GONIOMETRICKE VZORCE PDF

In the remaining parts of Chapter 4 we deal in detail with methods of solving trigonometric equations and their systems, as well goniomehricke proofs of other numerous identities for trigonometric functions. Masaryk University, Faculty of Science. Proofs of fundamental angle sum formulae are derived from their trigonometric versions discussed earlier. Your browser goniomehricke not have JavaScript enabled! Thesis defence Date of defence: The proofs of all the stated results are worked out in a unified original fashion. Then, we discuss the computational relevancy of representing complex numbers in their polar form.

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Goltimuro This chapter ends with a detailed description of trigonometric achievements of Leonhard Euler, who transformed the theory of trigonometric functions to its current version. The File Manager is not fully functional without JavaScript enabled. Go to top Current date and time: Thesis defence Date of defence: The concluding Chapter 6 deals with some other applications of trigonometric functions. Masaryk University, Faculty of Science.

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.

Based on the study of vzotce textbooks and other literature, our explication is done in a compact and connected original form of six expository chapters. Your browser does not have JavaScript enabled! Firstly, we consider efficient trigonometric substitutions in solving various problems in elementary algebra. Citation record ISO compliant citation record: Finally, we describe the role of trigonometric functions in mathematical cartography.

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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