Analitičko zasnivanje trigonometrijskih funkcija

master's thesis

• Author: Magdalena Borić
• Mentor: Zvonko Iljazović (mentor)
• Committee member: Zvonko Iljazović (predsjednik povjerenstva)
• Committee member: Maja Starčević (član povjerenstva)
• Committee member: Ozren Perše (član povjerenstva)
• Committee member: Zrinka Franušić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2014-07-14, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu se postepeno, geometrijski i analitički, izgrađuju trigonometrijske funkcije sinus i kosinus. Rad se sastoji od pet poglavlja. U prvom se poglavlju bavimo pojmom konvergencije i omeđenosti nizova te svojstvima nizova. U drugom se poglavlju bavimo pojmom neprekidne funkcije te promatramo dosad uočena svojstva i u metričkom prostoru. U trećem poglavlju proučavamo derivabilne i integrabilne funkcije. U četvrtom poglavlju proučavamo pojam luka, rektifikabilnosti luka, a zatim definiramo duljinu luka. U zadnjem, petom poglavlju, geometrijski izgrađujemo trigonometrijske funkcije preko namatanja pravca na kružnicu, a zatim analitički preko redova potencija.

Abstract (english)

In this theses we gradually built geometrically and analytically trigonometric functions sine and cosine. This thesis is divided into five chapters. In the first chapter we examine notion of convergence and boundedness properties of sequences. In the second chapter we introduce the concept of a continuous function and consider the previously observed properties also in a metric space. In the third chapter we examine derivable and integrable functions. In the fourth chapter, we study the notions of an arc and a rectificable arc and then we define the length of an arc. In the final, fifth chapter, we build geometrically trigonometric functions through the winding of a line around the circle, and then analytically through the series.

• Keywords: trigonometrijske funkcije; sinus; kosinus; geometrijska izgradnja funkcije; analitička izgradnja funkcije
• Keywords (english): trigonometric functions; sine; cosine; geometrical building of functions; analytical building of functions
• Language: croatian
• URN:NBN: urn:nbn:hr:217:593096
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Access restricted to students and staff of home institution
• Created on: 2017-06-07 11:05:30