...College Trigonometry Version π Corrected Edition by Carl Stitz, Ph.D. Lakeland Community College Jeff Zeager, Ph.D. Lorain County Community College July 4, 2013 ii Acknowledgements While the cover of this textbook lists only two names, the book as it stands today would simply not exist if not for the tireless work and dedication of several people. First and foremost, we wish to thank our families for their patience and support during the creative process. We would also like to thank our students - the sole inspiration for the work. Among our colleagues, we wish to thank Rich Basich, Bill Previts, and Irina Lomonosov, who not only were early adopters of the textbook, but also contributed materials to the project. Special thanks go to Katie Cimperman, Terry Dykstra, Frank LeMay, and Rich Hagen who provided valuable feedback from the classroom. Thanks also to David Stumpf, Ivana Gorgievska, Jorge Gerszonowicz, Kathryn Arocho, Heather Bubnick, and Florin Muscutariu for their unwaivering support (and sometimes defense) of the book. From outside the classroom, we wish to thank Don Anthan and Ken White, who designed the electric circuit applications used in the text, as well as Drs. Wendy Marley and Marcia Ballinger for the Lorain CCC enrollment data used in the text. The authors are also indebted to the good folks at our schools’ bookstores, Gwen Sevtis (Lakeland CC) and Chris Callahan (Lorain CCC), for working with us to get printed copies to the students...
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...iOREGON DEPARTMENT OF TRANSPORTATION GEOMETRONICS 200 Hawthorne Ave., B250 Salem, OR 97310 (503) 986-3103 Ron Singh, PLS Chief of Surveys (503) 986-3033 BASIC SURVEYING - THEORY AND PRACTICE David Artman, PLS Geometronics (503) 986-3017 Ninth Annual Seminar Presented by the Oregon Department of Transportation Geometronics Unit February 15th - 17th, 2000 Bend, Oregon David W. Taylor, PLS Geometronics (503) 986-3034 Dave Brinton, PLS, WRE Survey Operations (503) 986-3035 Table of Contents Types of Surveys ........................................................................................... 1-1 Review of Basic Trigonometry ................................................................... 2-1 Distance Measuring Chaining ................................................................... 3-1 Distance Measuring Electronic Distance Meters ................................... 4-1 Angle Measuring .......................................................................................... 5-1 Bearing and Azimuths ................................................................................ 6-1 Coordinates .................................................................................................... 7-1 Traverse ........................................................................................................... 8-1 Global Positioning System ..........................................................
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...your answers. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 80. This document consists of 15 printed pages and 1 blank page. DC (JF/SW) 72417 © UCLES 2013 [Turn over www.maxpapers.com 2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation ax2 + bx + c = 0, x= Binomial Theorem () () b 2 − 4 ac . 2a −b () () n n n (a + b)n = an + 1 an–1 b + 2 an–2 b2 + … + r an–r br + … + bn, n n! where n is a positive integer and r = . (n – r)!r! 2. TRIGONOMETRY Identities sin2 A + cos2 A = 1 sec2 A = 1 + tan2 A cosec2 A = 1 + cot2 A Formulae for ∆ABC a b c sin A = sin B = sin C a2 = b2 + c2 – 2bc cos A ∆= © UCLES 2013 1 bc sin A 2 4037/22/M/J/13 www.maxpapers.com 3 1 For Examiner’s Use...
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...CARIBBEAN EXAMINATIONS COUNCIL Caribbean Secondary Education Certificate CSEC MATHEMATICS SYLLABUS Effective for examinations from May/June 2010 CXC 05/G/SYLL 08 Published in Jamaica © 2010, Caribbean Examinations Council All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form, or by any means electronic, photocopying, recording or otherwise without prior permission of the author or publisher. Correspondence related to the syllabus should be addressed to: The Pro-Registrar Caribbean Examinations Council Caenwood Centre 37 Arnold Road, Kingston 5, Jamaica, W.I. Telephone: (876) 630-5200 Facsimile Number: (876) 967-4972 E-mail address: cxcwzo@cxc.org Website: www.cxc.org Copyright © 2008, by Caribbean Examinations Council The Garrison, St Michael BB11158, Barbados CXC 05/OSYLL 00 Contents RATIONALE. .......................................................................................................................................... 1 AIMS. ....................................................................................................................................................... 1 ORGANISATION OF THE SYLLABUS. ............................................................................................. 2 FORMAT OF THE EXAMINATIONS ................................................................................................ 2 CERTIFICATION AND PROFILE DIMENSIONS .....
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...mathematics is the creation of about two thousand years before the birth of Christ. After that, moving from many nations and civilization, numbers and principles of numbers have gained an universal form at present. The mathematicians in India first introduce zero (0) and 10 based place value system for counting natural numbers, which is considered a milestone in describing numbers. Chinese and Indian mathematicians extended the idea zero, real numbers, negative number, integer and fractional numbers which the Arabian mathematicians accepted in the middle age. But the credit of expressing number through decimal fraction is awarded to the Muslim Mathematicians. Again they introduce first the irrational numbers in square root form as a solution of the quadratic equation in algebra in the 11th century. According to the historians, very near to 50 BC the Greek Philosophers also felt the necessity of irrational number for drawing geometric figures, especially for the square root of 2. In the 19th century European Mathematicians gave the real numbers a complete shape by systematization. For daily necessity, a student must have a vivid knowledge about ‘Real Numbers’. In this chapter real numbers are discussed in detail. At the end of this chapter, the students will be able to – Classify real numbers Express real numbers into decimal and determine approximate value Explain the classification of decimal fractions Explain recurring decimal numbers and...
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...GRE MATH FORMULAE Mixtures first.... 1. when you mix different quantities (say n1 and n2) of A and B, with different strengths or values v1 and v2 then their mean value vm after mixing will be: Vm*(n1 + n2) = (v1.n1 + v2.n2) you can use this to find the final price of say two types of rice being mixed or final strength of acids of different concentration being mixed etc.... the ratio in which they have to be mixed in order to get a mean value of vm can be given as: n1/n2 = (v2 - vm)/(vm - v1) When three different ingredients are mixed then the ratio in which they have to be mixed in order to get a final strength of vm is: n1 : n2 : n3 = (v2 - vm)(v3 - vm) : (vm - v1)(v3 - vm) : (vm - v2)(vm - v1) 2. If from a vessel containing M units of mixtures of A & B, x units of the mixture is taken out & replaced by an equal amount of B only .And If this process of taking out & replacement by B is repeated n times , then after n operations, Amount of A left/ Amount of A originally present = (1-x/M)^n 3. If the vessel contains M units of A only and from this x units of A is taken out and replaced by x units of B. if this process is repeated n times, then: Amount of A left = M [(1 - x/M)^n] This formula can be applied to problem involving dilution of milk with water, etc... EXPLAINATION TO THE ABOVE FORMULA when you mix different quantities (say n1 and n2) of A and B, with different strengths or values v1 and v2 then their mean value vm after mixing...
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...TLFeBOOK WHAT READERS ARE SAYIN6 "I wish I had had this book when I needed it most, which was during my pre-med classes. I t could have also been a great tool for me in a few medical school courses." Or. Kellie Aosley8 Recent Hedical school &a&ate "CALCULUS FOR THE UTTERLY CONFUSED has proven to be a wonderful review enabling me t o move forward in application of calculus and advanced topics in mathematics. I found it easy t o use and great as a reference for those darker aspects of calculus. I' Aaron Ladeville, Ekyiheeriky Student 'I1am so thankful for CALCULUS FOR THE UTTERLY CONFUSED! I started out Clueless but ended with an All' Erika Dickstein8 0usihess school Student "As a non-traditional student one thing I have learned is the Especially in importance of material supplementary t o texts. calculus it helps to have a second source, especially one as lucid and fun t o read as CALCULUS FOR THE UTTERtY CONFUSED. Anyone, whether you are a math weenie or not, will get something out of this book. With this book, your chances of survival in the calculus jungle are greatly increased.'I Brad &3~ker, Physics Student Other books i the Utterly Conhrsed Series include: n Financial Planning for the Utterly Confrcsed, Fifth Edition Job Hunting for the Utterly Confrcred Physics for the Utterly Confrred CALCULUS FOR THE UTTERLY CONFUSED Robert M. Oman Daniel M. Oman McGraw-Hill New York San Francisco Washington, D.C. Auckland Bogoth Caracas Lisbon...
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...Handbook of Formulae and Physical Constants For The Use Of Students And Examination Candidates Duplication of this material for student in-class use or for examination purposes is permitted without written approval. Approved by the Interprovincial Power Engineering Curriculum Committee and the Provincial Chief Inspectors' Association's Committee for the standardization of Power Engineer's Examinations n Canada. www.powerengineering.ca Printed July 2003 Table of Contents TOPIC PAGE SI Multiples..........................................................................................1 Basic Units (distance, area, volume, mass, density) ............................2 Mathematical Formulae .......................................................................5 Applied Mechanics .............................................................................10 Thermodynamics.................................................................................21 Fluid Mechanics..................................................................................28 Electricity............................................................................................30 Periodic Table .....................................................................................34 Names in the Metric System VALUE 1 000 000 000 000 1 000 000 000 1 000 000 1 000 100 10 0.1 0.01 0.001 0.000 001 0.000 000 001 0.000 000 000 001 EXPONENT 1012 109 106 103 102 101 10-1 10-2 10-3 10-6 10-9...
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...Mathematics HL First examinations 2008 b DIPLOMA PROGRAMME MATHEMATICS HL First examinations 2008 International Baccalaureate Organization Buenos Aires Cardiff Geneva New York Singapore Diploma Programme Mathematics HL First published in September 2006 International Baccalaureate Organization Peterson House, Malthouse Avenue, Cardiff Gate Cardiff, Wales GB CF23 8GL United Kingdom Phone: + 44 29 2054 7777 Fax: + 44 29 2054 7778 Web site: www.ibo.org c International Baccalaureate Organization 2006 The International Baccalaureate Organization (IBO) was established in 1968 and is a non-profit, international educational foundation registered in Switzerland. The IBO is grateful for permission to reproduce and/or translate any copyright material used in this publication. Acknowledgments are included, where appropriate, and, if notified, the IBO will be pleased to rectify any errors or omissions at the earliest opportunity. IBO merchandise and publications in its official and working languages can be purchased through the IB store at http://store.ibo.org. General ordering queries should be directed to the sales and marketing department in Cardiff. Phone: +44 29 2054 7746 Fax: +44 29 2054 7779 E-mail: sales@ibo.org Printed in the United Kingdom by Antony Rowe Ltd, Chippenham, Wiltshire. 5007 CONTENTS INTRODUCTION 1 NATURE OF THE SUBJECT 3 AIMS 6 OBJECTIVES 7 SYLLABUS OUTLINE 8 SYLLABUS DETAILS 9 ASSESSMENT OUTLINE 53 ASSESSMENT DETAILS ...
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...Basics Rounding to Decimal Places If the next number is below 5, round down by leaving thr previous digit untouched. Round 15.283 correct to 2 decimal places. The answer is 15.28 If the next number is 5 or more, round up Round 3.728 correct to 2 decimal places. The answer is 3.73 Rounding to significant figures For numbers between 0 and 1, start counting the significant figures from the first non-zero digit. Round 0.007851 correct to 2 significant figures. The answer is 0.0079 For numbers larger than 1, start counting the significant figures from the first digit. Round 583 200 correct to 2 significant figures. The answer is 580 000 Scientific notation. 13450700 in scientific notation is 1.34507 10 0.00125 in scientific notation is 1.25 10 7 3 Addition Sum Subtraction Difference Multiplication * : / Product Division Quotient Numbers Real Numbers Rational Numbers Irrational Numbers Definition of a rational number. are not rational. They are non-terminating & non-recurring decimals. A number is rational if it can be expressed as a fraction in p the form q ,where p & q have no common factor and q 0. Examples 2 8 Fractions, e.g. 3 , 17 Integers, e.g. 2 , 3, 15 Terminating decimals, e.g. 0.3562 Recurring decimals, e.g. 0.4 , 0.23, 0.17 Examples , e. Surds, e.g. 2 , 3 5 . Transcendental numbers, e.g. 0.100100010000100.... Recurring...
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...CHAPTER 0 Contents Preface v vii Problems Solved in Student Solutions Manual 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Matrices, Vectors, and Vector Calculus Newtonian Mechanics—Single Particle Oscillations 79 127 1 29 Nonlinear Oscillations and Chaos Gravitation 149 Some Methods in The Calculus of Variations 165 181 Hamilton’s Principle—Lagrangian and Hamiltonian Dynamics Central-Force Motion 233 277 333 Dynamics of a System of Particles Motion in a Noninertial Reference Frame Dynamics of Rigid Bodies Coupled Oscillations 397 435 461 353 Continuous Systems; Waves Special Theory of Relativity iii iv CONTENTS CHAPTER 0 Preface This Instructor’s Manual contains the solutions to all the end-of-chapter problems (but not the appendices) from Classical Dynamics of Particles and Systems, Fifth Edition, by Stephen T. Thornton and Jerry B. Marion. It is intended for use only by instructors using Classical Dynamics as a textbook, and it is not available to students in any form. A Student Solutions Manual containing solutions to about 25% of the end-of-chapter problems is available for sale to students. The problem numbers of those solutions in the Student Solutions Manual are listed on the next page. As a result of surveys received from users, I continue to add more worked out examples in the text and add additional problems. There are now 509 problems, a significant number over the 4th edition. The instructor will find a large...
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...1 Basic Arithmetic TERMINOLOGY Absolute value: The distance of a number from zero on the number line. Hence it is the magnitude or value of a number without the sign Directed numbers: The set of integers or whole numbers f -3, -2, -1, 0, 1, 2, 3, f Exponent: Power or index of a number. For example 23 has a base number of 2 and an exponent of 3 Index: The power of a base number showing how many times this number is multiplied by itself e.g. 2 3 = 2 # 2 # 2. The index is 3 Indices: More than one index (plural) Recurring decimal: A repeating decimal that does not terminate e.g. 0.777777 … is a recurring decimal that can be written as a fraction. More than one digit can recur e.g. 0.14141414 ... Scientific notation: Sometimes called standard notation. A standard form to write very large or very small numbers as a product of a number between 1 and 10 and a power of 10 e.g. 765 000 000 is 7.65 # 10 8 in scientific notation Chapter 1 Basic Arithmetic 3 INTRODUCTION THIS CHAPTER GIVES A review of basic arithmetic skills, including knowing the correct order of operations, rounding off, and working with fractions, decimals and percentages. Work on significant figures, scientific notation and indices is also included, as are the concepts of absolute values. Basic calculator skills are also covered in this chapter. Real Numbers Types of numbers Unreal or imaginary numbers Real numbers Rational numbers Irrational numbers Integers Integers are whole numbers...
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...Advanced Problems in Core Mathematics Stephen Siklos Fourth edition, October 2008 ABOUT THIS BOOKLET This booklet is intended to help you to prepare for STEP examinations. It should also be useful as preparation for any undergraduate mathematics course, even if you do not plan to take STEP. The questions are all based on recent STEP questions. I chose the questions either because they are ‘nice’ – in the sense that you should get a lot of pleasure from tackling them – or because I felt I had something interesting to say about them. In this booklet, I have restricted myself (reluctantly) to the syllabus for Papers I and II, which is the A-level core (i.e. C1 to C4) with a few additions. This material should be familiar to you if you are taking the International Baccalaureate, Scottish Advanced Highers or other similar courses. The first two questions (the sample worked questions) are in a ‘stream of consciousness’ format. They are intended to give you an idea how a trained mathematician would think when tackling them. This approach is much too long-winded to sustain, but it should help you to see what sort of questions you should be asking yourself as you work through the later questions. I have given each of the subsequent questions a difficulty rating ranging from (∗) to (∗ ∗ ∗). A question labelled (∗) might be found on STEP I; a question labelled (∗∗) might be found on STEP II; a question labelled (∗ ∗ ∗) might be found on STEP III. But difficulty in mathematics...
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...Higher Engineering Mathematics In memory of Elizabeth Higher Engineering Mathematics Sixth Edition John Bird, BSc (Hons), CMath, CEng, CSci, FIMA, FIET, MIEE, FIIE, FCollT AMSTERDAM • BOSTON • HEIDELBERG • LONDON • NEW YORK • OXFORD PARIS • SAN DIEGO • SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Newnes is an imprint of Elsevier Newnes is an imprint of Elsevier The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, UK 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA First edition 2010 Copyright © 2010, John Bird, Published by Elsevier Ltd. All rights reserved. The right of John Bird to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher. Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone (+44) (0) 1865 843830; fax (+44) (0) 1865 853333; email: permissions@elsevier.com. Alternatively you can submit your request online by visiting the Elsevier web site at http://elsevier.com/locate/permissions, and selecting Obtaining permission to use Elsevier material. Notice No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products...
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...The Project Gutenberg EBook of Calculus Made Easy, by Silvanus Thompson This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org Title: Calculus Made Easy Being a very-simplest introduction to those beautiful methods which are generally called by the terrifying names of the Differentia Author: Silvanus Thompson Release Date: October 9, 2012 [EBook #33283] Language: English Character set encoding: ISO-8859-1 *** START OF THIS PROJECT GUTENBERG EBOOK CALCULUS MADE EASY *** Produced by Andrew D. Hwang, Brenda Lewis and the Online Distributed Proofreading Team at http://www.pgdp.net (This file was produced from images generously made available by The Internet Archive/American Libraries.) transcriber’s note Minor presentational changes, and minor typographical and numerical corrections, have been made without comment. All A textual changes are detailed in the L TEX source file. This PDF file is optimized for screen viewing, but may easily be A recompiled for printing. Please see the preamble of the L TEX source file for instructions. CALCULUS MADE EASY MACMILLAN AND CO., Limited LONDON : BOMBAY : CALCUTTA MELBOURNE THE MACMILLAN COMPANY NEW YORK : BOSTON : CHICAGO DALLAS : SAN FRANCISCO THE MACMILLAN CO. OF CANADA, Ltd. TORONTO CALCULUS MADE EASY: BEING A VERY-SIMPLEST...
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