Further Reading 1. Andreescu, T.; Feng, Z., 101 <strong>Problems</strong> in Algebra from the Training of the USA IMO Team, Australian Mathematics Trust, 2001. 2. Andreescu, T.; Feng, Z., 102 Combinatorial <strong>Problems</strong> from the Training of the USA IMO Team, Birkhäuser, 2002. 3. Andreescu, T.; Feng, Z., USA and International Mathematical Olympiads 2003, Mathematical Association of America, 2004. 4. Andreescu, T.; Feng, Z., USA and International Mathematical Olympiads 2002, Mathematical Association of America, 2003. 5. Andreescu, T.; Feng, Z., USA and International Mathematical Olympiads 2001, Mathematical Association of America, 2002. 6. Andreescu, T.; Feng, Z., USA and International Mathematical Olympiads 2000, Mathematical Association of America, 2001. 7. Andreescu, T.; Feng, Z.; Lee, G.; Loh, P., Mathematical Olympiads: <strong>Problems</strong> and Solutions from around the World, 2001–2002, Mathematical Association of America, 2004. 8. Andreescu, T.; Feng, Z.; Lee, G., Mathematical Olympiads: <strong>Problems</strong> and Solutions from around the World, 2000–2001, Mathematical Association of America, 2003.
212 <strong>103</strong> <strong>Trigonometry</strong> <strong>Problems</strong> 9. Andreescu, T.; Feng, Z., Mathematical Olympiads: <strong>Problems</strong> and Solutions from around the World, 1999–2000, Mathematical Association of America, 2002. 10. Andreescu, T.; Feng, Z., Mathematical Olympiads: <strong>Problems</strong> and Solutions from around the World, 1998–1999, Mathematical Association of America, 2000. 11. Andreescu, T.; Kedlaya, K., Mathematical Contests 1997–1998: Olympiad <strong>Problems</strong> from around theWorld, with Solutions,American Mathematics Competitions, 1999. 12. Andreescu, T.; Kedlaya, K., Mathematical Contests 1996–1997: Olympiad <strong>Problems</strong> from around theWorld, with Solutions,American Mathematics Competitions, 1998. 13. Andreescu, T.; Kedlaya, K.; Zeitz, P., Mathematical Contests 1995–1996: Olympiad <strong>Problems</strong> from around the World, with Solutions, American Mathematics Competitions, 1997. 14. Andreescu, T.; Enescu, B., Mathematical Olympiad Treasures, Birkhäuser, 2003. 15. Andreescu, T.; Gelca, R., Mathematical Olympiad Challenges, Birkhäuser, 2000. 16. Andreescu, T.; Andrica, D., 360 <strong>Problems</strong> for Mathematical Contests, GIL Publishing House, 2003. 17. Andreescu, T.; Andrica, D., Complex Numbers from A to Z, Birkhäuser, 2004. 18. Beckenbach, E. F.; Bellman, R., An Introduction to Inequalities, New Mathematical Library, Vol. 3, Mathematical Association of America, 1961. 19. Coxeter, H. S. M.; Greitzer, S. L., Geometry Revisited, New Mathematical Library, Vol. 19, Mathematical Association of America, 1967. 20. Coxeter, H. S. M., Non-Euclidean Geometry, The Mathematical Association of America, 1998. 21. Doob, M., The Canadian Mathematical Olympiad 1969–1993, University of Toronto Press, 1993. 22. Engel,A., Problem-Solving Strategies, Problem Books in Mathematics, Springer, 1998.
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About the Authors Titu Andreescu re
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Titu Andreescu University of Wiscon
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vi Contents Vectors 41 The Dot Prod
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viii Preface Throughout MOSP, full
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Abbreviations and Notation Abbrevia
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103 Trigonometry Problems
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2 103 Trigonometry Problems First w
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4 103 Trigonometry Problems triangl
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6 103 Trigonometry Problems By sett
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8 103 Trigonometry Problems Q A B P
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10 103 Trigonometry Problems for co
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14 103 Trigonometry Problems (b) By
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20 103 Trigonometry Problems A A B
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30 103 Trigonometry Problems A F P
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36 103 Trigonometry Problems A B D
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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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52 103 Trigonometry Problems z x F
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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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5 Solutions to Advanced Problems 1.
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