URN 
etd0702110111823 
Author 
Yenhao Su 
Author's Email Address 
No Public. 
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Department 
Applied Mathematics 
Year 
2009 
Semester 
2 
Degree 
Master 
Type of Document 

Language 
zhTW.Big5 Chinese 
Title 
Trigonometry: Applications of Laws of Sines and Cosines 
Date of Defense 
20100528 
Page Count 
108 
Keyword 
Sum Identities
Difference Identities
DoubleAngle Identities
ProductSum Identities
SumProduct 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

Abstract 
Chapter 1 presents the definitions and basic properties of trigonometric functions including: Sum Identities, Difference Identities, ProductSum Identities and SumProduct 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. 
Advisory Committee 
MeiHui Guo  chair
MongNa Lo Huang  cochair
MayRu Chen  cochair
FuChuen Chang  advisor

Files 
indicate not accessible 
Date of Submission 
20100702 