation of, 778–784 translation of, 770–778 Base, of triangles, 126 Binary number system, 795–804 addition, 804 binary-to-decimal conversion, 798 binary-to-octal conversion, 814 bits, nibbles, and bytes, 797 decimal fraction to binary fraction conversion, 800 decimal integer to binary integer conversion, 799 decimal numbers, 795–796 decimal subtraction using complements, 806 decimal-to-binary conversion, 799 defined, 796–797 expanded notation, 707 finding the 9’s and 10’s complements, 806 negative numbers, 810 subnet masking, 801–802 subtraction, 805 subtraction using complements, 808 writing binary numbers, 797 See also Computer number systems Binomial, 73 square of a, 80 Binomial theorem, 962–968 binomial formula, 963–965 binomial series, 966 expansions and Pascal’s triangle, 962–963 Bits, nibbles, and bytes, 797 Box-and whisker diagrams, 642 Broken line graph, 240 Calculators adding sequences with, 949 algebraic logic, average slope, 1009 binomial coefficients with, 965 complex numbers, 692–693 conic sections in polar coordinates, 788 degrees and radians, 256 ellipses, 759–760 evaluating determinants on a calculator, 328–329 exponent evaluation, 557–558 exponential function ex, 598 factorials with, 964 finding logs with, 606 to graph parametric equations, 533–535 to graph polar equations, 547–549 graphing, 182 graphing for statistical measures, 646 graphing sine and cosine curves, 509–510 graphs of trigonometric functions, 519–523 hyperbolas, 767–768 for inverse functions, 281–282 inverses of matrices, 924 for modeling, 240–241, 243 modeling periodic functions, 501–502 parabolas, 749–751 piecewise-defined functions, 475–477 radical equations, 577–578 rounding off with, 54–55 scientific notation on, 58–59 sequences on, 937–938 for solving equations graphically, 217–227, 235–239 standard deviation, 657 translation of axes, 774–775 trigonometric equations, 997–998 for trigonometric function values, 264–266 trunction, 54 in values of trigonometric functions, 270 Calculus, 1005–1047 the area question, 1015–1022 rectangular methods for approximating area, 1015–1016 differential, 1005 integral, 1005 limits, 1023–1034 graphical approach, 1025 at infinity, 1030, 1037 limit of a function, 1023 numerical approach, 1024 rules for limits, 1026–1028 one-sided limits and continuity, 1034–1046 continuity, 1038 continuity at a point, 1038 continuity on intervals, 1040–1041 interval notation, 1040 one-sided and two-sided limits, 1035 properties of continuous functions, 1041–1042 the tangent question, 1006–1015 average slope, 1007 Cartesian coordinate system, 204 Center of gravity, 111 Centoid of triangles, 126 Central angle of circle, 141 Central tendency measures, 638–655 Circles, 141–148, 739–744 arc, 141 arc length, 143 central angle, 141 circumference and area of, 141–142 diameter of, 141 general equation of, 740 parts of, 141–142 secant, 141 sector area, 143–144 standard equation of, 739 tangent, 141 Copyright 2011 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part www.EngineeringBooksPDF.com 1155 INDEX Circumference and area, of circles, 141–142 Clearing the equation, 431 Coefficient matrix, 906 Cofactors defined, 325–326 Combined variation, 445 Common denominator, 26 Common factors, 352 Communtative property, Complementary angles, 124, 263 Complex numbers, 678–724 absolute value of, 697 in ac circuits, 716–722 addition of, 687 changing from polar to rectangular form, 698 changing from rectangular to polar form, 698 complex plane, 696 conjugates of, 683–684 DeMoivre’s formula, 710–712 division in polar form, 709 division of, 690–691 equality of, 682 exponential form of, 703–708 graphs of, 696–703 imaginary unit (j operator), 679–680 multiplication in polar form, 708 multiplication of, 689 multiplication of radicals, 681 multiplying and dividing in exponential form, 705 operations in polar form, 708–715 operations with, 687–696 polar form of, 697 pure imaginary number, 680 rectangular form of, 692 roots of, 712 subtraction of, 688 Complex plane, 696 Complex roots theorem, 843 Component vectors, 392–393 Composite functions, 198 Compound inequalities, 872 Compound interest (application of geometric series), 954–955 Compound interest formula, 588 Computer number systems, 794–832 See also Binary number system; Octal number system Computer programming languages, 794 Computers algebraic logic, nonlinear equalities, 880–883 Conditional inequalities, 873 Cones, 157 Congruent angles, 124 Conic sections in polar coordinates, 785–790 Conjugate of a radical expression, 571 Constants, 71–72 Continued proportion, 167 Continuity at a point, 1038 on intervals, 1040–1041 and one-sided limits, 1038 Continuous functions, properties of, 1041–1042 Contradictory inequalities, 873 Control charts, 664 for populations, 670 Correlation coefficients, 245 Corresponding segments of transversals, 124 Cosecant (csc), 258 Cosine (cos), 258 Cotangent (cot), 258 Coterminal angles, 258 Cramer’s Rule, 331–334 Cubes, 156 perfect, 348 Cylinders, 155–156 Decimal fractions to octal fractions conversions, 813 Decimal integer to octal integer conversions, 812 Decimal numbers, 795–796 Decimal-to-octal conversion, 812 Decimals, Degrees, 122–123 Degrees and radians, in trigonometry, 256–257 DeMoivre’s formula, 710–712 Denominators, 30 Dependent variables, 184 Determinants/minors/cofactors defined, 325–326 Diameter of circles, 141 Difference identities, 980–987 Difference of squares, 80 Differential calculus, 1005 Dimension, in matrices, 904 Dimensional analysis, 99–104 Direct variation, 438–440 Direction of vectors, 395 Discriminant of the trinomials, 357 Dispersion measures, 655–662 changing an x-value to a z-score, 659 normal curve, 658–659 variance and standard deviation, 655–658 Distributive law, 356 in special products, 344 Distributive property, Division of algebraic fractions, 369–375 of complex numbers, 690–691 of integers (Rules 4–5), 24–25 monomial by a monomial, 83–84 multinomial by a monomial, 84 multinomial by a multinomial, 85 polynomial by a polynomial, 85–88 of radicals, 570 synthetic, 837–838 Domain and range in functions, 182–183 in graphs, 182–183, 213–215 Double-angle identities, 987–988 Elimination method for solving by addition and subtraction, 311–314, 318–319 Ellipses, 755–763 Ellipsis, 2–3, Empirical methods See Statistics and empirical methods Engineering notation, 57–64, 64–65 on calculators, 64 English system, 49, 50 Equal rations, 95 Equations, 90 applications of, 104–116 for domain and range, 185–188 graphs of, 208 solving, 90–99 Equilateral triangles, 125 Equivalent equations, 90–93 Errors, 51 absolute, 51 percent, 51 relative, 51 Estimates, scientific notation for, 63 Estimation, 54 Event in probability, 633 Expansions and Pascal’s triangle, 962–963 Copyright 2011 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part www.EngineeringBooksPDF.com 1156 INDEX Explicit and implicit functions, 190 Exponential equations, 614–616 Exponential form of complex numbers, 703–708 Exponential functions, 585–597 common features of, 587 compound interest formula, 588 continuous formula, 599 defined, 585 ex, 597–598 graphing (asymptotes), 586–587 growth and decay, 599 modeling with, 589 Exponents, 38–43 fractional, 555–560 Ex, 597–598 Extrapolation, 245 Factor theorem, 836 Factoring, 352–356 common factors, 352 discriminant of the trinomials, 357 distributive law, 356 prime factors, 352 trinomials, 356–365 using the special products, 353, 363 See also Quadratic equations; Special products Flight terminology, 404 FOIL (First/Outside/Inside/Last) method for multiplying binomials, 79 in special products, 346 Fractional equations, 431–437 Fractional exponents, 555–560 basic rules (1–7), 555 rule 8, 555 rule 9, 556 Fractions See Algebraic fractions Frequency distribution, 638 Frustums, 159 Functional notation, 188–190 Functions, 179–203 composite functions, 198 defined, 183–184 domain and range, 182–183 explicit and implicit functions, 190 functional notation, 188–190 independent and dependent variables, 184 inverse functions, 194–196 operations on, 196–197 ordered pairs, 181–182, 184–185 and relations, 180–183 General quadratic trinomial, 346 Geometric solids, 155–167 areas and volumes of, 162 cones, 157 cylinders, 155–156 frustums, 159 prisms, 156 pyramids, 158 spheres, 161 Geometric sequences, 944 Geometric series, 953–955 Geometry, 120–178 circles, 141–148 defined, 120 lines, angles, and triangles, 121–134 other polygons, 134–140 rectangular shapes, 148–155 similar geometric shapes, 167–173 solids, 155–167 See also Analytic geometry Graphical and algebraic methods for solving two linear equations in two variables, 309–317 Graphs, 203–253 of an equation, 208 broken line graph, 240 calculators for solving equations graphically, 217–227, 235–239 in calculus limits, 1025 classifying the graph of a general quadratic equation, 781 of complex numbers, 696–703 computer spreadsheets to graph and solve equations, 227–235 domain and range, 182–183 for domain and range of a function, 213–215 exponential functions, 586–587 in frequency distribution, 638 histograms, 646–652 horizontal line test, 221–222 intercepts, 208–209 of rational functions, 855–859 rectangular coordinates, 203–204 slope, 209–210 that are not lines, 210–212 trigonometric equations, 997 to verify identities, 977 vertical line test, 212–213 x-axis, 204 y-axis, 204 See also Modeling Graphs of trigonometric functions, 487–553 applications of, 524–531 combinations of sine and cosine curves, 506–516 converting between polar and rectangular equations, 545–546 converting polar to rectangular coordinates, 542–543 cotangent, secant, and cosecant functions, 517–519 parametric equations, 531–541 polar coordinates, 541–550 polar equations, 544–545 sine and cosine curves, amplitude and period, 488–496 sine and cosine curves, horizontal and vertical displacement, 497–506 tangent function, 517 See also Trigonometric function values Gravity-influenced trajectories, 536 Half-angle identities, 989–990 Half-line or ray, 121 Hero’s or Heron’s formula, 127 Hexadecimal number system, 820–830 addition, 826 binary-to-hexidecimal conversion, 824 complements (subtraction), 827 decimal fractions to hexadecimal fractions conversion, 822 decimal integer to hexadecimal integer conversion, 822 decimal-to-hexadecimal conversion, 822 hexidecimal numbers, 821 hexidecimal-to-binary conversion, 823 hexidecimal-to-decimal conversion, 821 IPv6 addresses, 824 RGB color model, 829 See also Computer number systems Hexagons, 134 Higher-degree equations, 833–864 complex roots theorem, 843 constant and zero polynomials, 835 factor theorem, 836 Copyright 2011 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part www.EngineeringBooksPDF.com 1157 INDEX finding roots of, 835–853 graphing rational functions, 855–859 horizontal asymptotes, 857 vertical asymptotes, 856 linear factorization theorem, 841 polynomials defined, 834 rational functions, 854–862 remainder theorem, 835–836 roots of an equation, 841–845 synthetic division, 837–838 Histograms, 646–652 Horizontal and vertical lines in linear equations, 306–307 Horizontal asymptotes, 857 Horizontal displacement, in sine and cosine curves, 497–498 Horizontal line test, 221–222 Hyperbolas, 763–770 Hypotenuse of triangles, 128 Identities, 972–1004 basic identities, 973–980 graphs to verify identities, 977 proving identities, 974 Pythagorean identity, 973–974 double-angle identities, 987–988 half-angle identities, 989–990 sum and difference identities, 980–987 Identity element, Imaginary unit (j operator), complex numbers, 679–680 Implicit functions, 190 Independent and dependent variables, 184 Independent events, probability of, 635 Inequalities, 15–16, 872–900 defined, 872–873 linear inequality solutions, 876 nonlinear equalities, 879–890 properties of, 873–875 systems of (linear programming), 893–900 in two variables, 890–893 Infinite geometric series, 957–961 Infinity, in calculus limits, 1030, 1037 Integers, 2–3 addition of, 21–23 multiplication and division of, 24–25 subtraction of, 23–24 Integral calculus, 1005 Intercepts, in graphs, 208–209 Interpolation and extrapolation, 245 Interval notation, 1040 Intervals, continuity on, 1040–1041 Inverse element, Inverse functions, 194–196, 280–283 Inverse variation, 441–444 Inverses of matrices, 919–926 IPv6 addresses, 824 Irrational numbers, Irregular shapes area of, 148–151 rectangular approximation, 148 Simpson’s approximation, 151 trapezoidal approximation, 149 Isosceles trapezoid, 134 Isosceles triangles, 125 J operator (imaginary unit), 679–680 Joint variation, 444–445 Kite, 134 LCD (lowest common denominator), 431 Legs of triangles, 128 Liebniz, Gottfried Wilhelm, 1005 Limit of a function, 1023 Limits in calculus, 1023–1034 one-sided limits and continuity, 1034–1046 two-sided limits, 1035 Line segments, 121 Linear curve fitting, 243 Linear equations, 298–342, 833 algebraic methods for solving three linear equations in three variables, 317–323 Cramer’s Rule, 331–334 defined, 299–300 determinants/minors/cofactors defined, 325–326 elimination method for solving by addition and subtraction, 311–314, 318–319 evaluating determinants on a calculator, 328–329 evaluating determinants with a spreadsheet, 329–330 graphical and algebraic methods for solving two linear equations in two variables, 309–317 horizontal and vertical lines, 306–307 and matrices, 926–932 point-slope equation of a line, 300 slope-intercept equation of a line, 301 substitution method for solving, 310–311, 317–318 using the angle of the line, 302–305 Linear factorization theorem, 841 Linear inequality solutions, 876 Lines, graphs that are not, 210–212 Lines, angles, and triangles, 121–134 Lissajous figures, 533 Logarithmic equations, 616 Logarithmic functions, 604–609 change of base formula, 607 common and natural logs, 606 defined, 605 exponential and logarithmic equations, 614–620 graphs to determine an equation, 624 graphs using semilogarithmic and logarithmic paper, 620–627 logs of different bases, 607 properties of, 610–614 two properties of logarithms, 605 Logarithmic graph paper, 623–624 Lower control limit (LCL), 665 Lowest common denominator (LCD), 431 Magnitude and direction of vectors, 395 Major arc of circles, 141 Malcolm Baldridge National Quality Award, 671 Matrices, 903–934 addition and subtraction of, 907 augmented matrix, 906–907 coefficient matrix, 906 definition, 904 dimension, 904 inverses of, 919–926 and linear equations, 926–932 multiplication of, 913–915 properties of, 910 row and column vectors, 905 scalar multiplication, 909 square matrix, 905 zero matrix, 905 Mean (arithmetic mean), 643 Median of triangles, 126 Medians, 541 Metric system, 49, 50 Microsoft Excel spreadsheet, 11 Copyright 2011 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part www.EngineeringBooksPDF.com 1158 INDEX Minor arc of circles, 141 Minors defined, 325–326 Mixture problems, 110 Mode, 645 Modeling, 240–250 broken line graph, 240 correlation coefficients, 245 interpolation and extrapolation, 245 linear curve fitting, 243 for prediction, 240 using a calculator, 240–241, 243 using a spreadsheet, 241–242, 244 See also Graphs Modeling periodic functions, sine and cosine curves, 500–503 Moment of force, 111 Monomials, 73 Motorola Corporation, 571 Multiplication of algebraic fractions, 369–375 of complex numbers, 689 difference of squares, 80 FOIL (First/Outside/Inside/ Last) method for multiplying binomials, 79 of integers (Rules 4–5), 24–25 matrices, 913–915 monomials, 77–78 multinomials, 78–79 radicals with different indices, 569 radicals with same index, 569 special product, 80 square of a binomial, 80 Law of Cosines (alternate version), 421 Law of Sines, 412–413 Obtuse angles, 124 Obtuse triangles, 125 Octagons, 134 Octal number system, 812–820 addition, 817 ASCII (application of binary and octal numbers), 815–816 ASCII table, 816 binary-to-octal conversion, 814 complements (subtraction), 818–819 decimal fractions to octal fractions conversions, 813 decimal integer to octal integer conversions, 812 decimal-to-octal conversion, 812 octal-to-binary conversions, 814 octal-to-decimal conversion, 812 See also Computer number systems Odd-Five Rule, 53 Ohm’s law, 716 One-sided and two-sided limits, 1035 Operations on functions, 196–197 order of, 7–9 with zero, 9–10 Order of operations, 7–9 in special products, 347 Ordered pairs, 181–182, 184–185 Outcome and sample space, 632 Natural numbers, Negative angles, 235 Negative integers, Negative numbers, binary number system, 810 Newton, Isaac, 1005 Nominal target dimensions, 663 Nonlinear equalities, 879–890 Nonlinear solutions, in systems of equations, 866 Nonnegative integers, Notation in English and metric system, 50 functional, 188–190 Numerators, 30 Numerical approach in calculus limits, 1024 P chart (attribute charts), 668 Parabolas, 745–755 Parallelogram, 134 Parametric equations, 531–541 Partial sums, series, 951–952 Pascal’s triangle, 962–963 PEMDAS (Please excuse my dear aunt Sally), order of operations, Percent errors, 51 Perfect cubes, 348 Perfect square trinomials, 345 Perimeter of polygons, 135 of triangles, 126 Periodic and simple harmonic motion, 524–525 Perpendicular angles, 124 Phasors, 528–529 Place value, Oblique triangles, 412–419 Law of Cosines, 420–422 Please excuse my dear aunt Sally (PEMDAS), order of operations, Point-slope equation of a line, 300 Polar coordinates, 541–550 Polar equations, 544–545 complex numbers, 697, 708–715 of conic sections, 786 Polygons, 125, 134–140 area and perimeter of, 135 hexagons, 134 octagons, 134 See also Quadrilaterals Polynomial equations, 833 Polynomials, 85–88, 833 constant and zero polynomials, 835 defined, 834 See also Higher-degree equations Position vector, 392 Positive angles, 235 Prediction, modeling for, 240 Prime factors, 352 Prisms, 156 Probability, 632–638 Products, scientific notation for, 60–63 Proportion, 94–95 continued, 167 Pure imaginary number, 680 Pyramids, 158 Pythagorean identity, 973–974 Pythagorean theorem, 128, 135 Quadratic equations, 449–482, 833 completing the square, 458–460 defined, 449–450 finding roots by factoring, 451 quadratic formula, 461–462 roots of, 451 zero-product rule for real numbers, 450 Quadratic functions modeling with, 469–482 piecewise-defined functions, 472–473 Quadratic trinomial, 346 Quadrilaterals, 134–135 isosceles trapezoid, 134 kite, 134 parallelogram, 134 rectangle, 134 rhombus, 134 square, 134 trapezoid, 134 Copyright 2011 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part www.EngineeringBooksPDF.com 1159 INDEX Quartiles, 641 Quotient identities, 263 Quotients, scientific notation for, 60–63 Radians, 122–123 in trigonometry, 256–257 Radicals addition and subtraction, 567–569 basic operations, 567–673 conjugate of a radical expression, 571 defined, 561 division of, 570 equations with, 574–580 extraneous roots, 574 multiplying with different indices, 569 multiplying with same index, 569 rationalizing the denominator, 562–563 rules for, 561, 563 simplifying, 564 Ratio, 93–94 Rational functions, 854–862 Rational numbers, arithmetic of (Rules 6–8), 25–33 Ray or half-line, 121 Real number system, 1–69 basic operations with, 21–38 exponents and roots, 38–49 scientific and engineering notation, 57–64 sets and basic laws, 2–21 significant digits and rounding off, 49–57 Real numbers, 3–4 properties of, Reciprocal identities, 263 Reciprocals, 16–17 Rectangular approximation, 148 Rectangle, 134 Rectangular coordinate system, 204 Rectangular coordinates, 203–204 Rectangular methods for approximating area, 1015–1016 Rectangular parallelepipeds, 156 Rectangular shapes, 148–155 Recursion formula, sequences, 940 Reference angles, 276–277 Regular prisms, 156 Regular pyramids, 158 Relations, and functions, 180–183 Relative errors, 51 Remainder theorem, 835–836 Resultant vectors, 391 RGB color model, 829 Rhombus, 134 Right angles, 124 Right triangles, 125, 128, 268–276 See also Trigonometry Roots, 43–46 of an equation, 841–845 of complex numbers, 712 of higher-degree equations, 835–853 of quadratic equations, 451 in real number system, 38–49 Roses, 545 Rotation of axes, 778–784 Round-to-the-Even Rule, 53 Rounding off to a place value, 5–7 with calculators, 54–55 numbers, 53–54 and significant digits, 49–57 Row and column vectors, in matrices, 905 Scalar multiplication, matrices, 909 Scalars, 390 Scale drawings, and similar geometric shapes, 171 Scalene triangles, 125 Scientific notation, 57–65 on calculators, 58–59 for estimates, 63 products and quotients, 60–63 writing numbers in, 57–58 Secant (sec), 141, 258 Second-degree equations See Quadratic equations Sector area, of circles, 143–144 Semilogarithmic graph paper, 621–623 Sequences, 935–948 arithmetic, 942–943 definition, 936 geometric, 944 recursion formula, 940 See also Series Series, 948–957 arithmetic series, 952 compound interest (application of geometric series), 954–955 geometric series, 953–955 infinite geometric series, 957–961 partial sums, 951–952 sum of an infinite geometric series, 959 sum of first n in terms of a geometric sequence, 953 sum of first n in terms of an arithmetic sequence, 952 summation notation, 948–949 See also Sequences Sets and basic laws of real number system, 2–21 Significant digits and rounding off, in real number system, 49–57 Similar geometric shapes, 167–173 areas of, 170 continued proportion, 167 other figures, 169 scale drawings, 171 triangles, 168 volumes of, 171 Simpson’s approximation, 151, 162 Sine and cosine curves, 488–496 amplitude, 489–490 combinations of, 506–516 horizontal displacement, 497–498 modeling periodic functions, 500–503 period and frequency, 490–493 vertical displacement, 499–500 Sine (sin), 258 Six Sigma, 671 Slope, 209–210 Slope-intercept equation of a line, 301 Solids See Geometric solids SPC See Statistical process control Special products, 80, 344–351, 353, 363 difference of two squares, 345, 353 distributive law, 344 in factoring, 353 FOIL method, 346 general quadratic trinomial, 346 order of operations, 347 perfect cubes, 348 perfect square trinomials, 345 special products listed, 349, 363 sum and difference of two cubes, 348 two binomials, same first term, 346 See also Factoring Spheres, 161 Spreadsheets, 10–12 adding sequences with, 949–950 average slope, 1010 binomial coefficients with, 965 complex numbers, 694 Copyright 2011 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part www.EngineeringBooksPDF.com 1160 INDEX Spreadsheets (Continued) conic sections in polar coordinates, 789 ellipses, 760–761 evaluating determinants with, 329–330 exponential function ex, 598 factorials with, 964 finding logs with, 606 to graph and solve equations, 227–235 to graph parametric equations, 534–535 to graph polar equations, 547–549 graphing sine and cosine curves, 509–510 graphs of trigonometric functions, 520–523 higher-degree equations, 847–850 inverses of matrices, 925 for inverse functions, 282 for modeling, 241–242, 244 modeling periodic functions, 502–503 nonlinear equalities, 883–889 parabolas, 751 piecewise-defined functions, 477–478 radical equations, 578–579 rotation of axes, 788 semilogarithmic graphing with, 622–623 sequences on, 938–939 standard deviation, 657–658 for statistical measures, 648–652 translation of axes, 775 trigonometric equations, 998 for trigonometric function values, 266 SQC See Statistical quality control Square, 134 of a binomial, 80 completing the, 458–460 Square matrix, 905 Squares, difference of, 80 Statistics problems, 111 Statistical process control (SPC), 662–674 attribute charts (the p chart), 668 control charts, 664 control charts for populations, 670 lower control limit (LCL), 665 upper control limit (UCL), 665 variables charts, 665 Statistical quality control (SQC), 662–663 Statistics and empirical methods, 631–677 central tendency measures, 638–655 dispersion measures, 655–662 probability, 632–638 Six Sigma, 671 statistical process control (SPC), 662–674 statistical quality control (SQC), 662–663 Straight angles, 124 Straight lines, 729–739 Sub-orbital projectile motion, 536 Subnet masking, 801–802 Substitution method for solving linear equations, 310–311, 317–318 Subtraction algebraic fractions, 377 binary number system, 805 of complex numbers, 688 decimal subtraction using complements, 806 hexadecimal number system, 827 integers (Rule 3), 23–24 matrices, 907 multinomials, 71–77, 73–74 octal number system, 818–819 radicals, 567–569 in solving linear equations, 311– 314, 318–319 vectors, 399–407 Sum and difference identities, 980–987 Sum and difference of two cubes, 348 Sum of an infinite geometric series, 959 Sum of first n in terms of a geometric sequence, 953 Sum of first n in terms of an arithmetic sequence, 952 Summation notation, series, 948–949 Supplementary angles, 124 Synthetic division, 837–838 Systems of equations, 865–872 nonlinear solutions, 866 Systems of inequalities (linear programming), 893–900 Table of trigonometric functions, 279 Tangent, of circles, 141 Tangent function, 517 Tangent question, in calculus, 1006–1015 Tangent (tan), 258 Tolerance limits, 663 Torque, 111 Translation of axes, 770–778 Transversal lines, 124 Trapezoid, 134 Trapezoidal approximation, 149, 162 Triangles, 121–134, 168 acute, 125 altitude of, 126 area of, 126, 422–423 base of, 126 centoid of, 126 equilateral, 125 Hero’s or Heron’s formula, 127 hypotenuse, 128 isosceles, 125 legs of, 128 median of, 126 obtuse, 125 perimeter of, 126 Pythagorean theorem, 128, 135 right, 125, 128 scalene, 125 See also Trigonometry Trigonometric functions, 258– 260 See also Graphs of trigonometric functions Trigonometric equations, 995–1002 Trigonometric function values, 261–268 of any angle, 276–286 of complementary angles, 263 inverse functions, 280–283 quotient identities, 263 reciprocal identities, 263 reference angles, 276–277 table of trigonometric functions, 279 trigonometric values, 264 using calculators, 264–266 using calculators for inverse functions, 281–282 using spreadsheets, 266 using spreadsheets for inverse functions, 282 Trigonometric identities See Identities Trigonometry, 254–294 angles of elevation or depression, 273 applications of, 286–293 coterminal angles, 258 Copyright 2011 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part www.EngineeringBooksPDF.com 1161 INDEX degrees and radians, 256–257 positive and negative angles, 235 trigonometric functions, 258–260 See also Right triangle; Trigonometric function values Trinomials, 73, 356–365 discriminant of the, 357 perfect square, 345 Trunction in calculators, 54 Two binomials, same first term, 346 Two cubes, sum and difference of, 348 Two-sided limits, 1035 Two squares, difference of, 345, 353 Uniform motion problems, 106 Upper control limit (UCL), 665 Variables, 71, 184 Variables charts, 665 Variation combined, 445 direct, 438–440 inverse, 441–444 joint, 444–445 Vectors, 390–398 adding and subtracting, 399–407 application of, 407–412 component vectors, 392–393 defined, 390–391 magnitude and direction of, 395 position vector, 392 resultant vectors, 391 scalars, 390 Vertex or vertices of polygons, 125 Vertical asymptotes, 856 Vertical displacement, sine and cosine curves, 499–500 Vertical line test, 212–213 Vertical lines in linear equations, 306–307 Volumes of geometric solids, 162 of similar geometric shapes, 171 Whole numbers, Word problems, 104–105 mixture problems, 110 statics problems, 111 uniform motion problems, 106 work problems, 109 Work problems, 109 Writing numbers in scientific notation, 57–58 x-axis, 204 y-axis, 204 Zero, operations with, 9–10 Zero matrix, 905 Zero-product rule for real numbers, 450 Copyright 2011 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part www.EngineeringBooksPDF.com Copyright 2011 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part www.EngineeringBooksPDF.com Properties of Exponents b b bm n (bm)n bmn (ab)n anbn a am ¢ ≤ m m, b b b bm bm2n, b bn b0 1, b b2n n , b b Binomial Formula m n n n x y n xn ¢ ≤ xn21y ¢ ≤ xn22y2 n    c1 ¢ ≤ xyn21 yn n21 Special Products and Factors a(x y) ax ay (x y) (x y) x2 y2 (x y)2 x2 2xy y2 (x y)3 x3 3x2y 3xy2 y3 x3 y3 (x y) (x2 xy y2) x3 y3 (x y) (x2 xy y2) Properties of Radicals n n !ab ! a! b n a ! a n n Äb !b n n !b bn/n b n !b b1/n n m n Basic Operations on Complex Numbers (a bj) (c dj) (a c) (b d)j (a bj) (c dj) (ac bd) (ad bc)j a bj ac bd bc ad j 1 c dj c 1d c2 d2 a bj "a2 b2 mn " !b !b Properties of Logarithms logb xy logb x logb y x logb x logb y y logb xp p logb x logb logb b logb bn n Properties of Inequalities If a, b, and c are real numbers, and If a , b, then a c , b c If a , b and c 0, then ac , bc If a , b and c , 0, then ac bc logb n n If a , b and n 0, then an , bn and "a , !b Quadratic Formula 2b "b2 4ac If ax2 bx c and a  0, then x 2a Properties of Absolute Value If x and a are real numbers, a 0, x b If |x| , a, then 2a , x , a If |x| a, then x , 2a or x a 2x if x , x if x $ Copyright 2011 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part www.EngineeringBooksPDF.com Double-Angle Identities sin 2u sin u cos u cos 2u cos2 u sin2u 2cos2u 2sin2u tan u tan 2u tan2 u Variation If k is a constant Direct: y kx k Indirect: y or yx k x Joint: y kxz DeMoivre’s Formula For any complex number z r cis u r lu reju, and n an integer, then zn (rej u)n rn ejn u rnlnu rn cis (n u) rn (cos n u j sin n u) Roots of a Complex Number If z r (cos u j sin u), then the nth roots of z are given by the formula 360 # k 360 # k u u n wk "r B cos ¢ ≤ j sin ¢ ≤R n n n n where k 0, 1, 2, n Some Trigonometric Identities Reciprocal Identities 1 sin u  cos u  tan u csc u sec u cot u 1 csc u  sec u  cot u sin u cos u tan u Pythagorean Identities sin2 u cos2 u tan2 u 1 sec2 u 1 cot2 u csc2 u Half-Angle Identities cos u u sin Å 1 cos u u cos Å 2 cos u u tan Å 1 cos u sin u 1 cos u cos u sin u Sine Law a b c 5 sin A sin B sin C Cosine Law a2 b2 c2 2bc cos A b2 a2 c2 2ac cos B or c2 a2 b2 2ab cos C © Cengage Learning 2013 Quotient Identities sin u cos u tan u   cot u cos u sin u Sum and Difference Identities sin (u f) sin u cos f cos u sin f cos (u f) cos u cos f  sin u sin f tan u tan f tan (u f) tan u tan f Cosine Law (Alternative Version) b2 c2 a2 cos A 2bc a2 c2 b2 cos B 2ac a b 2 c2 or cos C 2ab Copyright 2011 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part www.EngineeringBooksPDF.com ... www.EngineeringBooksPDF.com PReFace Technical Mathematics, fourth edition, is a student-oriented textbook designed to be easily read and understood by students who are preparing for technical or scientific... or in part www.EngineeringBooksPDF.com xiii PrEFaCE MajOr changes tO the FOurth editiOn There are seven major differences between the fourth edition and the third edition: (1) new section on dimensional... www.EngineeringBooksPDF.com Technical MaTheMaTics 4th Edition Copyright 2011 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part www.EngineeringBooksPDF.com