103 Trigonometry Problems: From the Training of the USA IMO Team103 Trigonometry Problems contains highly-selected problems and solutions used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Though many problems may initially appear impenetrable to the novice, most can be solved using only elementary high school mathematics techniques. Key features: * Gradual progression in problem difficulty builds and strengthens mathematical skills and techniques * Basic topics include trigonometric formulas and identities, their applications in the geometry of the triangle, trigonometric equations and inequalities, and substitutions involving trigonometric functions * Problem-solving tactics and strategies, along with practical test-taking techniques, provide in-depth enrichment and preparation for possible participation in various mathematical competitions * Comprehensive introduction (first chapter) to trigonometric functions, their relations and functional properties, and their applications in the Euclidean plane and solid geometry expose advanced students to college level material 103 Trigonometry Problems is a cogent problem-solving resource for advanced high school students, undergraduates, and mathematics teachers engaged in competition training. Other books by the authors include 102 Combinatorial Problems: From the Training of the USA IMO Team (0-8176-4317-6, 2003) and A Path to Combinatorics for Undergraduates: Counting Strategies (0-8176-4288-9, 2004). |
Contents
Trigonometric Fundamentals | 1 |
Think Within the Box | 4 |
Youve Got the Right Angle | 6 |
Think Along the Unit Circle | 10 |
Graphs of Trigonometric Functions | 14 |
The Extended Law of Sines | 18 |
Area and Ptolemys Theorem | 19 |
Existence Uniqueness and Trigonometric Substitutions | 23 |
The Dot Product and the Vector Form of the Law of Cosines | 46 |
CauchySchwarz Inequality | 47 |
Constructing Sinusoidal Curves with a Straightedge | 50 |
Three Dimensional Coordinate Systems | 51 |
Traveling on Earth | 55 |
Where Are You? | 57 |
De Moivres Formula | 58 |
Introductory Problems | 63 |
Cevas Theorem | 28 |
Think Outside the Box | 33 |
The Law of Cosines | 34 |
Stewarts Theorem | 35 |
Herons Formula and Brahmaguptas Formula | 37 |
Brocard Points | 39 |
Vectors | 41 |
Advanced Problems | 73 |
Solutions to Introductory Problems | 83 |
Solutions to Advanced Problems | 125 |
Glossary | 199 |
Further Reading | 211 |
Other editions - View all
103 Trigonometry Problems: From the Training of the USA IMO Team Titu Andreescu,Zuming Feng Limited preview - 2006 |
103 Trigonometry Problems: From the Training of the USA IMO Team Titu Andreescu,Zuming Feng Limited preview - 2004 |
103 Trigonometry Problems: From the Training of the USA IMO Team Andreescu No preview available - 2005 |