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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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.

Thesis defence Date of defence: Thus we deal 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.

In Chapter 2 we deal with trigonometric elements based on similar right-angled triangles. Institution archiving the thesis and making it accessible: Citation record ISO compliant citation record: 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. Your browser does not have JavaScript enabled! We begin with usual unit-circle definitions to obtain all needed properties including basic useful identities.


Goniometrické funkce by Jupíman One on Prezi

Go to top Current date and time: Masaryk University, Faculty of Science. Then, we discuss the computational relevancy of representing complex numbers in their polar form. In Chapter 3 we proceed to the trigonometry of general planar triangles. At the end of Chapters 2, 3 and 4, we present rich collections of nonstandard problems provided with complete solutions.

Corresponding to the presented project, this thesis is devoted to the systematic explanation of the role of trigonometric functions in elementary mathematics.

Theses on a related topic List of theses with an identical keyword. 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.

Geometrie úvodní stránka

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


The File Manager gonuometricke not fully functional without JavaScript enabled. The proofs of all the stated results are worked out in a unified original fashion.

Metody a užití goniometrických funkcí v elementární matematice – Mgr. Radka Smýkalová, Ph.D.

In the remaining parts of Chapter 4 we deal in detail with methods of solving trigonometric equations and their systems, as well as proofs of other numerous identities for trigonometric functions. This chapter ends with a detailed description goniometricje trigonometric achievements of Leonhard Euler, who transformed the theory of trigonometric functions to its current version.

The concluding Chapter 6 deals with some other applications of trigonometric functions. The final Bibliography consists of 50 items including Internet resources. Finally, we describe the role of trigonometric functions in mathematical cartography.

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