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Journal articles on the topic 'Applications of trigonometry'
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1
Hersberger, Jim, and James O. Farlow. "Applications: Tracking Dinosaurs With Trigonometry." Mathematics Teacher 83, no. 1 (January 1990): 46–50. http://dx.doi.org/10.5951/mt.83.1.0046.
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If you and your trigonometry students grow weary of fictitious forest rangers and contrived scenarios involving ships that may or may not pass in the night, then the following real-life application will probably appeal to you. It demonstrates the usefulness of several trigonometric concepts and identities and can be used in a variety of classroom formats.
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Anantha, Anantha. "Spiritual and Cosmological Applications of Triangles." International Journal of Contemporary Research and Review 10, no. 04 (April 6, 2019): 21467–79. http://dx.doi.org/10.15520/ijcrr.v10i04.689.
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It is well known that the laws of triangles are widely applied in classical mathematical branches, physics, engineering and almost all the areas of science, technology and other fields. Trigonometry is the extension of triangles. Cosmology is the application of trigonometry. The Jews, Vedic Aryans, Islam and Taoism were all well versed with triangles and other geometrical figures. In this article, the author attempts to unlock the hidden spiritual mysteries of triangles and also about the part played by triangles in cosmology.
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Stephens, Gregory P. "Applications: Trigonometry for the Energy-Conscious Architect." Mathematics Teacher 90, no. 7 (October 1997): 564–65. http://dx.doi.org/10.5951/mt.90.7.0564.
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My favorite trigonometry problem has to do with controlling the entry of sunlight through a window. Sunlight is radiant energy and a significant source of heat in a building. I ask students to be energy-conscious architects and design a window overhang that will block the midday summer sun but allow plenty of sunlight in the winter. Both goals are reachable because the apex of the sun's circuit in the sky is much higher in summer than in winter.
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Caples, Linda Griffin. "Applications: Squeal Those Tires!: Automobile-Accident Reconstruction." Mathematics Teacher 85, no. 1 (January 1992): 56–61. http://dx.doi.org/10.5951/mt.85.1.0056.
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The procedures used by law-enforcement officers in traffic-accident reconstruction contain a wealth of material that can be applied in teaching secondary school mathematics. Students are highly interested in the milestone of obtaining a driver's license, It is important that they recognize their responsibility of driving within the speed limits to reduce the chance of their involvement in an accident. Should they be in an accident, they may be surprised to know that methods of estimating minimum speeds are available. These methods require a basic knowledge of vectors and trigonometry, which makes their use an ideal real-life application for students in precalculus, mathematical analysis, or trigonometry.
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Izhakian, Zur, Manfred Knebusch, and Louis Rowen. "Supertropical quadratic forms II: Tropical trigonometry and applications." International Journal of Algebra and Computation 28, no. 08 (December 2018): 1633–76. http://dx.doi.org/10.1142/s021819671840012x.
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This paper is a sequel of [Z. Izhakian, M. Knebusch and L. Rowen, Supertropical semirings and supervaluations, J. Pure Appl. Algebra 220(1) (2016) 61–93], where we introduced quadratic forms on a module [Formula: see text] over a supertropical semiring [Formula: see text] and analyzed the set of bilinear companions of a quadratic form [Formula: see text] in case the module [Formula: see text] is free, with fairly complete results if [Formula: see text] is a supersemifield. Given such a companion [Formula: see text], we now classify the pairs of vectors in [Formula: see text] in terms of [Formula: see text] This amounts to a kind of tropical trigonometry with a sharp distinction between the cases for which a sort of Cauchy–Schwarz (CS) inequality holds or fails. This distinction is governed by the so-called CS-ratio [Formula: see text] of a pair of anisotropic vectors [Formula: see text] in [Formula: see text]. We apply this to study the supertropicalizations (cf. [Z. Izhakian, M. Knebusch and L. Rowen, Supertropical semirings and supervaluations, J. Pure Appl. Algebra 220(1) (2016) 61–93]) of a quadratic form on a free module [Formula: see text] over a field in the simplest cases of interest where [Formula: see text]. In the last part of the paper, we introduce a suitable equivalence relation on [Formula: see text], whose classes we call rays. (It is coarser than usual projective equivalence.) For anisotropic [Formula: see text] the CS-ratio [Formula: see text] depends only on the rays of [Formula: see text] and [Formula: see text]. We develop essential basics for a kind of convex geometry on the ray-space of [Formula: see text], where the CS-ratios play a major role.
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Lokutsievskiy, L. V. "Convex trigonometry with applications to sub-Finsler geometry." Sbornik: Mathematics 210, no. 8 (August 2019): 1179–205. http://dx.doi.org/10.1070/sm9134.
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Austin, Joe Dan, and F. Barry Dunning. "Applications: Mathematics of the Rainbow." Mathematics Teacher 81, no. 6 (September 1988): 484–88. http://dx.doi.org/10.5951/mt.81.6.0484.
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Figure 1 shows a picture of a rainbow. Have you wondered what causes a rainbow, why it is brighter inside than out, or why more than one rainbow may appear? The answers to these questions involve optics, geometry, trigonometry, and calculus. This article presents some of the optics and mathematics related to these questions.
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Zamorano Urrutia, Francisco Javier, Catalina Cortés Loyola, and Mauricio Herrera Marín. "A Tangible User Interface to Facilitate Learning of Trigonometry." International Journal of Emerging Technologies in Learning (iJET) 14, no. 23 (December 6, 2019): 152. http://dx.doi.org/10.3991/ijet.v14i23.11433.
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In mathematics education, studies reveal difficulties in the teaching-learning of trigonometry in secondary and higher education, due to the fact that students are not encouraged to achieve a deep conceptual understanding of abstract concepts. Several studies demonstrate that incorporating digital technologies has a positive impact on students’ learning. However, most of the existing technologies do not consider the use of the body and multiple senses. Tangible User Interfaces (TUIs) in contrast, can host bodily interactions that have the potential of enhancing learning. Nonetheless, there is a lack of applications of TUIs for trigonometry education. This study consisted in designing and validating a tangible interface for the teaching-learning of basic concepts of trigonometry. The interface hosts a pedagogical experience that privileges exploration through physical manipulation and fosters intuitive and collaborative learning. A Pre-Test was applied to 121 students to determine previous knowledge, yielding a 29.1% performance. After two sessions using the interface, the results of a Post-Test reveal an increase of 37.1%, confirming the educational effectiveness of the interface and the pedagogical experience to facilitate learning of basic concepts of trigonometry.
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Luz Pelissari de Oliveira, Christian, and Fernando Pereira de Souza. "TRIGONOMETRIA ESFÉRICA APLICADA NA ASTRONOMIA DE POSIÇÃO." COLLOQUIUM EXACTARUM 10, no. 2 (June 1, 2018): 60–67. http://dx.doi.org/10.5747/ce.2018.v10.n2.e239.
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The present article is the result of a research work of the Degree in Mathematics in the scope of the Tutorial Education Program -PET. The work deals with concepts of Spherical Trigonometry, which has several fields of applications between mathematics and physics, related to cartographic problems, navigation and astronomy. The goal is to explore problems of astronomy applications of celestial bodies by making use of trigonometry concepts in the sphere to study positions and directions of stars in terms of a celestial sphere. In order to reach this objective, the article presents concepts of a smaller distance between two points in the sphere, a triangle of position that is the spherical triangle, the fundamental relation known as law of cosines, the Celestial Sphere, its elements, its coordinates in the equatorial system, horizontal system and time system. Thus, the work seeks to encourage students and teachers to work on Spherical Geometry in the classroom
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Abrianto, Oktavian Rosa. "PENERAPAN METODE TUTOR SEBAYA UNTUK MENINGKATKAN HASIL BELAJAR DAN MOTIVASI BELAJAR SISWA PADA MATERI TRIGONOMETRI KELAS XI MIPA 4 SMA NEGERI 1 AMBARAWA." Satya Widya 35, no. 1 (June 28, 2019): 62–74. http://dx.doi.org/10.24246/j.sw.2019.v35.i1.p62-74.
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This research is observed to increase the result and motivate the students in learning mathematics in Grade XI MIPA 4 of Ambarawa Senior High School with topic trigonometry by using peer tutor method. This research is includes class act observed. The method that I used in this research is called Kurt Lewin with 4 steps, they are planning, action, observing, and reflection. The increasing result of the study and motivation to learn in learning mathematics with can see it by points and questionnaire scores. The result shows that the average learning outcomes in cycle 1 and cycle 2 were 73,55 and 86,67 respectively with the percentage of class completeness in the first cycle and the second cycle respectively 64% and 85%. As for the aspects of learning motivation by 52% based on this, it can be concluded that the applications of peer tutoring methods cam improve learning outcomes and learning motivation in the trigonometry material of students of Grade XI MIPA 4 of Ambarawa Senior High School.
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Wood, Eric F. "Mathematics and Meteorology." Mathematics Teacher 79, no. 8 (November 1986): 602–3. http://dx.doi.org/10.5951/mt.79.8.0602.
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One of the ironies of teaching mathematics is that real-life problems, although interesting, are often too difficult to consider in a secondary school classroom. Consequently the problems that are used in texts are often somewhat contrived. While working at the local weather office, I came upon several applications of trigonometry that are both interesting and instructive for high school students. The problems require that some background knowledge be presented to the students, but often they will have at least heard about the ideas from the nightly weather forecasts on television. These ideas make an interesting discussion for both teacher and student.
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Edwards, Thomas. "Building Mathematical Models of Simple Harmonic and Damped Motion." Mathematics Teacher 88, no. 1 (January 1995): 18–22. http://dx.doi.org/10.5951/mt.88.1.0018.
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Given the recent public mania over bungee jumping, stimulating students' interest in a model of that situation should be an easy “leap.” Students should investigate the connections among various mathematical representations and their relationships to applications in the real world, asserts the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989). Mathematical modeling of real-world problems can make such connections more natural for students, the standards document further indicates. Moreover, explorations of periodic real-world phenomena by all students, as well as the modeling of such phenomena by college-intending students, is called for by Standard 9: Trigonometry.
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Henderson, Ronald W., and Edward M. Landesman. "The Interactive Videodisc System in the Zone of Proximal Development: Academic Motivation and Learning Outcomes in Precalculus." Journal of Educational Computing Research 9, no. 1 (February 1993): 29–43. http://dx.doi.org/10.2190/j53a-v7vt-22d0-vgek.
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High school students enrolled in precalculus/trigonometry classes were randomly assigned to receive instruction either by a master teacher in a regular classroom or via interactive videodisc instructional modules. The interactive modules were designed to help students understand mathematical concepts by means of real-world video exemplars of the concepts, and by modeling problem-solving strategies and metacognitive processes. Evaluation results showed that students who learned solely by means of the interactive videodisc materials achieved as well or better than students who received traditional instruction organized around the same objectives. The relation of student goal orientations and self-perceptions to learning outcomes was also investigated. The results of multiple regression analyses for each of eight instructional topics revealed a pattern supportive of Dweck's theory regarding the role of goal orientations in academic motivation.
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Schloemer, Cathy G. "Sharing Teaching Ideas: I Found Sinusoids in My Gas Bill." Mathematics Teacher 93, no. 1 (January 2000): 10–12. http://dx.doi.org/10.5951/mt.93.1.0010.
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With the current emphasis on real-world mathematics applications, many recent trigonometry textbooks include examples of sinusoidal functions for which students are required to find a model. These examples typically refer to the height of a person above the ground as a function of length of time riding on a Ferris wheel or to the number of hours of daylight in a U.S. city as a function of the day of the year. Unfortunately, as real-world as these examples are, many students still reject them as artificial and contrived. Complaints of “I'll never do this in my adult life” and “Who cares how high the Ferris wheel rider is?” are common among the eleventh- and twelfth-grade students that I teach.
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Budiwati, Anisah. "TONGKAT ISTIWA‘, GLOBAL POSITIONING SYSTEM (GPS) DAN GOOGLE EARTH UNTUK MENENTUKAN TITIK KOORDINAT BUMI DAN APLIKASINYA DALAM PENENTUAN ARAH KIBLAT." Al-Ahkam 26, no. 1 (April 14, 2016): 65. http://dx.doi.org/10.21580/ahkam.2016.26.1.808.
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<p>There are at least three ways to determine the position or the coordinates of a spot on the Earth's surface. They are: istiwa' sticks, Global Positioning System (GPS), and Google Earth. Istiwa' stick is used without technology operations, while GPS and Google Earth are used with technology. Until now, the use of GPS and Google Earth is still a passively consumptive, without their critical analytical effort. This qualitative research using descriptive analytic mathematical methods. The objective of this study is the to know the theory, applications, and accuracy of the istiwa' stick, GPS, and Google Earth comparatively. The study found that the istiwa' stick is one of the alternatives way to determine the coordinates of the Earth which uses the theory of spherical trigonometry calculations simply without assistance. Whereas GPS and Google Earth use principles of geodetic scientifically. In terms of applications, the most practical and accurate is GPS,<br />and then followed by Google Earth, and the last is istiwa' stick.</p><p><strong><br /></strong></p><p><strong></strong>Setidaknya ada tiga cara untuk menentukan posisi atau titik koordinat suatu tempat di permukaan Bumi, yaitu tongkat istiwa’, Global Positioning System (GPS), dan Google Earth. Tongkat istiwa’ digunakan tanpa bantuan teknologi, sedangkan GPS dan Google Earth digunakan dengan teknologi. Sampai saat ini, penggunaan GPS maupun Google Earth masih bersifat konsumtif pasif, tanpa adanya upaya analitis kritis. Penelitian<br />kualitatif ini menggunakan metode deskriptif analitik matematis. Penelitian ini memiliki tujuan untuk mengetahui teori, aplikasi, maupun akurasi tongkat istiwa’, GPS, dan Google<br />Earth secara komparatif. Penelitian ini menemukan bahwa tongkat istiwa’ adalah salah satu alternatif penentuan titik koordinat Bumi yang menggunakan teori perhitungan<br />spherical trigonometry secara sederhana tanpa bantuan, sedangkan GPS dan Google Earth menggunakan prinsip keilmuan geodesi yang lebih teliti. Dari segi aplikasi, yang<br />paling praktis dan akurat adalah GPS. Kemudian disusul Google Earth, dan tongkat istiwa’.</p>
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Pereira, Ana Carolina Costa, and Bernadete Barbosa Morey. "Revisitando a lei dos cossenos para triângulos esféricos: um aporte histórico do século XV." História da Ciência e Ensino: construindo interfaces. ISSN 2178-2911 15 (May 5, 2017): 81. http://dx.doi.org/10.23925/2178-2911.2017v15p81-95.
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ResumoA Trigonometria, ramo da Matemática, percorreu um longo caminho até se consolidar como ciência independente da Astronomia. Dentre as obras que contribuíram para a história da Trigonometria Plana e Esférica está De Triangulis Omnimodis Libri Quinque de Regiomontanus, trabalho que recebeu destaque no século XVI por sua organização sistemática. Nesse artigo discutiremos a lei dos cossenos em relação aos lados de um triângulo esférico exposto nessa obra, apresentando os conceitos preliminares, o enunciado e a demonstração. Acreditamos que conhecer as origens dos conteúdos estudados por meio de fontes históricas pode possibilitar uma maior compreensão da matemática e de sua aplicação no mundo moderno. Palavras-chave: Lei dos Cossenos; Trigonometria; Regiomontanus; De Triangulis Omnimodis Libri Quinque.AbstractTrigonometry, branch of mathematics, has come a long way to be consolidated as an independent science of Astronomy. Among the compositions that contributed to the history of Flat and Spherical Trigonometry, De triangulis Omnimodis Libri Quinqueof the Regiomontanus,work that was highlighted in the sixteenth century by its systematic organization. This article will discuss the law of cosines regarding to the sides of a spherical triangle exposed in this work, showing the previous concepts, statement and demonstration. We believe that, knowing the origins of the contents studied through historical sources can enable greater understanding of mathematics and its application in the modern world.Keywords: Law of cosines; Trigonometry; Regiomontanus; De triangulis Omnimodis Libri Quinque.
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Adhikari, Tara Nath, and Abatar Subedi. "Difficulties of Grade X students in learning Trigonometry." Siddhajyoti Interdisciplinary Journal 2, no. 01 (August 21, 2021): 90–99. http://dx.doi.org/10.3126/sij.v2i01.39243.
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Abstract This paper aims to explain the difficulties of grade X students in learning trigonometry that were explored from an empirical study in the year 2017 AD. The researcher used explanatory mixed research design where 155 students of grade X were selected randomly from the four schools of Kirtipur municipality to conduct initial survey to find low achievers and most difficult content areas of trigonometry by using achievement test. Then five low achievers and respective three mathematics teachers were selected and interviewed with the help of semi-structured interview guidelines to explore what difficulties had they experienced and encountered in learning trigonometry. The results revealed that mean achievement score of students in institutional schools was greater than that of students of community schools. However, there are some common areas of difficulties of students in both types of schools for learning trigonometry including the difficulties related to memorization of facts; comprehension of new concepts; transformation of verbal problems; derivation and proofs of trigonometric relations and unfamiliarity with the solving process of problems in application level. These difficulties are due to several reasons including abstract nature of contents, poor prerequisites among students, demonstration of teacher centered instruction, and focusing on rote memorization rather than conceptual understanding. Hence, it is recommended that both students and teachers need to focus on conceptual learning rather than rote memorization for meaningful understanding in trigonometry.
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Lu, Mei-Kuei, Tzeng Yih Lam, Bo-Hao Perng, and Ho-Tung Lin. "Close-range photogrammetry with spherical panoramas for mapping spatial location and measuring diameters of trees under forest canopies." Canadian Journal of Forest Research 49, no. 8 (August 2019): 865–74. http://dx.doi.org/10.1139/cjfr-2018-0430.
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Measurement of tree attributes is important to collect information for forest management. Close-range photogrammetry with spherical panoramas has seen very little development and applications compared with aerial photography. This study develops methods to extract azimuth, horizontal distance, diameter at breast height, and upper stem diameters of individual trees from spherical panoramas based on (i) the trigonometry principle (TRIGO), (ii) the TRIGO corrected for terrain slope (TRIGOSLP), and (iii) the pinhole camera model (PINHOLE). Twenty-three horizontal point sample plots were randomly established in plantations in Taiwan, for a sample size of 486 trees. Results showed that tree azimuth was accurately and precisely estimated. TRIGO performed the worst in accuracy and precision for all other tree attributes. TRIGOSLP improved the results of TRIGO but had large estimation errors. PINHOLE achieved the best overall precision for all other tree attributes but was slightly inaccurate for estimating upper stem diameters. PINHOLE requires approaching a tree to attach a target of known size but has the ability to extract an almost continuous set of upper stem diameters from the tree, which could improve estimation of tree volume. Thus, PINHOLE could potentially be an alternative measurement system for hard-to-measure tree attributes.
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Sisala, Joseph, and Abdi T. Abdalla. "Multipath Exploitation-Based Indoor Target Localization Model Using Single Marginal Antenna." Tanzania Journal of Engineering and Technology 39, no. 1 (June 30, 2020): 13–20. http://dx.doi.org/10.52339/tjet.v39i1.515.
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Recently, indoor target localization became an area of interest due to its diverse applications. In indoor target localization, surrounding environment creates multipath components, which can be exploited to aid in localization process. A number of studies have been proposed to employ multipath exploitation in localizing indoor targets. However, their localization errors can still be improved. This study proposed a new localization model based on multipath exploitation techniques by using triangulation method. Ultra-wide band signals were resolved and associated using marginal antenna-based scheme. The estimate of the target location was then obtained using measured round-trip time delays. The location was determined by applying the simple trigonometry on the triangle in which real radar, virtual radars, and the target location are the vertices of the triangle in question. Simulation results show that the proposed method has improved the localization error over a wide range of timing errors, target locations and room sizes with the overall maximum localization error of 1.4 m equivalent to 22.2% improvement as compared to 1.8 m localization error obtained using the method developed by the Muqaibel et al. (2017).
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Alsadik, Bashar. "A MODIFIED METHOD FOR IMAGE TRIANGULATION USING INCLINED ANGLES." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLI-B3 (June 9, 2016): 453–58. http://dx.doi.org/10.5194/isprsarchives-xli-b3-453-2016.
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The ongoing technical improvements in photogrammetry, Geomatics, computer vision (CV), and robotics offer new possibilities for many applications requiring efficient acquisition of three-dimensional data. Image orientation is one of these important techniques in many applications like mapping, precise measurements, 3D modeling and navigation. <br><br> Image orientation comprises three main techniques of resection, intersection (triangulation) and relative orientation, which are conventionally solved by collinearity equations or by using projection and fundamental matrices. However, different problems still exist in the state – of –the –art of image orientation because of the nonlinearity and the sensitivity to proper initialization and spatial distribution of the points. In this research, a modified method is presented to solve the triangulation problem using inclined angles derived from the measured image coordinates and based on spherical trigonometry rules and vector geometry. The developed procedure shows promising results compared to collinearity approach and to converge to the global minimum even when starting from far approximations. This is based on the strong geometric constraint offered by the inclined angles that are enclosed between the object points and the camera stations. <br><br> Numerical evaluations with perspective and panoramic images are presented and compared with the conventional solution of collinearity equations. The results show the efficiency of the developed model and the convergence of the solution to global minimum even with improper starting values.
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Alsadik, Bashar. "A MODIFIED METHOD FOR IMAGE TRIANGULATION USING INCLINED ANGLES." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLI-B3 (June 9, 2016): 453–58. http://dx.doi.org/10.5194/isprs-archives-xli-b3-453-2016.
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The ongoing technical improvements in photogrammetry, Geomatics, computer vision (CV), and robotics offer new possibilities for many applications requiring efficient acquisition of three-dimensional data. Image orientation is one of these important techniques in many applications like mapping, precise measurements, 3D modeling and navigation. <br><br> Image orientation comprises three main techniques of resection, intersection (triangulation) and relative orientation, which are conventionally solved by collinearity equations or by using projection and fundamental matrices. However, different problems still exist in the state – of –the –art of image orientation because of the nonlinearity and the sensitivity to proper initialization and spatial distribution of the points. In this research, a modified method is presented to solve the triangulation problem using inclined angles derived from the measured image coordinates and based on spherical trigonometry rules and vector geometry. The developed procedure shows promising results compared to collinearity approach and to converge to the global minimum even when starting from far approximations. This is based on the strong geometric constraint offered by the inclined angles that are enclosed between the object points and the camera stations. <br><br> Numerical evaluations with perspective and panoramic images are presented and compared with the conventional solution of collinearity equations. The results show the efficiency of the developed model and the convergence of the solution to global minimum even with improper starting values.
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Sudarman, Satrio Wicaksono, and Ira Vahlia. "Pengembangan Bahan Ajar Trigonometri Dengan Pendekatan RME Berbasis Aplikasi Schoology." Jurnal Derivat: Jurnal Matematika dan Pendidikan Matematika 5, no. 1 (March 28, 2019): 9–18. http://dx.doi.org/10.31316/j.derivat.v5i1.142.
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This study aims to determine the benefits of teaching materials based on the application of Schoology in the course of trigonometry in the lecture. One of the hallmarks of Schoology-based teaching materials is to use the Schoology app which is one of the web-based social web pages which offers the same learning as in a class free and easy to use. Through Schoology, the management of learning is very easy. Schoology is also almost the same function with other web pages in which it offers lecturers to load materials, learning materials, structured quizzes. This research is a kind of research development. Research methodology used as follows: (1) research and information gathering, (2) planning, (3) product development, (4) initial test, (5) product revision, (6) field trial, (7) field trial products, (8) product operational trials, (9) product revisions and (10) implementation. The achievement of this research is teaching materials based on Schoology which can support lecturer of trigonometry in the mathematics education program. This teaching material is feasible to use and the achievements generated in the development of teaching materials based on this schoology is to improve students' learning outcomes in trigonometric courses.Keywords: development, teaching materials, schoology, trigonometry
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Latinčić, Dragan. "Possible principles of mathematical music analysis." New Sound, no. 51 (2018): 153–74. http://dx.doi.org/10.5937/newso1851153l.
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The text is a summary of many years of research in the domains of micro-intervals, metric-rhythmic projection of the spectrum harmonics, and the establishment of a link with mathematics, more precisely, geometry, with a special focus on the application of the Pythagorean Theorem. Mathematical music analysis enables the establishment of methods for constructing right, obtuse, and acute musical triangles as well as projections of their edges (sides), which are recognized in trigonometry as the functions of angles: the sine, cosine, and so on; as well as the establishment of methods for constructing spectral and scalar (intonative-temporal) trigonometric unit circles with their function graphs.
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Prayitno, Prayitno, and Abdillah Abdillah. "Metode Komunikasi Semut (Komusem) untuk Meningkatkan Keaktifan Belajar Trigonometri Peserta Didik." MATEMATIKA DAN PEMBELAJARAN 6, no. 2 (December 29, 2018): 201. http://dx.doi.org/10.33477/mp.v6i2.670.
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Abstrak
Penelitian ini bertujuan untuk mendeskripsikan penerapan metode komunikasi semut untuk meningkatkan keaktifan belajar trigonometri peserta didik kelas X IPS-4 SMA Negeri 3 Jombang tahun pelajaran 2013/2014. Penelitian ini merupakan penelitian tindakan sebagai upaya menguji cobakan ide-ide ke dalam praktek untuk memperbaiki atau merubah sesuatu agar memperoleh dampak nyata dari situasi. Adapun indikator keaktifan yang diamati meliputi: (1) data hasil pengamatan peserta didik dalam membentuk kelompok, (2) data hasil pengamatan peserta didik dalam menyampaikan ide atau pertanyaan, (3) data hasil pengamatan peserta didik dalam bekerja sama dengan peserta lain, dan (4) data hasil pengamatan peserta didik dalam mengikuti proses belajar mengajar (PBM) dan (5) data hasil pengamatan peserta didik dalam mencatat materi. Hasil penelitian ini menunjukkan bahwa penerapan metode komunikasi semut dapat meningkatkan keaktifan belajar trigonometri peserta didik kelas X IPS-4 SMA Negeri 3 Jombang tahun pelajaran 2013/2014. Hal ini dapat ditunjukkan dengan meningkatnya persentase hasil observasi keaktifan peserta didik yang meningkat dari siklus 1 ke siklus berikutnya
Kata kunci: Penerapan, metode komunikasi semut, keaktifan siswa
Abstract
This research aims to describe application of ants’ communication to improve students’ activeness when learn trigonometry on grade 10th in SMA Negeri 3 Jombang, academic year 2013/2014. This research is action reseach as an effort to make ideas in action to improve or change something to real effect. There are some indicators such as, 1) observation data when formed a group 2) observation data when student told idea or question 3) observation data when student collaborative with the other 3) observation data when student noted material. Result of this research shows that ants’ communication can improve students’ activeness when learn trigonometry on grade 10th in SMA Negeri 3 Jombang, academic year 2013/2014. It can be showed by the percetage progress when observed students’ activeness from first cycle to the second cycle.
Keywords: application, ants’ communication, students’ activeness
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Pambayun, Hanifa Prahastami, and Endah Retnowati. "Penerapan teknik faded examples untuk meningkatkan kemampuan pemecahan masalah materi pengayaan trigonometri SMA." Jurnal Riset Pendidikan Matematika 5, no. 1 (May 25, 2018): 73. http://dx.doi.org/10.21831/jrpm.v5i1.12149.
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Penelitian ini bertujuan untuk menghasilkan dan mendeskripsikan pengembangan bahan ajar pengayaan trigonometri SMA menggunakan teknik faded examples yang berkualitas untuk meningkatkan kemampuan pemecahan masalah siswa. Kualitas bahan ajar yang dikembangkan mencakup aspek kevalidan, keefektifan, dan kepraktisan. Penelitian ini merupakan penelitian pengembangan dengan model Plomp yang mencakup tiga tahapan. (1) penelitian awal mencakup analisis kebutuhan dan analisis konteks, (2) pengembangan yang mencakup desain produk dan pembuatan produk, dan (3) evaluasi yang meliputi proses validasi dan proses implementasi. Proses pengembangan melibatkan dua ahli, satu orang guru dan 50 siswa (siswa kelas X pengayaan 1 dan X pengayaan 2) SMA IPA di Mataram. Hasil dari penelitian ini adalah bahan ajar pengayaan berupa buku guru dan buku siswa yang dikembangkan dengan menerapkan teknik faded examples. Pada buku pengayaan terdapat paket faded examples dengan jenis backward dan forward fading dimana pada akhir paket, siswa diminta untuk membuat sendiri soal sesuai dengan materi yang sedang dipelajari. Teknik ini dikembangkan oleh teori desain pembelajaran bernama Cognitive Load Theory (CLT). Hasil penelitian menunjukkan bahwa bahan ajar ini layak digunakan karena dinilai sangat baik secara isi dan penyajian oleh dosen validator, praktis oleh guru matematika dan praktis digunakan oleh siswa. Hasil ketuntasan belajar adalah sebanyak 100% siswa mencapai nilai minimal kemampuan pemecahan masalah. The application of faded examples techniques to improve student’s problem solving ability on trigonometry at high school level AbstractThis study was aimed to produce and describe the quality of the developed Trigonometric Senior High School Science Program Enrichment’s Instructional Materials using Faded-Examples Techniques to Improve Problem Solving Ability. The quality of the developed teaching materials include all aspects of validity, effectiveness, and practicality. This was a developmental research used three phases Plomp’s model which consists of: (1) preliminary studies which involved the needs and context analysis, (2) product design development, and (3) the evaluation process of product validation and implementation. The development process involves two experts as validator, one teacher, and 50 students (X pengayaan 1 and X pengayaan 2). The study results the trigonometric enrichment’s teaching materials which consists of the teacher’s textbook and the student’s textbook that was developed using the faded-examples technique. This technique based on The Cognitive Load Theory (CLT) instructional design. The results of the study showed that the quality of the developed trigonometric enrichment’s teaching materials is “very good” according to lecturer validation and “practical” according to the evaluation from the teachers and students. The results of the learning showed that 100% of the students passed the minimum grade criteria of problem solving skills.
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Qandil, Hassan, Shuping Wang, and Weihuan Zhao. "Algorithmically Optimized Hemispherical Dome as a Secondary Optical Element for the Fresnel Lens Solar Concentrator." Applied Sciences 9, no. 13 (July 8, 2019): 2757. http://dx.doi.org/10.3390/app9132757.
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The significance of this work lies in the development of a novel code-based, detailed, and deterministic geometrical approach that couples the optimization of the Fresnel lens primary optical element (POE) and the dome-shaped secondary optical element (SOE). The objective was to maximize the concentration acceptance product (CAP), while using the minimum SOE and receiver geometry at a given f-number and incidence angle (also referred to as the tracking error angle). The laws of polychromatic light refraction along with trigonometry and spherical geometry were utilized to optimize the POE grooves, SOE radius, receiver size, and SOE–receiver spacing. Two literature case studies were analyzed to verify this work’s optimization, both with a spot Fresnel lens POE and a spherical dome SOE. Case 1 had a 625 cm2 POE at an f-number of 1.5, and Case 2 had a 314.2 cm2 POE at an f-number of 1.34. The equivalent POE designed by this work, with optimized SOE radiuses of 13.6 and 11.4 mm, respectively, enhanced the CAP value of Case 1 by 52% to 0.426 and that of Case 2 by 32.4% to 0.45. The SOE’s analytical optimization of Case 1 was checked by a simulated comparative analysis to ensure the validity of the results. Fine-tuning this design for thermal applications and concentrated photovoltaics is also discussed in this paper. The algorithm can be further improved for more optimization parameters and other SOE shapes.
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Tamurih. "SUDUT-SUDUT BERELASI DENGAN GRAFIK FUNGSI SINUS DAN COSINUS." M A T H L I N E : Jurnal Matematika dan Pendidikan Matematika 1, no. 1 (February 1, 2016): 53–62. http://dx.doi.org/10.31943/mathline.v1i1.14.
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Trigonometry is the uppermost group of the most difficult materials collection in mathematics. Trigonometry is belonging to the materials that have the greatest number of concept even trigonometry is well known by the quantity of formula or identity and application from trigonometry. They are establish that trigonometry is a very important material. In fact, the majority of students which dislike the trigonometry and they have low mark even the lowest from another topics in mathematics. The main factor is the teacher. The teacher is lack innovative in teaching trigonometry material even the difficulties degree of trigonometry material same with the difficulties degree of the students which receive the material from their teacher. In order that, the writer try to give an idea which can be an alternative in teaching learning trigonometry, especially angles relations which have tens of angles relations. In determine the angles relations each quadrant, it can using the graph functions of sinus and cosines. It means that the graphs method can be an alternative in teaching learning trigonometry, especially angles relations.
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Hadi, Windia, and Ayu Faradillah. "Application of Discovery Learning Method in Mathematical Proof of Students in Trigonometry." Desimal: Jurnal Matematika 3, no. 1 (January 23, 2020): 73–82. http://dx.doi.org/10.24042/djm.v3i1.5713.
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Trigonometry is a part of mathematics in learning that is related to angles. The purpose of this study was to determine the effect of the application of discovery learning methods in students' mathematical proof ability on trigonometry. The research method used in this study is quasi-experimental. The population in this study was the second semester of 2016/2017. The sample was 66 people who were determined by purposive sampling. The instrument used in this study was a mathematically proof ability test. Analysis of the data used is the t-test. The results of this study are (1) based on an average score of mathematical proof ability The student's mathematical proof ability in applying the Discovery Learning Method to trigonometry is not higher than the mathematical proof ability of students who do not use the discovery method (2) there is no significant influence in the application of learning methods Discovery in students' mathematical proofs on trigonometry.
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Tuluk, Güler. "Knowledge of Slope Concept in Mathematics Textbooks in Undergraduate Education." Journal of Curriculum and Teaching 9, no. 3 (August 20, 2020): 161. http://dx.doi.org/10.5430/jct.v9n3p161.
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This questions the prevailing approach in the presentation of the concept of slope in teaching undergraduate in Turkey. For this purpose, five mathematics textbooks, were analyzed for problems related to slope, and similarities and differences were revealed. First, the subjects related to the slope in the textbooks were categorized and examined within the context in which they were handled. Therefore, this study is a qualitative study that adopts the interpretive paradigm. These categories are discussed in the form of connectivity, exploration, and purpose using the study for the context (Rezat, 2006). Stump (1999; 2001b) and Moore-Russo et al. (2011) studies were used for cognitive development. These are determined as geometric ratio, behavioral indicator, property determiner, algebraic ratio, parametric coefficient, functional property, linear constant, real life, physical property and trigonometry. Representations of the process skills were chosen as algebraic expressions, tables, and graphics. The concept is discussed in the form of calculus. In the use of technology (Akkoyunlu, 2002; Schware & Jaramillo, 1998), BCS, Scientific and Graphing Calculators, Internet are arranged. Definition, justification, and explanation for performance are arranged. When textbooks are compared, Turkey's textbooks contains more algebraic expressions, the use of the grounds and explanations and real-life connection, contains applications that use more formulas, the description is to use less highlighted is technology, other math they do not explicitly state their links with the subject areas. In general, it was seen that translated textbooks were mostly related to real life, equipped with explanations and justifications requiring cognitive competencies, and proceeded harmoniously between the subject area's main ideas and related ideas. These books use multi-step solved problems. Turkish textbooks need to be reviewed in terms of their functional areas in terms of context, cognitive need, representations, technology, and performance.
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Sathyapriya, S. "Application of Trigonometry in Meteorology and Seismology." International Journal for Research in Applied Science and Engineering Technology 7, no. 2 (February 28, 2019): 534–39. http://dx.doi.org/10.22214/ijraset.2019.2074.
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Ratnasari, Gamarina Isti. "The Application of Trigonometry on Problem Solving Strategy." Proceeding International Conference on Science and Engineering 3 (April 30, 2020): 389–92. http://dx.doi.org/10.14421/icse.v3.534.
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This study aims to: (1) describe students' problem solving strategies to solve trigonometric problems using a clinometer media and (2) comparison of the strategies used against student analysis in processing the data obtained. This type of research uses qualitative research. The population of this study was all students of class X consisting of 7 classes, with 39 research subjects. Data collection is done by direct observation of the results of student work. The results showed that (1) students' problem solving strategies to solve trigonometric problems using a clinometer media were divided into two strategies: students pay attention to angular size rather than distance and students pay attention to distance than angular size to determine the height of an object and (2) the strategy used students paying attention to angles rather than distance show more accurate results when students use angles than students pay attention to distances rather than angles to determine the height of an object.
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Wigati, Sri. "PENGARUH KEAKTIFAN DAN MINAT TERHADAP HASIL BELAJAR SISWA POKOK BAHASAN TRIGONOMETRI MELALUI MODEL PEMBELAJARAN BERBASIS MASALAH DI KELAS XSMA 15 SEMARANG." Jurnal Karya Pendidikan Matematika 5, no. 2 (October 29, 2018): 58. http://dx.doi.org/10.26714/jkpm.5.2.2018.58-62.
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Student's enthusiasm and interest in learning mathematics are factors that influence learning outcomes. Where in the application of problem-based learning models on trigonometric material that aims to improve learning outcomes, but in the application process will also appear the activeness of students during the learning process takes place. This is intended to supplement the problem-based learning process in stages, including: understanding the problem, making a solution plan, implementing the plan, and reviewing the results obtained. From these stages there will also appear student activity and interest in the mathematics learning process which certainly contributes to learning outcomes. So the purpose of the study is to determine the effect of activeness and interest in student learning outcomes on trigonometry subjects through problem-based learning models. This research was designed using the One-Shot Case Study design. In this design there is only one group treated. The population in this study were all students of SMA Negeri 15 Semarang. With the sampling technique in this study using the Random sampling technique, obtained a sample of students in class X 7. The variables used are the activeness and interest of students and are learning outcomes. The results of the study concluded that there was a significant influence between activity and interest in learning outcomes with a significant effect of 81.8% in the implementation of problem-based learning models.
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Denysyuk, V. P. "Generalized trigonometric functions and their applications." Astronomical School’s Report 11, no. 2 (2015): 163–66. http://dx.doi.org/10.18372/2411-6602.11.2163.
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Miana, Pedro J. "Convolutions, Fourier trigonometric transforms and applications." Integral Transforms and Special Functions 16, no. 7 (October 2005): 583–85. http://dx.doi.org/10.1080/10652460410001672951.
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Fonseca, Carlos M. da, M. Lawrence Glasser, and Victor Kowalenko. "Basic trigonometric power sums with applications." Ramanujan Journal 42, no. 2 (March 28, 2016): 401–28. http://dx.doi.org/10.1007/s11139-016-9778-0.
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Obaid, S. A. "Two new trigonometric formulas with applications." Applied Mathematics Letters 2, no. 4 (1989): 367–70. http://dx.doi.org/10.1016/0893-9659(89)90089-x.
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Alzer, Horst, and Man Kam Kwong. "Inequalities for trigonometric sums and applications." Aequationes mathematicae 94, no. 2 (June 6, 2019): 235–51. http://dx.doi.org/10.1007/s00010-019-00657-6.
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Dattoli, Giuseppe, Emanuele Di Palma, Federico Nguyen, and Elio Sabia. "Generalized Trigonometric Functions and Elementary Applications." International Journal of Applied and Computational Mathematics 3, no. 2 (April 1, 2016): 445–58. http://dx.doi.org/10.1007/s40819-016-0168-5.
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Alsadik, B. "ROBUST RESECTION MODEL FOR ALIGNING THE MOBILE MAPPING SYSTEMS TRAJECTORIES AT DEGRADED AND DENIED URBAN ENVIRONMENTS." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences V-1-2020 (August 3, 2020): 215–22. http://dx.doi.org/10.5194/isprs-annals-v-1-2020-215-2020.
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Abstract. Mobile mapping systems MMS equipped with cameras and laser scanners are widely used nowadays for different geospatial applications with centimetric accuracy either in project wise or national wise scales. The achieved positioning accuracy is very much related to the navigation unit, namely the GNSS and IMU onboard. Accordingly, in GNSS denied and degraded environments, the absolute positioning accuracy is worsened to few meters in some cases. Frequently, ground control points GCPs of a high positioning accuracy are used to align the MMS trajectories and to improve the accuracy when needed.The best way to integrate the MMS trajectories to the GCPs is by measuring them on the MMS images where the positioning accuracy is dropped. MMS images are mostly spherical panoramic (equirectangular) images and sometimes perspective and, in both types, it is required to precisely determine the images orientation in what is called as space resection or camera pose determination. For perspective images, the pose is conventionally determined by collinearity equations or by using projection and fundamental matrices. Whereas for equirectangular panoramic images it is based on resecting vertical and horizontal angles. However, there is still a challenge in the state–of–the–art of image pose determination because of the model nonlinearity and the sensitivity to proper initialization and spatial distribution of the points.In this research, a generic method is presented to solve the pose resection problem for the perspective and equirectangular images using oblique angles. The oblique angles are derived from the measured image coordinates and based on spherical trigonometry rules and vector geometry. The developed algorithm has proven to be highly stable and steadily converge to the global minimum. This is related to the robust geometric constraint offered by the oblique angles that are enclosed between the object points and the camera. As a result, the MMS trajectories are realigned accurately to the GCPs and the absolute accuracy is highly refined. Four experimental tests are presented where the results show the efficiency of the proposed angular based model in different cases of simulated and real data with different image types.
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Juaini, Muhammad. "Efektivitas Model Pembelajaran Kooperatif Tipe Teams Games Tournaments (TGT) untuk Meningkatkan Aktivitas dan Prestasi Belajar Siswa." MANDALIKA Mathematics and Educations Journal 2, no. 1 (June 21, 2020): 43. http://dx.doi.org/10.29303/jm.v2i1.1893.
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AbstractOne of the problems of education in Indonesia is the low quality at every level and unit of education, mainly primary and secondary education. Based on observations made by researchers at SMAN 3 Selong, it was shown that the learning outcomes of Grade X MIPA-3 students obtained the lowest classical completeness, which was 37.5%, so that they had not yet achieved the classical completeness set, namely students who achieved KKM ≥ 85%. This is because teachers still use the conventional approach that is dominated by the lecture method. To overcome this, we need a learning approach that can improve student learning outcomes by connecting students' initial knowledge with the material being studied, where students are more active in the teaching and learning process. One approach that can overcome the above is the Teams Games Tournaments (TGT) cooperative learning model approach. This study aims to determine the application of the TGT type learning model in improving student learning activities and achievement on the trigonometric subject matter in class X MIPA-3 SMAN 3 Selong academic year 2019/2020 with 36 students. This type of research is Classroom Action Research consisting of planning, implementation, observation, evaluation, and reflection. The results of the study show that students are more active in the teaching and learning process, and there is an increase in mathematics learning achievement in class X MIPA-3 SMAN 3 Selong by applying a cooperative model type of TGT on trigonometric subject matter learning. This improvement in achievement can be seen from the increase in the percentage of students completeness in classical learning in the first cycle with classical completeness of 65.71%, the second cycle with classical completeness of 76.47%, and in the third cycle with classical completeness of 90.09%. Besides that, after implementing the TGT type cooperative model, student learning activities increase each cycle with active, active, and very active criteria. From the results of this study, it can be concluded that the application of the TGT type cooperative model in trigonometric subject matter learning can improve student learning activities and achievement Class X MIPA-3 SMAN 3 Selong in the academic year 2019/2020. AbstrakSalah satu permasalahan pendidikan di Indonesia adalah rendahnya mutu pada setiap jenjang dan satuan pendidikan, khususnya pendidikan dasar dan menengah. Berdasarkan hasil pengamatan yang dilakukan peneliti di SMAN 3 Selong menunjukkan bahwa hasil belajar siswa kelas X MIPA-3 memperoleh ketuntasan klasikal yang paling rendah yaitu sebesar 37,5% sehingga belum mencapai ketuntasan klasikal yang ditetapkan yaitu siswa yang mencapai KKM ≥ 85%. Hal ini disebabkan karena guru masih menggunakan pendekatan konvensional yang di dominasi metode ceramah. Untuk mengatasinya, diperlukan suatu pendekatan pembelajaran yang mampu meningkatkan hasil belajar siswa dengan menghubungkan pengetahuan awal siswa dengan materi yang sedang dipelajari, dimana siswa lebih aktif dalam proses belajar mengajar. Salah satu pendekatan yang dapat mengatasi hal tersebut di atas adalah pendekatan model pembelajaran kooperatif tipe Teams Games Tournaments (TGT).Penelitian ini bertujuan untuk mengetahui penerapan model pembelajaran tipe TGT dalam meningkatkan aktivitas dan prestasi belajar siswa pada materi pokok trigonometri di kelas X MIPA-3 SMAN 3 Selong tahun pelajaran 2019/2020 dengan jumlah siswa 36 orang. Jenis penelitian ini adalah Penelitian Tindakan Kelas yang terdiri dari perencanaan, pelaksanaan, observasi, evaluasi dan refleksi.Hasil penelitian menunjukkan bahwa siswa lebih aktif dalam proses belajar mengajar dan terjadi peningkatan prestasi belajar matematika siswa kelas X MIPA-3 SMAN 3 Selong dengan menerapkan model kooperatif tipe TGT pada pembelajaran materi pokok trigonometri. Peningkatan prestasi ini dilihat dari meningkatnya presentase ketuntasan belajar siswa secara klasikal pada siklus I dengan ketuntasan klasikal sebesar 65,71%, siklus II dengan ketuntasan klasikal sebesar 76,47% dan pada siklus III dengan ketuntasan klasikal sebesar 90,09%. Selain itu setelah mengimplementasikan dengan model kooperatif tipe TGT, aktivitas belajar siswa meningkat tiap siklusnya dengan kriteria aktif, aktif, dan sangat aktif.Dari hasil penelitian ini dapat disimpulkan bahwa penerapan model kooperatif tipe TGT pada pembelajaran materi pokok trigonometri dapat meningkatkan aktivitas dan prestasi belajar siswa kelas X MIPA-3 SMAN 3 Selong tahun pelajaran 2019 / 2020.
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Bukovská, Z., and T. Šalát. "Topological results on sequences $\{n_k x\}^\infty_{k=1}$ and their applications in the theory of trigonometric series." Czechoslovak Mathematical Journal 43, no. 1 (1993): 115–23. http://dx.doi.org/10.21136/cmj.1993.128387.
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Et. al., Nitesh Kumar Sharma,. "A NewSpeed Power Area and Accuracy (SPAA) Aware Cordic Processing Unit By Vedic Mathematics For The Application of Computer Vision." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 2 (April 10, 2021): 3199–209. http://dx.doi.org/10.17762/turcomat.v12i2.2377.
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we are living in the era of fast processing applications like 3D, 5G, 9D. These types of application need a processing unit which have separate arithmetic unit & separate trigonometric unit which is well known as CORDIC processing unit. As we know Graphics processing unit is the brain of any graphics systems now a days there is Gaming specific systems are available which require ultra-high-speed GPU on those GPU there is separate trigonometric calculation processing unit is there which is called CORDIC. So, in this paper basically we proposed a novel architecture of CORDIC unit which is able to give the output in very less time. In this paper we also try to do the justice with the speed power area and accuracy Metrix.
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Rahmad, Fajar Maulana, and Abd Qohar. "Improving Proof Ability of Prospective Teachers with a Contextual Model on Trigonometry." Malikussaleh Journal of Mathematics Learning (MJML) 3, no. 1 (May 25, 2020): 4. http://dx.doi.org/10.29103/mjml.v3i1.2339.
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Proof ability of prospective teachers on Trigonometry material is still lacking. It can be seen when they carry out trigonometry proof that does not meet the proof indicators to conduct the research. This study aimed at improving proof ability of prospective teachers with a contextual model on Trigonometry materials. The research method used was classroom action research with the subjects of 30 students of Mathematics Education Study Program, State University of Malang, 2019. The research was conducted in two cycles by providing scaffolding action regarding proof steps, trigonometry identity scaffolding, and conflict cognitive of proof results. The research results showed that an increase of material indicator was 4%, an increase of completeness indicator was 24%, an increase of reason indicator was 59%, an increase of clarity indicator was 31%, an increase of conclusion indicator was 2%, and an increase of application capability indicator was 4% with a total increase of student’s ability was 23%.
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Sun, Yan Ling, Qi Cheng Xu, and Jing Hou. "Application of Computer Graphics with Truncated Trigonometric Series." Applied Mechanics and Materials 543-547 (March 2014): 1743–46. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.1743.
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In the visualization of nonlinear dynamic systems with computer, we construct the planar symmetry dynamic systems with truncated trigonometric series by Clifford A.Reiters method of constructing crystallographic groups. To analyze the characteristics of the iteration mapping with truncated trigonometric series. It used the operation of matrix product as tool. To construct dynamic systems of the nonlinear function with truncated trigonometric series. We construct two planar dynamic systems with truncated trigonometric series. Monte Carlo method is used to search the parameter vectors in the parameter space. The Lyapunov exponent is used to judge the characteristics of dynamical systems. We construct chaotic graphics in the cyclic windows. We present a method to construct symmetry dynamical systems which can be used to generate square plane tiling. A great of chaotic attractors in the fundamental regions can be continuously tiled without gaps in the plane. Furthermore, we can provide a plenty of material with a novel and unique structure for the decorative patterns of the buildings.
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VIROSZTEK, DÁNIEL. "APPLICATIONS OF AN INTERSECTION FORMULA TO DUAL CONES." Bulletin of the Australian Mathematical Society 97, no. 1 (October 17, 2017): 94–101. http://dx.doi.org/10.1017/s000497271700082x.
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We give a succinct proof of a duality theorem obtained by Révész [‘Some trigonometric extremal problems and duality’, J. Aust. Math. Soc. Ser. A 50 (1991), 384–390] which concerns extremal quantities related to trigonometric polynomials. The key tool of our new proof is an intersection formula on dual cones in real Banach spaces. We show another application of this intersection formula which is related to integral estimates of nonnegative positive-definite functions.
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Lai, Wan. "High-Precision Parallaxes and Their Astrophysical Applications." Symposium - International Astronomical Union 156 (1993): 213–18. http://dx.doi.org/10.1017/s0074180900173243.
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As demonstrated by USNO CCD parallax program, a CCD attached to a modest aperature telescope is capable of measuring stellar trigonometric parallax to a precision better than 1.0 mas. consequently, many objects previously regarded as being too distant for ground-based trigonometric distance determinations can now be considered.In this paper we show the High-precision parallaxes will provide a very good opportunity for the refinement of H-R digrammes and the calibration of luminosity criteria, we also refer to the open cluster and to determination of accurate stellar masses from close binanies.
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Baica, Malvina. "Trigonometric identities." International Journal of Mathematics and Mathematical Sciences 9, no. 4 (1986): 705–14. http://dx.doi.org/10.1155/s0161171286000844.
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In this paper the author obtains new trigonometric identities of the form2(p−1)(p−2)2∏k=1p−2(1−cos2πkp)p−1−k=pp−2which are derived as a result of relations in a cyclotomic fieldℛ(ρ), whereℛis the field of rationals andρis a root of unity.Those identities hold for every positive integerp≥3and any proof avoiding cyclotomic fields could be very difficult, if not insoluble. Two formulas∑k=1p−12(−1)(p2k)tanp−1−2kϕ=0 and−1+∑k=0p−12(−1)k(∑i=0p−1−2k2(p2k+2i)(k+1k))cosp−2kϕ=0stated only by Gauss in a slightly different form without a proof, are obtained and used in this paper in order to give some numeric applications of our new trigonometric identities.
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Sun, Wei, and Jun She An. "Design of High Performance Fixed Point CORDIC Processor." Advanced Materials Research 998-999 (July 2014): 597–601. http://dx.doi.org/10.4028/www.scientific.net/amr.998-999.597.
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To meet the demand for aerospace applications, high-speed computing transcendental functions such as trigonometric functions, we design a high-speed full-parallel CORDIC processor. On this basis,combining the optimized algorithm of simplifing pathway and adding-bits high-precision method , the original design has been improved. The experimental results show that improved design reduces hardware overhead compared to adding-bits high-precision design,and improves accuracy compared to fully parallel design. This high-speed fixed-point CORDIC has high precision and is suitable for high-speed applications in computing trigonometric and inverse trigonometric functions.
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Chen, Ting, and Shou Jiang Zhao. "Improved Trigonometric Grey Prediction and Application." Advanced Materials Research 912-914 (April 2014): 1276–78. http://dx.doi.org/10.4028/www.scientific.net/amr.912-914.1276.
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By the Markov chain trigonometric grey prediction model(TGM(1,1)) was improved. At last, the validity and applicability of the model are demonstrated by a simulation of container throughput of Fujian Province.
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Backhouse, John K. "From Heathrow to Hong Kong: An Application of Trigonometry." Mathematical Gazette 70, no. 452 (June 1986): 104. http://dx.doi.org/10.2307/3615767.
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