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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Corresponding to the presented project, this thesis is devoted to the systematic explanation of the role of trigonometric functions in elementary mathematics. 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.
Chapter 1 describes the main historical periods of the development of the trigonometric theory. 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.
This chapter ends with a detailed description of trigonometric achievements of Leonhard Euler, who transformed the theory of trigonometric functions to its current version. In Chapter 2 we deal with trigonometric elements based on similar right-angled triangles.
In Chapter 3 we proceed to the trigonometry of general planar triangles. 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. We begin with usual unit-circle definitions to obtain all needed properties including basic useful identities. Proofs of fundamental angle sum formulae are derived from their trigonometric versions discussed earlier.
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.
At the end of Chapters 2, 3 and 4, we present rich collections of nonstandard problems provided with complete solutions.
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.
The concluding Chapter 6 deals with some other applications of trigonometric functions. Firstly, we consider efficient trigonometric substitutions in solving various problems in elementary algebra.
Goniometrická rovnice – Wikipedie
Then, we discuss the computational relevancy of representing complex numbers in their polar form. Finally, we describe the role of trigonometric functions in mathematical cartography. 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 final Bibliography consists of 50 items including Internet resources.
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