Relevant bibliographies by topics / Trigonometry functions

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Trigonometry functions'

Author: Grafiati
Published: 4 June 2021
Last updated: 17 February 2022

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Journal articles on the topic "Trigonometry functions"

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Deddiliawan Ismail, Agung, and Rizal Dian Azmi. "PEMANFAATAN GEOMETER’S SKETCHPAD DALAM MELUKIS FUNGSI TRIGONOMETRI." JINoP (Jurnal Inovasi Pembelajaran) 3, no. 2 (November 28, 2017): 560. http://dx.doi.org/10.22219/jinop.v3i2.4690.

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ABSTRAK Trigonometri merupakan salah satu cabang ilmu Matematika yang banyak digunakan di berbagai bidang. Materi trigonometri kadang menyulitkan bagi para pendidik saat mengajarkan kepada mahasiswa. Ini dikarenakan materi – materi dalam trigonometri memerlukan suatu gambaran simulasi untuk mengajarkan konsep trigonometri kepada peserta didik. Untuk menggambarkan simulasi dari fungsi trigonometri tersebut diperlukan suatu media sebagai tuntunan mahasiswa, dimana media yang tepat untuk itu adalah Geometer’s Sketchpad. Berdasarkan hasil penelitian yang telah dilakukan maka dapat disimpulkan bahwa pembelajaran dengan memanfaatkan Geometer’s Sketchpad dapat membantu mahasiswa dalam melukis fungsi Trigonometri. Terlihat dari nilai probabilitas 0,000 < 0,05 yang menyatakan bahwa adanya peningkatan keterampilan mahasiswa dalam melukis grafik fungsi Trigonometri. Kata kunci: Trigonometri, Geometer’s Sketchpad. ABSTRACTTrigonometry is a part of the Mathematics which is used in various science area. Trigonometry material is sometimes difficult for teachers to teach students. This is due to the materials in trigonometry requires an illustration of the simulation to teach the basic concepts of trigonometry to students. To illustrate the simulation of the trigonometric functions need a media as the guidance of students, where appropriate media for that is Geometer's Sketchpad. Based on the research that has been done, it can be concluded that learning by utilizing Geometer's Sketchpad can assist students in painting Trig functions. Seen from a probability value 0.000 <0.05, which states that an increase in students' skills in drawing graphs of functions Trig.Keywords: Trigonometry, Geometer’s Sketchpad.
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Boyes, G. R. "Trigonometry for Non-Trigonometry Students." Mathematics Teacher 87, no. 5 (May 1994): 372–75. http://dx.doi.org/10.5951/mt.87.5.0372.

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This team-oriented student activity is designed to study selected trigonometric functions by constructing tables of values. These tables are then put to practical use. Familiarity with trigonometry is not needed, since all pertinent information is included. The activities, which could take up to three days, are aimed at ordinary middle school students or any students desiring an introduction to trigonometry.
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Weber, Keith. "Connecting Research to Teaching: Teaching Trigonometric Functions: Lessons Learned from Research." Mathematics Teacher 102, no. 2 (September 2008): 144–50. http://dx.doi.org/10.5951/mt.102.2.0144.

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Trigonometry is an important subject in the high school mathematics curriculum. As one of the secondary mathematics topics that are taught early and that link algebraic, geometric, and graphical reasoning, trigonometry can serve as an important precursor to calculus as well as collegelevel courses relating to Newtonian physics, architecture, surveying, and engineering. Unfortunately, many high school students are not accustomed to these types of reasoning (Blackett and Tall 1991), and learning about trigonometric functions is initially fraught with difficulty. Trigonometry presents many first-time challenges for students: It requires students to relate diagrams of triangles to numerical relationships and manipulate the symbols involved in such relationships. Further, trigonometric functions are typically among the first functions that students cannot evaluate directly by performing arithmetic operations.
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Weber, Keith. "Connecting Research to Teaching: Teaching Trigonometric Functions: Lessons Learned from Research." Mathematics Teacher 102, no. 2 (September 2008): 144–50. http://dx.doi.org/10.5951/mt.102.2.0144.

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Trigonometry is an important subject in the high school mathematics curriculum. As one of the secondary mathematics topics that are taught early and that link algebraic, geometric, and graphical reasoning, trigonometry can serve as an important precursor to calculus as well as collegelevel courses relating to Newtonian physics, architecture, surveying, and engineering. Unfortunately, many high school students are not accustomed to these types of reasoning (Blackett and Tall 1991), and learning about trigonometric functions is initially fraught with difficulty. Trigonometry presents many first-time challenges for students: It requires students to relate diagrams of triangles to numerical relationships and manipulate the symbols involved in such relationships. Further, trigonometric functions are typically among the first functions that students cannot evaluate directly by performing arithmetic operations.
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Antippa, Adel F. "The combinatorial structure of trigonometry." International Journal of Mathematics and Mathematical Sciences 2003, no. 8 (2003): 475–500. http://dx.doi.org/10.1155/s0161171203106230.

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The native mathematical language of trigonometry is combinatorial. Two interrelated combinatorial symmetric functions underlie trigonometry. We use their characteristics to derive identities for the trigonometric functions of multiple distinct angles. When applied to the sum of an infinite number of infinitesimal angles, these identities lead to the power series expansions of the trigonometric functions. When applied to the interior angles of a polygon, they lead to two general constraints satisfied by the corresponding tangents. In the case of multiple equal angles, they reduce to the Bernoulli identities. For the case of two distinct angles, they reduce to the Ptolemy identity. They can also be used to derive the De Moivre-Cotes identity. The above results combined provide an appropriate mathematical combinatorial language and formalism for trigonometry and more generally polygonometry. This latter is the structural language of molecular organization, and is omnipresent in the natural phenomena of molecular physics, chemistry, and biology. Polygonometry is as important in the study of moderately complex structures, as trigonometry has historically been in the study of simple structures.
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John Hornsby, E. "A Method of Graphing f(x) = A sin (Bx + C) + D." Mathematics Teacher 83, no. 1 (January 1990): 51–53. http://dx.doi.org/10.5951/mt.83.1.0051.

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Baric, Mate, David Brčić, Mate Kosor, and Roko Jelic. "An Axiom of True Courses Calculation in Great Circle Navigation." Journal of Marine Science and Engineering 9, no. 6 (May 31, 2021): 603. http://dx.doi.org/10.3390/jmse9060603.

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Based on traditional expressions and spherical trigonometry, at present, great circle navigation is undertaken using various navigational software packages. Recent research has mainly focused on vector algebra. These problems are calculated numerically and are thus suited to computer-aided great circle navigation. However, essential knowledge requires the navigator to be able to calculate navigation parameters without the use of aids. This requirement is met using spherical trigonometry functions and the Napier wheel. In addition, to facilitate calculation, certain axioms have been developed to determine a vessel’s true course. These axioms can lead to misleading results due to the limitations of the trigonometric functions, mathematical errors, and the type of great circle navigation. The aim of this paper is to determine a reliable trigonometric function for calculating a vessel’s course in regular and composite great circle navigation, which can be used with the proposed axioms. This was achieved using analysis of the trigonometric functions, and assessment of their impact on the vessel’s calculated course and established axioms.
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Anand, M. Clement Joe, and Janani Bharatraj. "Gaussian Qualitative Trigonometric Functions in a Fuzzy Circle." Advances in Fuzzy Systems 2018 (June 3, 2018): 1–9. http://dx.doi.org/10.1155/2018/8623465.

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We build a bridge between qualitative representation and quantitative representation using fuzzy qualitative trigonometry. A unit circle obtained from fuzzy qualitative representation replaces the quantitative unit circle. Namely, we have developed the concept of a qualitative unit circle from the view of fuzzy theory using Gaussian membership functions, which play a key role in shaping the fuzzy circle and help in obtaining sharper boundaries. We have also developed the trigonometric identities based on qualitative representation by defining trigonometric functions qualitatively and applied the concept to fuzzy particle swarm optimization using α-cuts.
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Kaplan, Gail. "Activities for Students: Trigonometry through a Ferris Wheel." Mathematics Teacher 102, no. 2 (September 2008): 138–43. http://dx.doi.org/10.5951/mt.102.2.0138.

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In the traditional study of trigonometry, students graph the basic trigonometric functions. They study phase shifts, horizontal and vertical translations, and changes in period so that they can sketch the graph of generalized functions such as f(x) = acosb(x − c) + d by recognizing the information provided by the constants a, b, c, and d. Far too often, students master this material by memorizing it and thus have little comprehension of why and how each value in an equation affects the graph.
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Kaplan, Gail. "Activities for Students: Trigonometry through a Ferris Wheel." Mathematics Teacher 102, no. 2 (September 2008): 138–43. http://dx.doi.org/10.5951/mt.102.2.0138.

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In the traditional study of trigonometry, students graph the basic trigonometric functions. They study phase shifts, horizontal and vertical translations, and changes in period so that they can sketch the graph of generalized functions such as f(x) = acosb(x − c) + d by recognizing the information provided by the constants a, b, c, and d. Far too often, students master this material by memorizing it and thus have little comprehension of why and how each value in an equation affects the graph.
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Dissertations / Theses on the topic "Trigonometry functions"

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Jennings, Paul Richard. "Hyperspherical trigonometry, related elliptic functions and integrable systems." Thesis, University of Leeds, 2013. http://etheses.whiterose.ac.uk/6892/.

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The basic formulae of hyperspherical trigonometry in multi-dimensional Euclidean space are developed using multi-dimensional vector products, and their conversion to identities for elliptic functions is shown. The basic addition formulae for functions on the 3-sphere embedded in four-dimensional space are shown to lead to addition formulae for elliptic functions, associated with algebraic curves, which have two distinct moduli. Application of these formulae to the cases of a multi-dimensional Euler top and Double Elliptic Systems are given, providing a connection between the two. A generalisation of the Lattice Potential Kadomtsev-Petviashvili (LPKP) equation is presented, using the method of Direct Linearisation based on an elliptic Cauchy kernel. This yields a (3 + 1)-dimensional lattice system with one of the lattice shifts singled out. The integrability of the lattice system is considered, presenting a Lax representation and soliton solutions. An associated continuous system is also derived, yielding a (3 + 1)- dimensional generalisation of the potential KP equation associated with an elliptic curve.
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Silva, Jander Carlos Silva e. "As novas tecnologias no contexto escolar: uma abordagem sobre aplicações do GeoGebra em trigonometria." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/55/55136/tde-17122015-104430/.

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Este trabalho apresenta uma abordagem sobre as novas tecnologias no contexto escolar, com vistas para aplicação do GeoGebra em trigonometria. O objetivo é nortear professores da educação básica na preparação de aulas usando o GeoGebra, visando ao enriquecimento do tema trigonometria em sala de aula. As atividades propostas estão divididas em três grupos: trigonometria básica, funções trigonométricas e equações trigonométricas. Cada uma possui um alto nível de detalhamento, com o objetivo de incentivar o uso por professores com pouco ou nenhum conhecimento do software, bem como incentivar atividades que promovam a criação por parte dos alunos. A ideia é que os alunos construam as atividades, aprendendo a utilizar o software, interagindo por meio da movimentação dos objetos, e tirando suas conclusões pertinentes às atividades. De maneira geral, pretende-se contribuir para o desenvolvimento do raciocínio lógico do aluno por meio do ensino de Matemática agregando a utilização de tecnologia, de forma que o aluno não seja somente um expectador, mas sim, participante da construção da própria atividade.
This work presents na approach to new Technologies in the educational context, with a view to applications of the GeoGebra in trigonometry. The goal is to guide teachers of the basic education in preparing lessons using GeoGebra, aiming to enrich trigonometry the in the classroom. The proposed activities are divided into three groups : basic trigonometry, trigonometry functions and trigonometry equations. Each one has a high level of details, in order to encourage the use by teachers with little or no knowledge of the software, and also encourage activities that promote the creation by the students. The idea is that students build the activities, learning how to use the software, interacting by moving objects, and taking their conclusions about the activities. In general, one intends to contribute to the development of logical thinking of students through the teaching of Mathematics adding the use of technology, so that the student is not only a spectator, but, participant of the construction of their own activity.
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Baines, Clare Elizabeth. "Topics in functions with symmetry." Thesis, University of Liverpool, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.343778.

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Malambo, Priestly. "Exploring Zambian Mathematics student teachers' content knowledge of functions and trigonometry for secondary schools." Thesis, University of Pretoria, 2015. http://hdl.handle.net/2263/52943.

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This was a qualitative case study that explored Zambian mathematics student teachers? content knowledge of functions and trigonometry in secondary schools. The students were in their final year of study and had studied advanced university mathematics and had completed Mathematics Education courses. Content knowledge was investigated as Common Content Knowledge (CCK) and Specialised Content Knowledge (SCK). Data was collected in two phases: Phase 1 utilised a mathematics test to gather CCK and SCK data from 22 conveniently chosen University of Zambia student teachers majoring in mathematics. Phase 2 used semi-structured interviews to collect SCK data from a sub-sample of six purposefully selected students. Descriptive statistics and qualitative techniques were used to analyse the test data and content analysis to analyse the interviews. Although the students achieved a mean score of about 52% in the CCK of functions, an item by item analysis suggested that they were not proficient therein. They had a shallow understanding of composite functions, domains and ranges, extreme values, and turning points. They also had a superficial understanding of the definitions of concepts. While the students managed to identify functions, the majority could not coherently explain concepts and justify their reasoning. The students showed a limited understanding of the Cartesian plane representations of functions and the algebraic representation of quadratic functions. The students achieved a mean score of approximately 53% in the CCK of trigonometry, and 68% of the sample achieved scores above 50%. An item by item analysis suggests that most of the students were proficient in CCK. However, the students could not comprehensively explain concepts and justify their reasoning. While most of the students could apply rules and formulas, they could not coherently explain and prove these. Similarly, they could not translate algebraic trigonometric functions to the Cartesian plane. Generally, there seemed to be a disconnection between the students? CCK and SCK of trigonometry. These findings suggested that the study of advanced mathematics does not automatically result in students? comprehensive understanding of school mathematics. While the students had studied advanced UNZA mathematics, it was found out that they had not acquired an in-depth understanding of the functions and trigonometry required at secondary school level.
Thesis (PhD)--University of Pretoria, 2015.
Science, Mathematics and Technology Education
PhD
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Yadollahi, Farsani Leila. "Topics in the calculus of variations : quasiconvexification of distance functions and geometry in the space of matrices." Thesis, University of Sussex, 2017. http://sro.sussex.ac.uk/id/eprint/68825/.

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OLIVEIRA, Carlos André Carneiro de. "Trigonometria: o radiano e as funções seno, cosseno e tangente." Universidade Federal de Campina Grande, 2014. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/2169.

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Este trabalho apresenta um estudo sobre o ensino da trigonometria no ensino médio, contemplando as recomendações sobre esse conteúdo encontradas nos Parâmetros Curriculares Nacionais e uma breve análise desses conteúdos em alguns dos livros recomendados pelo Guia de Livros Didáticos de Matemática - PNLP 2012. Destacando a formação do conceito de radiano; a extensão das razões trigonométricas seno, cosseno e tangente definidas no triângulo retângulo para as funções Trigonométricas de domínio real, além das demonstrações geométricas das fórmulas da adição e da subtração de arcos das funções seno, cosseno e tangente. Apresenta, também, uma sequência didática, com atividades contemplando os conteúdos destacados acima. As atividades foram elaboradas tendo como referência a teoria da aprendizagem significativa e adaptadas ao uso do software GeoGebra.
This work presents a study on the teaching of trigonometry in high school, in accordance with the recommendations about this subject found in National Curriculum Guidelines (Parâmetros Curriculares Nacionais) and a analysis of the content of some of the books recommended by the Mathematics Textbook Guide - PNLP 2012. It highlight the formation of the concept of radian; the extension of trigonometric ratios sine, cosine and tangent defined in the triangle for Trigonometric functions of real field, in addition to the geometrical proofs of the formula of addition and subtraction arches functions sine, cosine and tangent. It also presents a didactic sequence, with activities covering the highlighted contents above. The activities were developed with reference to the meaningful learning theory and adapted to the use of GeoGebra software.
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Calderaro, André Bispo. "Análise da possibilidade de inclusão de abordagens alternativas para a função cosseno no ensino médio." Mestrado Profissional em Matemática, 2013. https://ri.ufs.br/handle/riufs/6504.

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This work establishes itself as objective analysis of the process of elaboration of the definitions of the trigonometric functions, particularly the definition of the cosine function. Thus, it is given a guideline regarding the development of a curriculum in which students are not sparked off the concept of trigonometric function based only on the triangle and trigonometric cycle. Therefore, the biggest challenge is to develop arguments for teaching about and investigate further the concepts of trigonometry. Thus, although we like the first chapter a brief explanation about the history of trigonometry, the work focuses on the development of the definition cosine of some forms, namely: the one presented in textbooks as it observes that it is made with support Euler function, setting via power series, the setting based on the exponential function domain in complex and, finally, setting as a solution of an initial value problem, that is, a differential equation that satisfies a given initial condition. From there will be an analysis of these definitions by observing the viability of each to be presented to high school students.
Neste trabalho, se estabelece como objetivo a análise do processo de elaboração das definiçõoes das funçõoes trigonométricas, particularmente, a definição da funçãao cosseno. Desse modo, é dada uma diretriz no que toca a elaboração de um currículo em que os alunos não fiquem ateados ao conceito de função trigonométrica apenas com base no triângulo retângulo e no ciclo trigonométrico. Portanto, o maior desafio é desenvolver argumentos didáticos para tal, bem como investigar mais detalhadamente as concepções da trigonometria. Com isso, apesar de termos como primeiro capítulo uma breve explanação sobre a história da trigonometria, o trabalho tem como foco o desenvolvimento da definição cosseno de algumas formas, sendo elas: a apresentada nos livros didáticos em que se observa que a mesma é feita com suporte da função de Euler, a definição através de séries de potências, a definição com base na função exponencial com domínio nos complexos e, por fim, a definição como solução de um problema de valor inicial, isto é, uma equação diferencial que satisfaz uma determinada condição inicial. A partir daí será feita uma análise dessas definições observando-se a viabilidade de cada uma delas ser apresentada para os alunos do Ensino Médio.
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Souza, Francine Dalavale Tozatto. "Trigonometria no ensino médio e suas aplicações." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/55/55136/tde-26102018-170937/.

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Neste trabalho fazemos um estudo detalhado sobre o tema Trigonometria. A trigonometria é um tema bastante discutido em sala de aula durante o ensino médio. Não apenas apresentamos resultados sobre o tema mas também suas provas e justificativas, assim como exemplos e exercícios com o objetivo de ter um material completo para professores do ensino médio que desejem estudar tais tópicos. Em seguida apresentamos algumas aplicações da Trigonometria que podemos encontrar em nosso dia-a-dia, também aqui o objetivo é apresentar motivação para o estudo deste importante assunto e tão frequente nos vestibulares atualmente. Finalmente, apresentamos uma atividade realizada com meus alunos em sala de aula. Esta dissertação foi desenvolvida como parte dos requisitos necessários para a obtenção do título de mestrado acadêmico junto ao Instituto de Ciências Matemáticas e de Computação (ICMC), da Universidade de São Paulo (USP).
In this dissertation we present a detailed study about Trigonometry. This subject is frequently discussed em classes during High school courses. We do not only present the main results about Trigonometry but also their proofs, as well examples and exercises. Our main objective here is obtain a complete text for high school teachers. We also present some applications of Trigonometry that can be easily find in our life. Here our main objective is to motivate the study of this important subject that appears so frequently in the exams for universities entrance. To conclude, we present an activity realized with high school students. This dissertation was developed as part of the requirements necessary for the obtension of the degree of Mathematics Professional Master at Instituto de Ciências Matemáticas e de Computação da Universidade de São Paulo (ICMC-USP).
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Bruginski, Willian José. "Desenvolvimento de planilhas dinâmicas utilizando o software Geogebra para o estudo de funções trigonométricas." Universidade Tecnológica Federal do Paraná, 2014. http://repositorio.utfpr.edu.br/jspui/handle/1/802.

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Esta dissertação foi desenvolvida com o intuito de criar uma ferramenta para auxiliar no ensino da trigonometria. A ferramenta foi criada com o apoio de recursos tecnológicos e o Geogebra foi o software escolhido para a elaboração deste projeto. Devido a quantidade de recursos que o software dispõe principalmente a possibilidade de trabalhar de forma integrada a geometria com a álgebra, este foi um grande aliado na criação das planilhas dinâmicas. Na sequencia foi desenvolvida a parte teórica das funções trigonométricas com as suas definições, as características, construções dos gráficos e foram apresentadas as contribuições que as planilhas dinâmicas proporcionam neste estudo.
This work was developed with the intention of creating a new tool to assist in teaching trigonometry. The tool has been created with the support of technological resources and Geogebra software has been chosen for the development of this project. Because the amount of resources that the software provides, especially the ability to work seamlessly geometry and algebra, this was a great ally in the creation of dynamic spreadsheets. Following was developed theoretical part of trigonometric functions with their definitions, characteristics, construction of graphs and contributions that dynamic spreadsheets provide this study were presented.
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Dionizio, Fátima Aparecida Queiroz. "CONHECIMENTOS DOCENTES: UMA ANÁLISE DOS DISCURSOS DE PROFESSORES QUE ENSINAM MATEMÁTICA." UNIVERSIDADE ESTADUAL DE PONTA GROSSA, 2013. http://tede2.uepg.br/jspui/handle/prefix/1349.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
This study presents an analysis of pedagogical, curricular and content knowledge that teachers of mathematics in basic education, in Ponta Grossa/PR have on Trigonometry. Empirical data was obtained with the use of a tool containing different kinds of errors made by students in Trigonometry exercises to be analyzed and point out possible intervention by the teachers as well as to present responses to Trigonometry concepts. This data was analyzed based on Shulman’s (1986,2001) theoretical contributions and on the functions and discursive operations according to the Register of Semiotic Representation theory by Raymond Duval (2004, 2009, 2011). The research question was: How is knowledge about Trigonometry characterized and what is the nature of the knowledge related to learning issues and Trigonometry teaching presented by mathematics teachers who work in basic education? And the objectives of the study were: to characterize the knowledge of Trigonometry of mathematics teachers working in basic education and; to reveal the nature of mathematics teachers’ knowledge in relation to Trigonometry learning and teaching issues.The research had a qualitative approach, with descriptive and elucidative characteristics, and the analysis methodological procedures were assisted by Bardin’s (2009) content analysis. The organization of data was carried out with the aid of the software Atlas.ti, through which the subject content knowledge, the pedagogical knowledge of content, and the curricular knowledge were gathered within the discourse expansion function proposed by Duval (2004) for later analysis. The results of this study indicate that teachers’ knowledge that was more evident was the knowledge of the subject content. These results point to the need for teachers to be more attentive to other aspects of knowledge also necessary to their education practice and which seem to have been disregarded.
Este trabalho apresenta uma análise dos conhecimentos pedagógicos, curricular e de conteúdo de professores de matemática da Educação Básica, do município de Ponta Grossa/PR, sobre Trigonometria. Os dados empíricos foram obtidos por meio da aplicação de um instrumento contendo diferentes tipos de erros cometidos pelos alunos em atividades de Trigonometria, para a análise e apontamento de possíveis intervenções pedagógicas pelos professores e também respostas a conceitos de Trigonometria. Esses dados foram analisados tendo por subsídios teóricos as contribuições de Shulman (1986, 2001) e as funções e operações discursivas apresentadas na teoria dos Registros de Representação Semiótica segundo Raymond Duval (2004, 2009, 2011). O problema de pesquisa que se buscou responder foi: Como se caracterizam os conhecimentos sobre Trigonometria e qual a natureza dos conhecimentos relativos a questões sobre a aprendizagem e o ensino de Trigonometria apresentados por professores de matemática que atuam na Educação Básica? A partir disso os objetivos da pesquisa foram: caracterizar os conhecimentos sobre Trigonometria apresentados por professores de matemática que atuam na Educação Básica e; desvelar a natureza desses conhecimentos dos professores de matemática em relação a questões sobre o ensino e a aprendizagem da Trigonometria. Para a realização da pesquisa foi adotada a abordagem qualitativa, de cunho descritivo e explicativo, com os procedimentos metodológicos de análise sustentados pela análise de conteúdo de Bardin (2009). A organização dos dados contou com o auxílio do software Atlas.ti por meio do qual foram elencados o conhecimento de conteúdo da matéria, o conhecimento pedagógico de conteúdo e o conhecimento curricular e as funções de expansão dos discursos propostas por Duval (2004), para posterior análise. Os resultados dessa pesquisa indicam que os conhecimentos docentes que se sobressaíram foram os conhecimentos de conteúdo da matéria a ser ensinada. Esses resultados apontam para a necessidade de um olhar mais atento pelos professores sobre os demais saberes necessários à prática educativa e que parecem não estarem sendo postos em prática.
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Books on the topic "Trigonometry functions"

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Keedy, Mervin Laverne. Trigonometry: Triangles and functions. 4th ed. Reading, Mass: Addison-Wesley Pub. Co., 1986.

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Keedy, Mervin Laverne. Algebra & trigonometry: A functions approach. 4th ed. Reading, Mass: Addison-Wesley, 1986.

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Blitzer, Robert. Algebra & trigonometry. 3rd ed. Upper Saddle River, NJ: Pearson Education, 2007.

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Blitzer, Robert. Algebra & trigonometry. 2nd ed. Upper Saddle River, NJ: Prentice Hall, 2004.

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Blitzer, Robert. Algebra & trigonometry. Upper Saddle River, NJ: Prentice Hall, 2001.

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1943-, Miller Robert, ed. Precalc with trigonometry. 2nd ed. New York: McGraw-Hill, 1998.

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Precalc with trigonometry. 3rd ed. New York: McGraw-Hill, 2005.

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Demana, Franklin D. Precalculus: Functions and graphs. 3rd ed. Reading, Mass: Addison-Wesley Pub. Co., 1997.

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Demana, Franklin D. Precalculus: Functions and graphs. 2nd ed. Reading, Mass: Addison-Wesley, 1993.

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Waldner, Bruce. Algebra 2/trigonometry. Hauppauge, N.Y: Barron's Educational Series, 2009.

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Book chapters on the topic "Trigonometry functions"

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Gelfand, I. M., and Mark Saul. "Graphs of Trigonometric Functions." In Trigonometry, 173–206. Boston, MA: Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0149-6_9.

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Gelfand, I. M., and Mark Saul. "Inverse Functions and Trigonometric Equations." In Trigonometry, 207–29. Boston, MA: Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0149-6_10.

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Berry, John, and Patrick Wainwright. "Trigonometric Functions." In Foundation Mathematics for Engineers, 107–40. London: Macmillan Education UK, 1991. http://dx.doi.org/10.1007/978-1-349-11717-8_4.

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Grozin, Andrey. "Trigonometric Functions." In Introduction to Mathematica® for Physicists, 125–26. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00894-3_15.

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Morais, João Pedro, Svetlin Georgiev, and Wolfgang Sprößig. "Trigonometric Functions." In Real Quaternionic Calculus Handbook, 107–16. Basel: Springer Basel, 2013. http://dx.doi.org/10.1007/978-3-0348-0622-0_6.

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Beebe, Nelson H. F. "Trigonometric functions." In The Mathematical-Function Computation Handbook, 299–340. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-64110-2_11.

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Moll, Victor. "Trigonometric functions." In The Student Mathematical Library, 309–54. Providence, Rhode Island: American Mathematical Society, 2012. http://dx.doi.org/10.1090/stml/065/12.

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Marsden, Jerrold, and Alan Weinstein. "Trigonometric Functions." In Calculus I, 251–306. New York, NY: Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4612-5024-1_8.

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Soon, Frederick H. "Trigonometric Functions." In Student’s Guide to Calculus by J. Marsden and A. Weinstein, 221–71. New York, NY: Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4612-5146-0_7.

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Eriksson, Kenneth, Donald Estep, and Claes Johnson. "Trigonometric Functions." In Applied Mathematics: Body and Soul, 505–16. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-05798-8_6.

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Conference papers on the topic "Trigonometry functions"

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Lorenzo, Carl F. "The Fractional Meta-Trigonometry Based on the R-Function: Part I—Background, Definitions, and Complexity Function Graphics." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86731.

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The current fractional trigonometries and hyperboletry are based on three forms of the fractional exponential R-function, Rq,v(a,t), Rq,v(ai,t), and Rq,v(a,it). The fractional meta-trigonometry extends this to an infinite number of bases using the form Rq,v(aiα,iβt). Meta-definitions, meta-Laplace transforms, and meta-identities are developed for these generalized fractional trigonometric functions. Graphic results are presented. Extensions of the fractional trigonometries to the negative time domain and complementary fractional trigonometries are considered. Part I provides; background on the ongoing development of the fractional trigonometries, the definitions of the meta-trigonometry and its motivation, and a limited set of graphic results for the complexity based fractional trigonometric functions.
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Lorenzo, Carl F. "The Fractional Morphology and Growth Rate of the Nautilus Pompilius: Preliminary Results Based on the R1-Fractional Trigonometry." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87393.

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This paper studies the morphology and evolutionary growth of the Nautilus pompilius based on the fractional R1-trigonometry. Morphological models based on the fractional trigonometry are shown to be superior to those of the commonly assumed logarithmic spiral. The R1-trigonometric functions further infer fractional differential equations which, based on power law parametric functions, are used to develop a fractional growth equation modeling evolution from conception to maturity.
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Lorenzo, Carl F. "The Fractional Meta-Trigonometry Based on the R-Function: Part II—Parity Function Graphics, Laplace Transforms, Fractional Derivatives, Meta-Properties." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86733.

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The current fractional trigonometries and hyperboletry are based on three forms of the fractional exponential R-function, Rq,v(a,t), Rq,v(ai,t), and Rq,v(a,it). The fractional meta-trigonometry extends this to an infinite number of bases using the form Rq,v(aiα,iβt). Meta-definitions, meta-Laplace transforms, and meta-identities are developed for these generalized fractional trigonometric functions. Graphic results are presented. Extensions of the fractional trigonometries to the negative time domain and complementary fractional trigonometries are considered. Part II continues from the definition set and graphics given in Part I. It provides a minimal set of graphic results for the parity meta-fractional trigonometry and develops the meta-properties described above.
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Woolley, Ronald Lee. "Transitional Trigonometric Functions." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-66426.

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Crash pulses in automotive collisions often exhibit acceleration shapes somewhere between a sine and a step function and velocity shapes somewhere between a cosine and a linear decay. This is an example of real world behavior that is only somewhat like the familiar sine, cosine, or tangent shapes so commonly used in physical modeling. To adjust the mathematics to the problem, two familiar ordinary differential equations are merged to create a mathematical transition between trigonometric functions and polynomials by introducing one new parameter. The merged ODE produces a new set of “transitional trigonometry” functions that include both sets of familiar shapes and everything in between. For example, the sine function transitions smoothly into a constant or step function. The corresponding cosine function becomes a straight line. When the sine and cosine are plotted against each other the familiar unit circle undergoes a metamorphosis into a square. Integrals of these transitional trigonometric functions transition into a parabola, cubic polynomial, etc. These functions were developed to model a crash pulse in a vehicle collision, a task for which they work remarkably well. Basically, these functions are able to model a structure with force-deflection properties somewhere between a spring with linearly increasing force and a device that produces a constant force. One wonders what other applications in physics may exist besides crashing cars and what other pairs of physical models (represented by ODEs) might be merged together to produce other new and useful transitions.
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Lorenzo, Carl F., and Tom T. Hartley. "Mathematical Classification of the Spiral and Ring Galaxy Morphologies Based on the Fractional Trigonometry." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46279.

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The ongoing development of the fractional trigonometry has created a new set of spiral functions, the fractional spiral functions. These spirals include both barred and normal spirals in a common formulation. This paper studies the applicability of the fractional spirals to the mathematical classification of spiral and ring galaxy morphologies. The fractional spirals are found to provide a high quality fit to a variety of ring and spiral galaxies over a significant range of the spiral length. Further, the r–s character of the de Vaucouleurs classification is found to relate to particular parameters of the spirals. Additional benefits include; direct inference of galaxies inclination, estimates of major deviations of the galaxy optical center from the geometric center, and further application of the mathematical description of the galaxy morphology.
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Sun, Baoju. "Inequalities On Generalized Trigonometric Functions." In 2016 3rd International Conference on Mechatronics and Information Technology. Paris, France: Atlantis Press, 2016. http://dx.doi.org/10.2991/icmit-16.2016.2.

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Lorenzo, Carl F., Rachid Malti, and Tom T. Hartley. "The Solution of Linear Fractional Differential Equations Using the Fractional Meta-Trigonometric Functions." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47395.

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A new method for the solution of linear constant coefficient fractional differential equations of any commensurate order based on the Laplace transforms of the fractional meta-trigonometric functions and the R-function is presented. The new method simplifies the solution of such equations. A simplifying characterization that reduces the number of parameters in the fractional meta-trigonometric functions is introduced.
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Detrey, Jeremie, and Florent de Dinechin. "Floating-Point Trigonometric Functions for FPGAs." In 2007 International Conference on Field Programmable Logic and Applications. IEEE, 2007. http://dx.doi.org/10.1109/fpl.2007.4380621.

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Biloti, Ricardo, and Felipe Mariscal Aranha. "How are trigonometric functions indeed computed?" In XXIII Congresso de Iniciação Científica da Unicamp. Campinas - SP, Brazil: Galoá, 2015. http://dx.doi.org/10.19146/pibic-2015-37236.

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Malik, Pradeep, Saiful R. Mondal, and A. Swaminathan. "Fractional Integration of Generalized Bessel Function of the First Kind." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48950.

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Generalizing the classical Riemann-Liouville and Erde´yi-Kober fractional integral operators two integral transforms involving Gaussian hypergeometric functions in the kernel are considered. Formulas for composition of such integrals with generalized Bessel function of the first kind are obtained. Special cases involving trigonometric functions such as sine, cosine, hyperbolic sine and hyperbolic cosine are deduced. These results are established in terms of generalized Wright function and generalized hypergeometric functions.
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Reports on the topic "Trigonometry functions"

1

Wester, D. W. Trigonometric functions of nonlinear quantities. Office of Scientific and Technical Information (OSTI), August 1994. http://dx.doi.org/10.2172/10182638.

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