103 Trigonometry Problems: From the Training of the USA IMO Team

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Springer Science & Business Media, Dec 15, 2004 - Mathematics - 214 pages

103 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
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