Title page for etd-0702110-111823


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URN etd-0702110-111823
Author Yen-hao Su
Author's Email Address No Public.
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Department Applied Mathematics
Year 2009
Semester 2
Degree Master
Type of Document
Language zh-TW.Big5 Chinese
Title Trigonometry: Applications of Laws of Sines and Cosines
Date of Defense 2010-05-28
Page Count 108
Keyword
  • 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
  • Abstract 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.
    Advisory Committee
  • Mei-Hui Guo - chair
  • Mong-Na Lo Huang - co-chair
  • May-Ru Chen - co-chair
  • Fu-Chuen Chang - advisor
  • Files
  • etd-0702110-111823.pdf
  • indicate not accessible
    Date of Submission 2010-07-02

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