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An Engineers Quick Trigonometry Laws and Identities Reference. Tato stránka navrhuje vyučovat všechny poznatky z algebry, geometrie a trigonometrie za prvních 12 let a sledovat předmětu z několika zemí;. Součtové vzorce pro goniometrické funkce a jejich aplikace. Titile (in english). Sum Formulas for Trigonometric Functions and Their Applications. Type.

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We begin with usual unit-circle definitions to obtain all needed properties including basic useful identities. Go to top Current date and time: Then, we discuss the computational relevancy of representing complex numbers in their polar form. Your browser does not have JavaScript enabled!

Proofs of fundamental angle sum formulae are derived from their trigonometric versions discussed earlier.

Příklady ze cvičení

Theses on a vzoece topic List of theses with an identical gonoimetricke. Corresponding to the presented project, this thesis is devoted to the systematic explanation of the role of trigonometric functions in elementary mathematics. Institution archiving the thesis and making it accessible: Based on the study of various textbooks and other literature, our explication is done in a compact and connected original form of six expository chapters.


Firstly, we consider efficient trigonometric substitutions in solving various problems in elementary algebra. 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.

Thus we deal subsequently with the results of the ancient astronomer Claudius Ptolemy, medieval mathematicians of India and Arabia and European mathematicians of Renaissance. At the end of Czorce 2, 3 and 4, we present rich collections of nonstandard problems provided with complete solutions.

Dvojnásobný a polovičný argument – examples of problems with solutions

The final Bibliography consists of 50 items including Internet resources. Citation record ISO compliant citation record: Finally, we describe the role of trigonometric functions in mathematical cartography. This chapter ends with a detailed description of trigonometric achievements of Leonhard Euler, who transformed gonkometricke theory of trigonometric functions to its current version.

The File Manager is not fully functional without JavaScript enabled. Thesis defence Date of defence: Chapter 1 describes the main historical periods of the development of the trigonometric theory. The proofs of all the stated results are worked out in a unified original fashion. The concluding Chapter 6 deals with some other applications of trigonometric functions. 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.


In the remaining parts of Chapter 4 we deal in detail with methods of solving trigonometric equations and vzorde systems, as well as proofs of other numerous identities for trigonometric functions. Masaryk University, Faculty of Goniometrcike.

Full text of thesis Vzorxe of on-line thesis archive Published in Theses: 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.

In Chapter 2 we deal with trigonometric elements based on similar right-angled triangles.