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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Go to top Current date and time: Institution archiving the thesis and making it accessible: Citation record ISO compliant citation record: Full text of thesis Contents of on-line thesis archive Published in Theses: Corresponding to the presented project, this thesis is devoted to the systematic explanation of the role of trigonometric functions in elementary mathematics.

We begin goniometridke usual unit-circle definitions to obtain all needed properties including basic useful identities.

Příklady ze cvičení

Chapter 1 describes the main historical periods of the development of the trigonometric vzodce. 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.


This chapter ends with a detailed description of trigonometric achievements of Leonhard Euler, who transformed the theory of trigonometric functions to its current version. Thus we deal subsequently with the results of the ancient astronomer Claudius Ptolemy, medieval mathematicians of India and Arabia and European mathematicians of Renaissance.

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

Then, we discuss the computational relevancy of representing complex numbers in their polar form. The File Manager is not fully functional without JavaScript enabled.

Masaryk University, Faculty of Science. Firstly, we consider efficient trigonometric substitutions in solving various problems in elementary algebra.

Dvojnásobný a polovičný argument – examples of problems with solutions

In Boniometricke 3 we proceed to the trigonometry of general 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.

Thesis defence Date of defence: Theses on a related topic List of theses with an identical keyword. Chapter 4, a pivotal part of the thesis, is devoted to a systematic exposition of the theory goniomehricke trigonometric functions in the domain of all real numbers.

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. Finally, we describe the role of trigonometric functions in mathematical cartography.

The final Bibliography consists of 50 items including Internet resources.

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. 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 proofs of all the stated results are worked out in a unified original fashion.

Your browser does not have JavaScript enabled! At the end of Chapters 2, 3 and 4, we present rich collections of nonstandard problems provided with complete solutions. The concluding Chapter 6 deals with some other applications of trigonometric functions.