Relevant bibliographies by topics / Trigonometric circle

Contents

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

Academic literature on the topic 'Trigonometric circle'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Trigonometric circle"

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Martín Fernández, Enrique, Juan Francisco Ruiz-Hidalgo, and Luis Rico Romero. "Conversions Between Trigonometric Representation Systems by Pre-service Secondary School Teachers." PNA. Revista de Investigación en Didáctica de la Matemática 16, no. 3 (2022): 237–63. http://dx.doi.org/10.30827/pna.v16i3.21957.

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Understanding trigonometry relational system is a school mathemat-ics demanding topic. The angle, the unit circle and the trigonometric functions are its foundational notions. Trigonometric contents mean-ing and their understanding involve these three concepts and their re-lationships. This research aims to deepen in the pre-service teachers’ understanding about the angle, the unit circle and the trigonometric function when converting notions between two trigonometric repre-sentation systems based on the unit circle and the trigonometric func-tions. The results indicate that pre-service mathem
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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 (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 t
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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 t
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Nurbayeva, D. M., Zh M. Nurmukhamedova, S. Yeraliyev, and B. M. Kossanov. "ABOUT DEVELOPMENT OF STUDENTS ' THINKING WHEN SOLVING TRIGONOMETRIC EQUATIONS AND INEQUALITIES IN THE SCHOOL ALGEBRA COURSE." BULLETIN Series of Physics & Mathematical Sciences 69, no. 1 (2020): 138–43. http://dx.doi.org/10.51889/2020-1.1728-7901.23.

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The article deals with solutions of trigonometric inequalities using the unit circle. Specific examples show its application for all trigonometric functions, namely sinus, cosine, tangent and cotangent. An explanation of how to correctly define the period for solving inequalities is also provided. Before analyzing the solution to trigonometric inequalities, the authors present the solution of trigonometric equations according to the formula, but his roots are depicted on the unit circle, where detailed explanation of the record of solutions of this equation. The pictures in the article demonst
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Coghetto, Roland. "Some Facts about Trigonometry and Euclidean Geometry." Formalized Mathematics 22, no. 4 (2014): 313–19. http://dx.doi.org/10.2478/forma-2014-0031.

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Summary We calculate the values of the trigonometric functions for angles: [XXX] , by [16]. After defining some trigonometric identities, we demonstrate conventional trigonometric formulas in the triangle, and the geometric property, by [14], of the triangle inscribed in a semicircle, by the proposition 3.31 in [15]. Then we define the diameter of the circumscribed circle of a triangle using the definition of the area of a triangle and prove some identities of a triangle [9]. We conclude by indicating that the diameter of a circle is twice the length of the radius
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Kamber Hamzić, Dina, Mirsad Trumić, and Ismar Hadžalić. "Construction and analysis of test in triangle and circle trigonometry." International Electronic Journal of Mathematics Education 20, no. 1 (2025): em0805. https://doi.org/10.29333/iejme/15734.

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Trigonometry is an important part of secondary school mathematics, but it is usually challenging for students to understand and learn. Since trigonometry is learned and used at a university level in many fields, like physics or geodesy, it is important to have an insight into students’ trigonometry knowledge before the beginning of the university courses. This research aimed to develop a test in triangle and circle trigonometry, which can be used to test students’ prior knowledge of basic trigonometric concepts. A test with multiple-choice questions was developed based on content and learning
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Hašková, V., and M. Lipták. "Processing of calibration measurements on EZB-3." Slovak Journal of Civil Engineering 19, no. 4 (2011): 18–23. http://dx.doi.org/10.2478/v10189-011-0019-7.

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Processing of calibration measurements on EZB-3The calibration of horizontal circles results in a set of discrete correction values. These corrections are obtained in specific circle positions chosen by the size of the calibration step. For further use it is necessary to know the correction values for any location on a horizontal circle; therefore, it is necessary to know the function of the continuous corrections of a horizontal circle. This could be achieved from the measured values by several methods. In the article two methods are presented for determining this function through the approxi
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Sh.L.Ermatov. "TRIGONOMETRIC IDENTITIES OF THE QUADRILATERAL." ACADEMIC RESEARCH IN MODERN SCIENCE 2, no. 10 (2023): 72–73. https://doi.org/10.5281/zenodo.7793925.

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It is known that there are many trigonometric identities regarding the Triangle. These mirrors represent the trigonometric relationship between the inner corners of a triangle, the trigonometric relationship between the inner corners of the Triangle and its main elements (surface, perimeter, sides, radius of the inner and outer drawn circle, bisector, median, height).
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MITAN, Carmen-Irena, Emerich BARTHA, Petru FILIP, Constantin DRAGHICI, Miron T. CAPROIU, and Robert M. Moriarty. "Manifold inversion on prediction dihedral angle from vicinal coupling constant with 3-sphere approach." Revue Roumaine de Chimie 68, no. 3-4 (2024): 185–91. http://dx.doi.org/10.33224/rrch.2023.68.3-4.08.

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Dihedral angles are predicted from vicinal coupling constant 3JHH[Hz] with 3-sphere approach, sphere or torus trigonometric equations of circle 1, 2 and circle inversion 3-5 for all cis-, trans-ee, trans-aa stereochemistry. The existence of circle inversion was demonstrated with conformational analysis on five and six membered rings. The sign and the stereochemistry result from vicinal coupling constant under trigonometric equations confirmed by algebraic equations, Hopf and Lie algebra theory. 3-Sphere, a hypersphere in 4D enable for all stereochemistry calculation dihedral angles under magne
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Barrera, Azael. "Unit Circles and Inverse Trigonometric Functions." Mathematics Teacher 108, no. 2 (2014): 114–19. http://dx.doi.org/10.5951/mathteacher.108.2.0114.

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Dissertations / Theses on the topic "Trigonometric circle"

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Borges, Carlos Francisco. "Transição das razoes trigonométricas do triângulo retângulo para o círculo trigonométrico: uma sequencia para o ensino." Pontifícia Universidade Católica de São Paulo, 2009. https://tede2.pucsp.br/handle/handle/11401.

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Made available in DSpace on 2016-04-27T16:58:55Z (GMT). No. of bitstreams: 1 Carlos Francisco Borges.pdf: 2604675 bytes, checksum: 815cc9155f159a14b24957f9b7ed0342 (MD5) Previous issue date: 2009-10-23<br>Secretaria da Educação do Estado de São Paulo<br>The purpose of this essay was to contribute to Trigonometry teaching, specially, to the transition of the trigonometric reasons in the rectangle triangle for the trigonometric circle. A sequence was elaborated with 12 activities, from which ten were created worrying about guiding the student to understand the trigonometric reasons of the rect
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Fernandes, Ricardo Uchoa. "Estratégias pedagógicas com uso de tecnologias para o ensino de trigonometria na circunferência." Pontifícia Universidade Católica de São Paulo, 2010. https://tede2.pucsp.br/handle/handle/11445.

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Made available in DSpace on 2016-04-27T16:59:03Z (GMT). No. of bitstreams: 1 Ricardo Uchoa Fernandes.pdf: 2015098 bytes, checksum: 6b4dff7832d9c478d3fbc8376b57a470 (MD5) Previous issue date: 2010-05-19<br>Secretaria da Educação do Estado de São Paulo<br>The effective learning of the student is the main goal of a reflective teacher, so it is not enough simply to have all the technical knowledge, you need something more, namely mediation, have a clear and objective, to mobilize material resources for the success of this process . Just thought, this work was to build a meaningful learning the b
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Oliveira, Luiz Fernando Mosolino de. "Funções trigonométricas." reponame:Repositório Institucional da UFABC, 2016.

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Orientador: Prof. Dr. Daniel Miranda Machado<br>Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional, 2016.<br>Este trabalho foi desenvolvido para auxiliar alunos ingressantes no ensino superior, revisando t opicos da trigonometria e de funcoes trigonometricas, podendo auxiliar tambem alunos do ensino medio, professores ou interessados no assunto. Este trabalho parte de estudos iniciais da trigonometria e aborda de maneira simples a construcao de graficos de funcoes trigonometricas da forma f(x) = a+b. sen(c.x+d
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Mascarin, Lucimar Aparecida. "A utilização de atividades lúdicas e exploratórias no ensino e aprendizagem de matemática." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/55/55136/tde-06122017-094120/.

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A partir de estudos acerca das teorias sócio-histórico-culturais para o ensino e a aprendizagem, e de uma experiência de aplicação das mesmas na Educação Matemática, apresenta-se uma sequência didática envolvendo noções de semelhança de triângulos, trigonometria no triângulo retângulo, comprimento da circunferência e área do círculo, com o uso de atividades lúdicas e exploratórias. A construção dessa sequência se justifica como algo relevante para a sala de aula, porque se percebe que os conteúdos matemáticos apresentados de forma tradicional já não são atrativos para os alunos. Esta dissertaç
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Marangon, Marcelo Damasceno. "O número π". Universidade Federal de Juiz de Fora (UFJF), 2017. https://repositorio.ufjf.br/jspui/handle/ufjf/5816.

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Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-09-27T13:49:03Z No. of bitstreams: 1 marcelodamascenomarangon.pdf: 420801 bytes, checksum: 1541d566ceb0fcd639f11dcc6f27070a (MD5)<br>Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-09-27T15:20:26Z (GMT) No. of bitstreams: 1 marcelodamascenomarangon.pdf: 420801 bytes, checksum: 1541d566ceb0fcd639f11dcc6f27070a (MD5)<br>Made available in DSpace on 2017-09-27T15:20:26Z (GMT). No. of bitstreams: 1 marcelodamascenomarangon.pdf: 420801 bytes, checksum: 1541d566ceb0fcd639f11dcc6f27070a (MD5) Previou
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Carlzon, Madeleine. "Att få grepp om begrepp : En kvalitativ studie av gymnasieelevers begreppsförståelse inom trigonometri." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-79936.

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Den här studien undersöker gymnasieelevers begreppsförståelse inom trigonometri. Eleverna, som samtliga läser Ma 4, besvarade anonymt två frågeformulär där det ena bestod av en öppen fråga, medan det andra var upplagt som ett test med uppgifter att lösa. Den kvalitativa analysen baseras på Tall och Vinners (1981) teori om begreppsbild och Sfards (1991) uppdelning av begreppsförståelse i de tre processerna interiorisering, kondensering och reifiering. Resultatet indikerar att elever tenderar att använda cirkeltrigonometri före triangeltrigonometri för att lösa uppgifter, men
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Soares, Vanessa Ribeiro. "Batalha naval e suas aplicações." Universidade Federal de Goiás, 2016. http://repositorio.bc.ufg.br/tede/handle/tede/5909.

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Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2016-08-10T13:40:03Z No. of bitstreams: 2 Dissertação - Vanessa Ribeiro Soares - 2016.pdf: 11844437 bytes, checksum: 03d509603ea96f2647ea2764aea87d17 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-08-10T13:42:09Z (GMT) No. of bitstreams: 2 Dissertação - Vanessa Ribeiro Soares - 2016.pdf: 11844437 bytes, checksum: 03d509603ea96f2647ea2764aea87d17 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Mad
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Lehmann, Rüdiger. "Ebene Geodätische Berechnungen: Internes Manuskript." Hochschule für Technik und Wirtschaft, 2018. https://htw-dresden.qucosa.de/id/qucosa%3A31824.

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Dieses Manuskript entstand aus Vorlesungen über Geodätische Berechnungen an der Hochschule für Technik und Wirtschaft Dresden. Da diese Lehrveranstaltung im ersten oder zweiten Semester stattfindet, werden noch keine Methoden der höheren Mathematik benutzt. Das Themenspektrum beschränkt sich deshalb weitgehend auf elementare Berechnungen in der Ebene.:0 Vorwort 1 Ebene Trigonometrie 1.1 Winkelfunktionen 1.2 Berechnung schiefwinkliger ebener Dreiecke 1.3 Berechnung schiefwinkliger ebener Vierecke 2 Ebene Koordinatenrechnung 2.1 Kartesische und Polarkoordinaten 2.2 Erste Geodätische Grundaufgab
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Chen, Nai-Rong, and 陳乃榮. "Exact D-optimal designs for linear trigonometric regression models on a partial circle." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/26213931695568216093.

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碩士<br>國立中山大學<br>應用數學系研究所<br>90<br>In this paper we consider the exact $D$-optimal design problem for linear trigonometric regression models with or without intercept on a partial circle. In a recent papper Dette, Melas and Pepelyshev (2001) found explicit solutions of approximate $D$-optimal designs for trigonometric regression models with intercept on a partial circle. The exact optimal designs are determined by means of moment sets of trigonometric functions. It is shown that the structure of the optimal designs depends on both the length of the design interval and the number of the design p
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Li, Chin-Han, and 李秦漢. "D-optimal designs for combined polynomial and trigonometric regression on a partial circle." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/16547328546859369157.

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碩士<br>國立中山大學<br>應用數學系研究所<br>93<br>Consider the D-optimal designs for a combined polynomial of degree d and trigonometric of order m regression on a partial circle [see Graybill (1976), p. 324]. It is shown that the structure of the optimal design depends only on the length of the design interval and that the support points are analytic functions of this parameter. Moreover, the Taylor expansion of the optimal support points can be determined efficiently by a recursive procedure.
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Books on the topic "Trigonometric circle"

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Theodore, Lee, and Sklar David, eds. Precalculus with unit-circle trigonometry. 4th ed. Thomson Brooks/Cole, 2006.

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Michael, Sullivan. Trigonometry: A unit circle approach. 8th ed. Pearson Prentice Hall, 2008.

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Michael, Sullivan. Trigonometry: A unit circle approach. 8th ed. Pearson Prentice Hall, 2008.

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David, Cohen. College algebra with unit-circle trigonometry. West Pub. Co., 1993.

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Wilhelm, Leibniz Gottfried. De quadratura arithmetica circuli ellipseos et hyperbolae cujus corollarium est trigonometria sine tabulis. Vandenhoeck & Ruprecht, 1993.

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Michael, Sullivan. Precalculus: Concepts through functions, a unit circle approach to trigonometry. 2nd ed. Prentice Hall, 2011.

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Michael, Sullivan. Precalculus: Concepts through functions, a unit circle approach to trigonometry. 2nd ed. Pearson, 2011.

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Sullivan, Michael, III, 1967- author, ed. Precalculus: Concepts through functions : a unit circle approach to trigonometry. Pearson, 2015.

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Sullivan, Michael, 1967 July 2-, ed. Precalculus: Concepts through functions, a unit circle approach. Pearson Prentice Hall, 2007.

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Sullivan, Michael. Trigonometry: A Unit Circle Approach. Pearson Education, Limited, 2011.

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Book chapters on the topic "Trigonometric circle"

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Lewis, Torina. "Trigonometric-Type Functions Derived from Polygons Inscribed in the Unit Circle." In Association for Women in Mathematics Series. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-19486-4_19.

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Nickl, Richard. "Uniform central limit theorems for sieved maximum likelihood and trigonometric series estimators on the unit circle." In Institute of Mathematical Statistics Collections. Institute of Mathematical Statistics, 2009. http://dx.doi.org/10.1214/09-imscoll522.

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Buckwell, Geoff. "The circle and further trigonometry." In Mastering Mathematics. Macmillan Education UK, 1997. http://dx.doi.org/10.1007/978-1-349-14131-9_14.

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Motz, Lloyd, and Jefferson Hane Weaver. "The Geometry of the Circle and Trigonometry." In Conquering Mathematics. Springer US, 1991. http://dx.doi.org/10.1007/978-1-4899-2774-3_6.

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Coxeter, H. S. M. "The Trigonometry of Escher’s Woodcut Circle Limit III." In M.C. Escher’s Legacy. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/3-540-28849-x_29.

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Knobloch, Eberhard, Armin Stock, Jürgen Jost, H. Gg Wagner, and Margarita Wolf. "De quadratura arithmetica circuli ellipseos et hyperbolae cujus corollarium est trigonometria sine tabulis." In Gottfried Wilhelm Leibniz. Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-662-52803-7_1.

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Bansal, Jagdish Chand, Prathu Bajpai, Anjali Rawat, and Atulya K. Nagar. "Advancements in the Sine Cosine Algorithm." In Sine Cosine Algorithm for Optimization. Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-19-9722-8_5.

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AbstractIn the last few decades, the development and advancement of meta-heuristic algorithms have become the focus of the research community as these algorithms face various challenges like, balance between exploration and exploitation, tuning of parameters, getting trapped in local optima, and very slow convergence rate. Sine cosine algorithm (SCA) also faces similar kinds of challenges and sometimes fails to perform effectively in finding the global optimal solution. Sine and cosine are trigonometric operators with a 90$$^\circ $$ phase shift from each other. The range of sine and cosine fu
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Monk, Paul, and Lindsey J. Munro. "Trigonometry." In Maths for Chemistry. Oxford University Press, 2021. http://dx.doi.org/10.1093/hesc/9780198717324.003.0011.

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This chapter provides an overview of trigonometry, starting with the process of naming a right-angled triangle. It considers the simple trigonometric functions, looking at sine, cosine, and tangent. A sine is the ratio of the length of the opposite to the length of the hypotenuse, and a cosine is the ratio of the length of the adjacent to the length of the hypotenuse. Meanwhile, a tangent is the ratio of the length of the opposite to the length of the adjacent. The chapter then discusses radians, which are a way of subdividing angles within a circle; Pythagoras' theorem, which requires a right
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Lützen, Jesper. "Circle Quadrature in the Seventeenth Century." In A History of Mathematical Impossibility. Oxford University PressOxford, 2023. http://dx.doi.org/10.1093/oso/9780192867391.003.0008.

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Abstract During the seventeenth century the quadrature of a circle was a controversial problem. Some mathematicians claimed that they had solved it, and others like Descartes declared it to be impossible. The mathematicians involved in the debates did not agree about what constituted a proper solution, and they did not agree what the problem was: was it the quadrature of a whole circle (the definite circle quadrature) or the quadrature of any sector of a circle (the indefinite circle quadrature)? Some mathematicians like Gregory and Wallis claimed that they had proved the impossibility of the
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"High School Mathematics." In Utilizing Visuals and Information Technology in Mathematics Classrooms. IGI Global, 2023. http://dx.doi.org/10.4018/978-1-6684-9987-0.ch003.

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This chapter selects some topics from high school mathematics and presents a dynamic visualization of their content development. It becomes mathematics completely from high school mathematics. Smoothly varying functions are also covered. The angle is also defined by the length of the arc that encloses it. Dynamic visualization is converted into content in almost all areas of high school mathematics, but here the authors describe the following six items as examples: Root of quadratic equations, Change in value of quadratic function, Sine theorem, Relationship between the diameter of the circle
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Conference papers on the topic "Trigonometric circle"

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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 “transitio
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Kryvyi, Petro D., Volodymyr O. Dzyura, Nadiya M. Tymoshenko, and Volodymyr V. Krupa. "Technological Heredity and Accuracy of the Cross-Section Shapes of the Hydro-Cylinder Cylindrical Surfaces." In ASME 2014 International Manufacturing Science and Engineering Conference collocated with the JSME 2014 International Conference on Materials and Processing and the 42nd North American Manufacturing Research Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/msec2014-3946.

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It was proposed to estimate the accuracy of the hydro-cylinder cross-section shapes basing on the analysis of the circle diagram of their inner cylindrical surfaces, formed by the manufacturing operations, such as rough and semi-finishing boring and finishing paying-out, taking advantage of the method of deflection approximation from the circle by the Fourier’s trigonometric series in the gap [0, 2π]. Characteristics of the deflection dispersion of the radius-vector as the random value (average value, dispersion, amplitude spectrum) have been obtained for every circle diagram separately. It is
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Asai, Hiroshi, Mototsugu Omura, Tomoyuki Shimono, and Yasutaka Fujimoto. "Bilateral control of a half-circle-shaped tubular linear motor with disturbance model based on trigonometric function of two variables." In 2014 7th International Conference on Information and Automation for Sustainability (ICIAfS). IEEE, 2014. http://dx.doi.org/10.1109/iciafs.2014.7069541.

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Nikiforov, I., P. Sobolev, and A. Veselova. "Velocities-distance optimization of the rotation model of a homogeneous flat subsystem of Galactic objects:masers." In Modern astronomy: from the Early Universe to exoplanets and black holes. Special Astrophysical Observatory of the Russian Academy of Sciences, 2024. https://doi.org/10.26119/vak2024.073.

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A statistically correct method for optimizing the parameters of the kinematic model for a homogeneous set of Galactic objects has been developed and implemented, which includes minimizing the squares of relative deviations from the observed radial velocity, proper motions, and distant characteristic. The latter refers to the trigonometric parallax (in the case of absolute distances) or the distance modulus (in the case of relative, i.e., photometric, distances). The solution lies in the technique of the principle of maximum likelihood. The presence of measurement errors and natural (dynamic, a
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Baidabekov, A., and E. Kemelbekova. "DETERMINING NEW HIGHER ORDER CURVES USING BIQUADRATIC TRANSFORMATION METHODS." In GRAPHICON 2024. Omsk State Technical University, 2024. http://dx.doi.org/10.25206/978-5-8149-3873-2-2024-755-760.

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The article deals with fourth-order curves and their construction methods. For the first time, the concept of four-order curves is mentioned in the works of ancient Greek scientists. One such scientist was Perseus who lived in the second century. He obtained fourth-order curves by cutting a torus with planes parallel to the axis. And Nicomedes, a Greek geometer who lived in the third century, used fourth-order curves (Nicomedes shells) to solve segment problems. At the same time, he used fourth-order curves to solve trigonometric problems, so he called this curve the "Nicomedian envelope". Sin
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6

Wang, Shanglong, and Kwun-Lon Ting. "A Unified Subdivision Scheme for Arcs and Circles." In ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/detc2006-99730.

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This paper proposes a subdivision scheme that is capable of expressing arcs and circles in a consistent form. This curve scheme is based on the unified subdivision rules for cubic B-splines, splines-in-tension, and some trigonometric splines that are capable of generating circles. The most important feature of the scheme is to change the end point rule such that the end points are forced to locate on lines connecting the center to the start point as well as the end point. With the proposed scheme, generating arcs and circles also becomes much more intuitive.
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