103 Trigonometry Problems

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Titu Andreescu Zuming Feng 103 Trigonometry Problems From the Training of the USA IMO Team Birkhäuser Boston • Basel • Berlin
Titu Andreescu University of Wisconsin Department of Mathematical and Computer Sciences Whitewater, WI 53190 U.S.A. Zuming Feng Phillips Exeter Academy Department of Mathematics Exeter, NH 03833 U.S.A. AMS Subject Classifications: Primary: 97U40, 00A05, 00A07, 51-XX; Secondary: 11L03, 26D05, 33B10, 42A05 Library of Congress Cataloging-in-Publication Data Andreescu, Titu, 1956- 103 trigonometry problems : from the training of the USA IMO team / Titu Andreescu, Zuming Feng. p. cm. Includes bibliographical references. ISBN 0-8176-4334-6 (acid-free paper) 1. Trigonometry–Problems, exercises, etc. I. Title: One hundred and three trigonometry problems. II. Feng, Zuming. III. Title. QA537.A63 2004 516.24–dc22 2004045073 ISBN 0-8176-4334-6 ©2005 Birkhäuser Boston Birkhäuser All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Birkhäuser Boston, c/o Springer Science+Business Media Inc., Rights and Permissions, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States of America. 9 8 7 6 5 4 3 2 1 SPIN 10982723 www.birkhauser.com Printed on acid-free paper. ®
Page 3: About the Authors Titu Andreescu re
Page 7 and 8: vi Contents Vectors 41 The Dot Prod
Page 9 and 10: viii Preface Throughout MOSP, full
Page 12 and 13: Abbreviations and Notation Abbrevia
Page 14: 103 Trigonometry Problems
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42 103 Trigonometry Problems tail o
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44 103 Trigonometry Problems b = 26
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46 103 Trigonometry Problems −−
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48 103 Trigonometry Problems a way
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50 103 Trigonometry Problems small
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52 103 Trigonometry Problems z x F
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54 103 Trigonometry Problems (a) Ho
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58 103 Trigonometry Problems Soluti
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62 103 Trigonometry Problems to tri
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64 103 Trigonometry Problems 5. Pro
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66 103 Trigonometry Problems (a) ta
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68 103 Trigonometry Problems (b) co
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70 103 Trigonometry Problems 40. Fi
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3 Advanced Problems 1. Two exercise
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3. Advanced Problems 75 9. Find the
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3. Advanced Problems 77 22. Let a 0
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3. Advanced Problems 79 35. Let x 1
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3. Advanced Problems 81 47. Let n b
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84 103 Trigonometry Problems 3. Com
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102 103 Trigonometry Problems Euler
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104 103 Trigonometry Problems prove
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106 103 Trigonometry Problems Solut
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108 103 Trigonometry Problems 34. P
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112 103 Trigonometry Problems if x
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114 103 Trigonometry Problems and (
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116 103 Trigonometry Problems or si
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120 103 Trigonometry Problems imply
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5 Solutions to Advanced Problems 1.
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5. Solutions to Advanced Problems 1
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or 5. Solutions to Advanced Problem
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It follows that ∑ 4 sin 3 A cos(B
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200 103 Trigonometry Problems Binom
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208 103 Trigonometry Problems Sum-t
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Further Reading 1. Andreescu, T.; F
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Further Reading 213 23. Fomin, D.;
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