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1	Trigonometry: Applications of Laws of Sines and Cosines Su, Yen-hao 02 July 2010 (has links) Chapter 1 presents the definitions and basic properties of trigonometric functions including: Sum Identities, Difference Identities, Product-Sum Identities and Sum-Product Identities. These formulas provide effective tools to solve the problems in trigonometry. Chapter 2 handles the most important two theorems in trigonometry: The laws of sines and cosines and show how they can be applied to derive many well known theorems including: Ptolemy¡¦s theorem, Euler Triangle Formula, Ceva¡¦s theorem, Menelaus¡¦s Theorem, Parallelogram Law, Stewart¡¦s theorem and Brahmagupta¡¦s Formula. Moreover, the formulas of computing a triangle area like Heron¡¦s formula and Pick¡¦s theorem are also discussed. Chapter 3 deals with the method of superposition, inverse trigonometric functions, polar forms and De Moivre¡¦s Theorem. Sum Identities Difference Identities Double-Angle Identities Product-Sum Identities Sum-Product Identities Ceva's Theorem Menelaus's Theorem Ptolemy's Theorem Law of Sines Law of Cosine Euler Triangle Formula Inverse Trigonometric Functions Euler's Formula De Moivre's Theorem Pick's Theorem Weitzenbock's Inequality Heron' Formula Polar Coordinates Angle Bisector Formula Brahmagupta's Formula Median Formula Stewart's Theorem Parallelogram Law