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The exceptional Chapter 5 is conceived as an encyclopaedia-like survey of numerous identities and inequalities which are provided by triples of angles of all planar triangles. The expository chapters are followed by a short section named Conclusion, in which we try to evaluate our contribution and beneficial aspects of the thesis. In Chapter 3 we proceed to the trigonometry of general planar triangles.
We begin with vxorce unit-circle definitions to obtain all needed properties including basic useful identities.
Corresponding to the presented project, this thesis is devoted to the systematic explanation of the role of trigonometric functions in elementary mathematics. Full text of thesis Contents of on-line thesis archive Published in Theses: The proofs of all the stated results are worked out in a unified original fashion.
In Chapter 2 we deal with trigonometric elements based on similar right-angled triangles. Thus we goniometrocke subsequently with the results of the ancient astronomer Claudius Ptolemy, medieval mathematicians of India and Arabia and European mathematicians of Renaissance. Proofs of fundamental angle sum formulae are derived from their trigonometric versions discussed earlier.
Chapter 1 describes the main historical periods of the development of the trigonometric theory. Chapter 4, a pivotal part of the thesis, is devoted to a systematic exposition of the theory of trigonometric functions in the domain of all real numbers. At the end of Chapters 2, 3 and 4, we present rich collections of nonstandard problems provided with complete solutions.
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