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Journal articles on the topic 'Trigonometry functions'
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1
Deddiliawan Ismail, Agung, and Rizal Dian Azmi. "PEMANFAATAN GEOMETER’S SKETCHPAD DALAM MELUKIS FUNGSI TRIGONOMETRI." JINoP (Jurnal Inovasi Pembelajaran) 3, no. 2 (November 28, 2017): 560. http://dx.doi.org/10.22219/jinop.v3i2.4690.
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ABSTRAK Trigonometri merupakan salah satu cabang ilmu Matematika yang banyak digunakan di berbagai bidang. Materi trigonometri kadang menyulitkan bagi para pendidik saat mengajarkan kepada mahasiswa. Ini dikarenakan materi – materi dalam trigonometri memerlukan suatu gambaran simulasi untuk mengajarkan konsep trigonometri kepada peserta didik. Untuk menggambarkan simulasi dari fungsi trigonometri tersebut diperlukan suatu media sebagai tuntunan mahasiswa, dimana media yang tepat untuk itu adalah Geometer’s Sketchpad. Berdasarkan hasil penelitian yang telah dilakukan maka dapat disimpulkan bahwa pembelajaran dengan memanfaatkan Geometer’s Sketchpad dapat membantu mahasiswa dalam melukis fungsi Trigonometri. Terlihat dari nilai probabilitas 0,000 < 0,05 yang menyatakan bahwa adanya peningkatan keterampilan mahasiswa dalam melukis grafik fungsi Trigonometri. Kata kunci: Trigonometri, Geometer’s Sketchpad. ABSTRACTTrigonometry is a part of the Mathematics which is used in various science area. Trigonometry material is sometimes difficult for teachers to teach students. This is due to the materials in trigonometry requires an illustration of the simulation to teach the basic concepts of trigonometry to students. To illustrate the simulation of the trigonometric functions need a media as the guidance of students, where appropriate media for that is Geometer's Sketchpad. Based on the research that has been done, it can be concluded that learning by utilizing Geometer's Sketchpad can assist students in painting Trig functions. Seen from a probability value 0.000 <0.05, which states that an increase in students' skills in drawing graphs of functions Trig.Keywords: Trigonometry, Geometer’s Sketchpad.
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Boyes, G. R. "Trigonometry for Non-Trigonometry Students." Mathematics Teacher 87, no. 5 (May 1994): 372–75. http://dx.doi.org/10.5951/mt.87.5.0372.
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This team-oriented student activity is designed to study selected trigonometric functions by constructing tables of values. These tables are then put to practical use. Familiarity with trigonometry is not needed, since all pertinent information is included. The activities, which could take up to three days, are aimed at ordinary middle school students or any students desiring an introduction to trigonometry.
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Weber, Keith. "Connecting Research to Teaching: Teaching Trigonometric Functions: Lessons Learned from Research." Mathematics Teacher 102, no. 2 (September 2008): 144–50. http://dx.doi.org/10.5951/mt.102.2.0144.
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Trigonometry is an important subject in the high school mathematics curriculum. As one of the secondary mathematics topics that are taught early and that link algebraic, geometric, and graphical reasoning, trigonometry can serve as an important precursor to calculus as well as collegelevel courses relating to Newtonian physics, architecture, surveying, and engineering. Unfortunately, many high school students are not accustomed to these types of reasoning (Blackett and Tall 1991), and learning about trigonometric functions is initially fraught with difficulty. Trigonometry presents many first-time challenges for students: It requires students to relate diagrams of triangles to numerical relationships and manipulate the symbols involved in such relationships. Further, trigonometric functions are typically among the first functions that students cannot evaluate directly by performing arithmetic operations.
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Weber, Keith. "Connecting Research to Teaching: Teaching Trigonometric Functions: Lessons Learned from Research." Mathematics Teacher 102, no. 2 (September 2008): 144–50. http://dx.doi.org/10.5951/mt.102.2.0144.
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Trigonometry is an important subject in the high school mathematics curriculum. As one of the secondary mathematics topics that are taught early and that link algebraic, geometric, and graphical reasoning, trigonometry can serve as an important precursor to calculus as well as collegelevel courses relating to Newtonian physics, architecture, surveying, and engineering. Unfortunately, many high school students are not accustomed to these types of reasoning (Blackett and Tall 1991), and learning about trigonometric functions is initially fraught with difficulty. Trigonometry presents many first-time challenges for students: It requires students to relate diagrams of triangles to numerical relationships and manipulate the symbols involved in such relationships. Further, trigonometric functions are typically among the first functions that students cannot evaluate directly by performing arithmetic operations.
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Antippa, Adel F. "The combinatorial structure of trigonometry." International Journal of Mathematics and Mathematical Sciences 2003, no. 8 (2003): 475–500. http://dx.doi.org/10.1155/s0161171203106230.
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The native mathematical language of trigonometry is combinatorial. Two interrelated combinatorial symmetric functions underlie trigonometry. We use their characteristics to derive identities for the trigonometric functions of multiple distinct angles. When applied to the sum of an infinite number of infinitesimal angles, these identities lead to the power series expansions of the trigonometric functions. When applied to the interior angles of a polygon, they lead to two general constraints satisfied by the corresponding tangents. In the case of multiple equal angles, they reduce to the Bernoulli identities. For the case of two distinct angles, they reduce to the Ptolemy identity. They can also be used to derive the De Moivre-Cotes identity. The above results combined provide an appropriate mathematical combinatorial language and formalism for trigonometry and more generally polygonometry. This latter is the structural language of molecular organization, and is omnipresent in the natural phenomena of molecular physics, chemistry, and biology. Polygonometry is as important in the study of moderately complex structures, as trigonometry has historically been in the study of simple structures.
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John Hornsby, E. "A Method of Graphing f(x) = A sin (Bx + C) + D." Mathematics Teacher 83, no. 1 (January 1990): 51–53. http://dx.doi.org/10.5951/mt.83.1.0051.
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Baric, Mate, David Brčić, Mate Kosor, and Roko Jelic. "An Axiom of True Courses Calculation in Great Circle Navigation." Journal of Marine Science and Engineering 9, no. 6 (May 31, 2021): 603. http://dx.doi.org/10.3390/jmse9060603.
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Based on traditional expressions and spherical trigonometry, at present, great circle navigation is undertaken using various navigational software packages. Recent research has mainly focused on vector algebra. These problems are calculated numerically and are thus suited to computer-aided great circle navigation. However, essential knowledge requires the navigator to be able to calculate navigation parameters without the use of aids. This requirement is met using spherical trigonometry functions and the Napier wheel. In addition, to facilitate calculation, certain axioms have been developed to determine a vessel’s true course. These axioms can lead to misleading results due to the limitations of the trigonometric functions, mathematical errors, and the type of great circle navigation. The aim of this paper is to determine a reliable trigonometric function for calculating a vessel’s course in regular and composite great circle navigation, which can be used with the proposed axioms. This was achieved using analysis of the trigonometric functions, and assessment of their impact on the vessel’s calculated course and established axioms.
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Anand, M. Clement Joe, and Janani Bharatraj. "Gaussian Qualitative Trigonometric Functions in a Fuzzy Circle." Advances in Fuzzy Systems 2018 (June 3, 2018): 1–9. http://dx.doi.org/10.1155/2018/8623465.
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We build a bridge between qualitative representation and quantitative representation using fuzzy qualitative trigonometry. A unit circle obtained from fuzzy qualitative representation replaces the quantitative unit circle. Namely, we have developed the concept of a qualitative unit circle from the view of fuzzy theory using Gaussian membership functions, which play a key role in shaping the fuzzy circle and help in obtaining sharper boundaries. We have also developed the trigonometric identities based on qualitative representation by defining trigonometric functions qualitatively and applied the concept to fuzzy particle swarm optimization using α-cuts.
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Kaplan, Gail. "Activities for Students: Trigonometry through a Ferris Wheel." Mathematics Teacher 102, no. 2 (September 2008): 138–43. http://dx.doi.org/10.5951/mt.102.2.0138.
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In the traditional study of trigonometry, students graph the basic trigonometric functions. They study phase shifts, horizontal and vertical translations, and changes in period so that they can sketch the graph of generalized functions such as f(x) = acosb(x − c) + d by recognizing the information provided by the constants a, b, c, and d. Far too often, students master this material by memorizing it and thus have little comprehension of why and how each value in an equation affects the graph.
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Kaplan, Gail. "Activities for Students: Trigonometry through a Ferris Wheel." Mathematics Teacher 102, no. 2 (September 2008): 138–43. http://dx.doi.org/10.5951/mt.102.2.0138.
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In the traditional study of trigonometry, students graph the basic trigonometric functions. They study phase shifts, horizontal and vertical translations, and changes in period so that they can sketch the graph of generalized functions such as f(x) = acosb(x − c) + d by recognizing the information provided by the constants a, b, c, and d. Far too often, students master this material by memorizing it and thus have little comprehension of why and how each value in an equation affects the graph.
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Lorenzo, Carl F., and Tom T. Hartley. "Fractional Trigonometry and the Spiral Functions." Nonlinear Dynamics 38, no. 1-4 (December 2004): 23–60. http://dx.doi.org/10.1007/s11071-004-3745-9.
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Moussa, Ali. "MATHEMATICAL METHODS IN ABŪ AL-WAFĀʾ'S ALMAGEST AND THE QIBLA DETERMINATIONS." Arabic Sciences and Philosophy 21, no. 1 (February 18, 2011): 1–56. http://dx.doi.org/10.1017/s095742391000007x.
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AbstractThe problem of the Qibla was one of the central issues in the scientific culture of Medieval Islam, and to solve it properly, one needed mathematics and observation. The mathematics consisted of two parts: plane trigonometry (to construct the trigonometric tables) and spherical trigonometry (as the problem belongs to spherical astronomy). Observation and its instruments were needed to find the geographical coordinates of Mecca and the given location; these coordinates (latitude, longitude) will be the input data in the formulas of the Qibla. In his Almagest, Abū al-Wafāʾ produced a brilliant work to solve the problem. He worked on both mathematics and observation, and reached accurate and easy “modern” solutions. In plane trigonometry, he introduced the trigonometric functions with new definitions, proved the formulas for sines, approximated the sine of degree one, and thus constructed the tables of sines and tangents with high accuracy. In spherical trigonometry, he proved four new spherical theorems, including the tangent rule (which was based on the new definitions and this rule allowed him to work out the easiest solution, as will be shown). In observation, he described three instruments which he used over several years in Baghdad. This paper is a detailed technical and analytical description of Abū al-Wafāʾ's mathematical methods and the Qibla determinations, supplemented with many important original Arabic texts with translation and commentary.
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Gambini, Alessandro, Giorgio Nicoletti, and Daniele Ritelli. "Keplerian trigonometry." Monatshefte für Mathematik 195, no. 1 (January 28, 2021): 55–72. http://dx.doi.org/10.1007/s00605-021-01512-0.
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AbstractTaking the hint from usual parametrization of circle and hyperbola, and inspired by the pathwork initiated by Cayley and Dixon for the parametrization of the “Fermat” elliptic curve $$x^3+y^3=1$$ x 3 + y 3 = 1 , we develop an axiomatic study of what we call “Keplerian maps”, that is, functions $${{\,\mathrm{{\mathbf {m}}}\,}}(\kappa )$$ m ( κ ) mapping a real interval to a planar curve, whose variable $$\kappa $$ κ measures twice the signed area swept out by the O-ray when moving from 0 to $$\kappa $$ κ . Then, given a characterization of k-curves, the images of such maps, we show how to recover the k-map of a given parametric or algebraic k-curve, by means of suitable differential problems.
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Abo Touk, Sarah, Zina Al Houchan, and Mohamed El Bachraoui. "On q-analogues for trigonometric identities." Analysis 40, no. 2 (May 1, 2020): 105–12. http://dx.doi.org/10.1515/anly-2018-0040.
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AbstractIn this paper we will give q-analogues for the Pythagorean trigonometric identity {\sin^{2}z+\cos^{2}z=1} in terms of Gosper’s q-trigonometry. We shall also give new q-analogues for the duplicate trigonometric identity {\sin(x-y)\sin(x+y)=\sin^{2}x-\sin^{2}y}. Moreover, we shall give a short proof for an identity of Gosper, which was also established by Mező. The main argument of our proofs is the residue theorem applied to elliptic functions.
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Putranti, Sri Rejeki Dwi. "Relationship between Trigonometry Functions with Hyperbolic Function." Aloha International Journal of Multidisciplinary Advancement (AIJMU) 1, no. 4 (April 30, 2019): 82. http://dx.doi.org/10.33846/aijmu10402.
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Many engineering problems can be solved by methods involving complex numbers and complex functions. In the definitions below we will prove the relationship between trigonometric functions and hyperbolic functions, where the hyperbolic function is an extension of the trigonometric function.
Keywords: trigonometric functions; hyperbolic functions
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Stavek, Jiri. "On the Hidden Beauty of Trigonometric Functions." Applied Physics Research 9, no. 2 (March 17, 2017): 57. http://dx.doi.org/10.5539/apr.v9n2p57.
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In the unit circle with radius R = E0 = mc2 = 1 we have defined the trigonometric function cos(Theta) = v/c. The known trigonometric functions revealed the hidden relationships between sensible energy, latent energy, sensible momentum and latent momentum of the moving object, and the absorbed momentum from outside and the available momentum in the outside of the moving object. We present the trigonometric concept inspired by the old Babylonian clay tablet IM 55357 and based on the knowledge of the School of Athens (the fresco of Raphael) and the work of many generations of the Masters of trigonometry. The concept of the Divided Line of Plato can be now quantitatively tested. For the experimental analysis of this concept we propose to study in details the very well known beta decay of RaE to determine the sensible and latent energy (heat) of those beta particles and the sensible and latent energy of the remaining nucleus. The longitudinal momentum and the transverse (latent) momentum can be studied on the effects of the slow neutrons. The longitudinal momentum and the transverse momentum of photons can be manipulated in a convenient medium in order to prepare slow photons. The photoormi effect might improve the efficiency of the light-to-electricity conversion and the efficiency of the light-to-heat conversion.
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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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Lewis, Barry. "Fibonacci numbers and trigonometry." Mathematical Gazette 88, no. 512 (July 2004): 194–204. http://dx.doi.org/10.1017/s002555720017490x.
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This article started life as an investigation into certain aspects of the Fibonacci numbers, ‘morphed’ seamlessly into the structure of some infinite matrices and finally resolved into a general set of results that link structural aspects of Fibonacci numbers with trigonometric and hyperbolic functions. It is a surprising fact, but while I can find evidence that the link between these areas has been noted in the past, I can find no evidence that the link has been systematically developed.
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Lewis, Barry. "Trigonometry and Fibonacci numbers." Mathematical Gazette 91, no. 521 (July 2007): 216–26. http://dx.doi.org/10.1017/s0025557200181550.
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This article sets out to explore some of the connections between two seemingly distinct mathematical objects: trigonometric functions and the integer sequences composed of the Fibonacci and Lucas numbers. It establishes that elements of Fibonacci/Lucas sequences obey identities that are closely related to traditional trigonometric identities. It then exploits this relationship by converting existing trigonometric results into corresponding Fibonacci/Lucas results. Along the way it uses mathematical tools that are not usually associated with either of these objects.
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Hermann, James P. "Animated Circular Functions with a Microcomputer." Mathematics Teacher 81, no. 5 (May 1988): 382–84. http://dx.doi.org/10.5951/mt.81.5.0382.
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Students often have difficulty conceptualizing the idea of a circular function as a winding process and associating real numbers with points P(u. u) on the unit circle. This concept and the idea of periodicity of circular functions are at the heart of trigonometry.
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Gould, Doug, and Denise A. Schmidt. "Trigonometry Comes Alive through Digital Storytelling." Mathematics Teacher 104, no. 4 (November 2010): 296–301. http://dx.doi.org/10.5951/mt.104.4.0296.
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Gould, Doug, and Denise A. Schmidt. "Trigonometry Comes Alive through Digital Storytelling." Mathematics Teacher 104, no. 4 (November 2010): 296–301. http://dx.doi.org/10.5951/mt.104.4.0296.
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Daire, Sandra Argüelles. "The Back Page: My Favorite Lesson: Transforming Functions." Mathematics Teacher 103, no. 9 (May 2010): 704. http://dx.doi.org/10.5951/mt.103.9.0704.
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The day I held a graphing calculator for the first time, I decided to use it as a tool to teach transformations of functions. After years of revisions and many calculators later, this lesson is still one of my favorites. Whether I am teaching algebra, trigonometry, or calculus, this topic is universal and as necessary to students struggling with high school mathematics as to more advanced students.
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Daire, Sandra Argüelles. "The Back Page: My Favorite Lesson: Transforming Functions." Mathematics Teacher 103, no. 9 (May 2010): 704. http://dx.doi.org/10.5951/mt.103.9.0704.
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The day I held a graphing calculator for the first time, I decided to use it as a tool to teach transformations of functions. After years of revisions and many calculators later, this lesson is still one of my favorites. Whether I am teaching algebra, trigonometry, or calculus, this topic is universal and as necessary to students struggling with high school mathematics as to more advanced students.
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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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Alajmi, Amal H. "Twelfth Grade Kuwaiti Students’ Identification of Domain and Range in Graphical Representation of Function and the Meaning they Ascribe to them." Journal of Educational and Psychological Studies [JEPS] 13, no. 3 (July 11, 2019): 576. http://dx.doi.org/10.24200/jeps.vol13iss3pp576-591.
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This research investigated twelfth grade students' performance in identification of domain and range of functions in a graphical representation. The study focused on four types of functions: polynomial, trigonometry, piecewise and discontinuous. The study also aimed to identify the meaning that students gave for the domain and range and how they identified them. To collect the data two instruments were used: a test and an interview. A sample of 216 students participated in the study. The results showed a low performance in identifying domain and range for functions in graphical representation. The T-test indicated a statistical difference in students’ performance in domain and range in favor of domain. The results indicated a statistically significant difference in students' performance among the different types of function. Tukey test showed that the difference was in favor of polynomial against the other types of function. Also there was a significant difference between trigonometry and piecewise items in favor of trigonometry. The interviews revealed that students’ meaning and common practices in identifying the domain and range reflected misunderstandings. Some of them highlighted that the domain is the x-axis and y-axis or the x-intercept and y- intercept. Others considered that the curve as the domain or the range.
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Griffiths, Martin. "Is trigonometry the preserve of the mathematical élite?" Mathematical Gazette 95, no. 533 (July 2011): 256–61. http://dx.doi.org/10.1017/s0025557200002977.
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This article, rather than purporting to be any sort of serious statistical analysis of the situation, is intended in some small way to foster further debate amongst school teachers, university lecturers, examiners, curriculum designers and policy makers regarding the level of mathematical skill and knowledge possessed in certain areas by students embarking on mathematics degree programmes. The title serves merely to set the scene, and to indicate our relatively narrow focus here. However, a whole host of mathematical words or phrases could have replaced ‘trigonometry’, and it would appear that much of the mathematics associated with straightforward A level work on functions causes even fairly bright students to struggle. Surely the study of functions ought to be regarded as a fundamental element of learning mathematics, and the acquisition of understanding in this area might consequently be seen as something of fundamental importance?
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Coghetto, Roland. "Some Facts about Trigonometry and Euclidean Geometry." Formalized Mathematics 22, no. 4 (December 1, 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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Olawale, Olanrewaju Rasaki. "On Two Covariates Cosine and Sine Noisy-Wave Trigonometry Regression of Heartbeats." Academic Journal of Applied Mathematical Sciences, no. 510 (October 25, 2019): 140–49. http://dx.doi.org/10.32861/ajams.510.140.149.
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This paper proposes and describes the acumen on alternate two covariates linear Cosine and Sine regression functions that possessed a noisy-wave or tone frequencies via wave-trend of actualized observations of regressors and responsive variable needed in fitting a wavy equation of trigonometry regression. The method of maximum likelihood was used in estimating parameters associated to the Cosine and Sine alternate functions via vector coefficients as well as their distributional and residual properties. The estimations obtained via the method were enthralled to the noisy-wave mesokurtic observations of babies’ rate of heartbeats exactly an hour after birth (HR1), two hours after birth (HR2) and three hours after birth (HR3). The implementation and illustrative application was via R using the heartbeat dataset. It was gleaned that the trigonometry equation line .......
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Wells, Cacey. "Exploring Accessibility: An Application of Inverse Trigonometric Functions." Mathematics Teacher 112, no. 6 (April 2019): 480. http://dx.doi.org/10.5951/mathteacher.112.6.0480.
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Each school year, students enter our classrooms with unique experiences and perspectives that ought to be shared. One year, I noticed a student in our school who used a wheelchair. When I saw how difficult it was for that student to navigate the ramps in our school, I began to think about a trigonometry lesson focused on accessibility. I wanted to use mathematics to explore what life was like—albeit to a minor degree—for those with disabilities. The lesson objective was to explore angles of incline in wheelchair ramps to determine whether such ramps truly offer accessibility.
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Mulyawati, Cut, Salmawaty Salmawati, Muhammad Subianto, and Reza Wafdan. "TEACHING MEDIA DEVELOPMENT OF MATHEMATIC IN THE MATERIALS TRIGONOMETRY SUM AND TWO ANGLES DIFFERENCE BY USING GUI MATLAB." Jurnal Natural 17, no. 2 (September 4, 2017): 69. http://dx.doi.org/10.24815/jn.v0i0.7032.
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Abstract. The aim of this research is to develop teaching media for mathematics specifically for materials on trigonometry using GUI Matlab. This media can be used as teaching and learning aid for students at senior high school, grade XI in the first semester. This learning media consists of instructions on how to use the media, learning materials, exercises and profile. The trigonometry materials which are discussed in this learning media consist of the sum and difference of two angles. The limitation on the angles that can be used are special angles in the interval -360o £ a,b £ 360o. The special angles are 0o, ±30o, ±45o, ±60o, ±90o, ±120o, ±135o, ±150o, ±180o, ±210o, ±225o, ±240o, ±270o, ±300o, ±315o, ±330o, and ±360o. The trigonometry functions such as sinus, cosine and as well as the operation addition (+) and subtraction (-) can be selected by hitting the appropriate button. Within each step, there is a check button and a next button to check the input true or false. If the value that entered incorrectly then the next step will not displayed and warning box will appear to report the location of error. Users have to fix the error in order to continue to the next step. Keywords: teaching learning media, trigonometry, GUI Matlab
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Willis, George. "A noncommutative half-angle formula." Bulletin of the Australian Mathematical Society 69, no. 3 (June 2004): 369–82. http://dx.doi.org/10.1017/s0004972700036157.
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The half-angle formulæ, familiar from trigonometry, can be used to compute the polar decomposition of the operator on l2(ℤ) of convolution by δ0 + δ1. This calculation is extended here to a non-commutative setting by computing the polar decomposition of certain convolution operators on the spaces of square integrable functions of free groups.
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Homa, Agostinho Iaqchan Ryokiti. "Robotics Simulators in STEM education." Acta Scientiae 21, no. 5 (October 7, 2019): 178–91. http://dx.doi.org/10.17648/acta.scientiae.5417.
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This article discusses STEM (Science, Technology, Engineering and Mathematics) education as an initiative from various countries around the world to address young people's lack of interest in careers in Science, Mathematics, Technology and Engineering. Understanding that STEM education must explore two or more of STEM themes, using transdisciplinarity, engaging the student in activities with this approach, we present the studies of an activity proposal integrating Engineering, Technology and Mathematics with the objective of learning Mathematics. In this activity students work with situations involving robotics and, for solution, use robotic arm simulators, developed in GeoGebra software, that simplify the real environment in which the robotic arm manipulates an object positioned in the plane, taking to organize strategies by identifying and applying mathematics, such as trigonometry with right triangle, trigonometric identities, inverse trigonometric functions, to solve the problem. An experiment was conducted to validate the simulators with undergraduate mathematics students from Universidade Luterana do Brasil (ULBRA) in the city of Canoas in Rio Grande do Sul. The results indicate that it is possible to integrate the STEM areas with the developed simulators, being indicated for activities with high school students (10th or 11th grade).
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Dantas, Aleksandre Saraiva. "O USO DO GEOGEBRA NO ENSINO DE TRIGONOMETRIA: UMA EXPERIÊNCIA COM ALUNOS DO ENSINO MÉDIO." Ciência e Natura 37 (August 7, 2015): 143. http://dx.doi.org/10.5902/2179460x14503.
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http://dx.doi.org/10.5902/2179460X14503This research analyzes if the work with GeoGebra facilitates learning concepts of trigonometry and knowing the perceptions of students about the use of GeoGebra in teaching trigonometry. For this, it makes use of application of assessments and interviews with the students of courses of IFRN. Data analysis shows that, with the use of GeoGebra, students showed more significant learning of several aspects of the behavior of the sine and cosine functions when compared with teaching through lectures with the use of teaching resources more common as book and whiteboard. The students themselves recognized that the use of this software is able to help you better understand the aspects of the behavior of these functions, highlighting the ease of use of GeoGebra and the importance of its use in teaching mathematics. However, for the current and future teachers feel able to work with GeoGebra or any other software, it is essential that the vocational training courses for teachers to develop strategies that ensure effectively the ability to use these tools, the critically and creatively way, and not just another fad that will in no way help improve the teacher’s work and the student’s learning.
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Putranti, Sri Rejeki Dwi. "The Application of The Use Integration Technique in Solving An Integral Problem." Aloha International Journal of Multidisciplinary Advancement (AIJMU) 2, no. 7 (July 28, 2020): 155. http://dx.doi.org/10.33846/aijmu20702.
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There are many integration techniques that can be used to solve an integral problem.In this material, several integration techniques will be discussed including substitution, the properties of algebra and trigonometry and techniques commonly used in test books.If we are faced with integral problems that cannot be solved by techniques ,what we have learned, we use partial integral techniques. Partial integration technique is obtained by integrating the derivative formula of the product by two functions.
Keywords: integration technique; substitution; partial integration technique
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Dorner, Bryan C. "Delving Deeper: Chordic vs. CORDIC: How Calculators and Students Compute Sines and Cosines." Mathematics Teacher 106, no. 6 (February 2013): 472–78. http://dx.doi.org/10.5951/mathteacher.106.6.0472.
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Students who have grown up with computers and calculators may take these tools' capabilities for granted, but I find something magical about entering arbitrary values and computing transcendental functions such as the sine and cosine with the press of a button. Although the calculator operates mysteriously, students generally trust technology implicitly. However, beginning trigonometry students can compute the sine and cosine of any angle to any desired degree of precision using only simple geometry and a calculator with a square root key.
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Hughes, Barnabas B., F. M., and Lois Whitman Freier. "The Sierra Curve—an Introduction to Periodic Concepts." Mathematics Teacher 84, no. 6 (September 1991): 434–41. http://dx.doi.org/10.5951/mt.84.6.0434.
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“Two important elements in trigonometry are the ideas of periodicity and periodic functions.” So began James E. Sconyers when he shared his teaching idea “A Simple Periodic Function” (Sconyers 1986). His clear exposition inspired what follows, although the technique used here differs radically from Sconyers's. The computer is used as a tool for making changes in an unusual periodic function-the Sierra curve, so called because it resembles a mountain chain in the western United States. By appropriate directed inputs, students transform the shape of the Sierra curve. In so doing, they investigate four characteristics of many periodic functions: period, amplitude, horizontal shift, and vertical shift. A listing of the program for the Apple II computer appears in the Appendix.
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Fonseca, Laerte Silva da, Edmo Fernandes Carvalho, Luciano Pontes da Silva, and Kleyfton Soares da Silva. "O papel das Funções Cognitivas em Praxeologias de Tipos de Tarefas Matemáticas." Jornal Internacional de Estudos em Educação Matemática 13, no. 3 (January 12, 2021): 321–28. http://dx.doi.org/10.17921/2176-5634.2020v13n3p321-328.
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ResumoO objetivo principal deste trabalho é descrever uma análise sobre como as funções cognitivas atuam diretamente em organizações praxeológicas relativas a tipos de tarefas trigonométricas, relevando a complexidade neurocognitiva para realização das mesmas. A metodologia considerou uma pesquisa bibliográfica, ressaltando-se a importância de aproximar elementos da Teoria Antropológica do Didático (TAD) e da Neurociência Cognitiva. Foi verificado que para a realização de tipos de tarefas matemáticas, no campo da Trigonometria, cuja organização praxeológica esteja bem definida é possível atribuí-las aos estudantes como um convite ao desafio e, de forma gradativa, respeitando-se as condições da neurofisiologia do cérebro. Desse modo, possíveis dificuldades de estudantes frente um determinado saber matemático, pode ser atribuído ao tipo de tarefa proposta. O estudo de algumas funções cognitivas corrobora de certo modo com o estudo dessas dificuldades. Permite inclusive, compreender as implicações da falta de sentido das matemáticas escolares na vida do sujeito. Outro ponto importante a ser destacado remete à necessidade dos cursos de formação de professores de matemática oportunizar aos licenciandos conhecimentos de neurociência cognitiva, pois quanto mais se sabe sobre o funcionamento do cérebro, melhor será a escolha dos tipos de tarefas matemáticas para apresentá-las tanto nas salas de aulas, como nos livros didáticos.
Palavras-chave: Funções Cognitivas. Praxelogias. Tipos de Tarefas Matemáticas.
AbstractThe main objective of this work is to describe an analysis of how cognitive functions act directly in praxeological organizations related to types of trigonometric tasks, emphasizing the neurocognitive complexity to perform them. The methodology considered a bibliographical research, highlighting the importance of approaching elements of the Didactic Anthropological Theory and Cognitive Neuroscience. It was verified that for the accomplishment of types of mathematical tasks, in the field of Trigonometry, whose praxeological organization is well defined, it is possible to attribute them to the students as an invitation to the challenge and, in a gradual way, respecting the conditions of the neurophysiology of the brain. Thus, possible difficulties of students in the face of certain mathematical knowledge, can be attributed to the type of task proposed. The study of some cognitive functions corroborates in a way with the study of these difficulties. It even allows us to understand the implications of the lack of meaning of school mathematics in people's lives. Another important point to be highlighted is the need for training courses for mathematics teachers to give graduates the knowledge of cognitive neuroscience, since the more we know about brain functioning, the better the choice of the types of mathematical tasks to present them in classrooms, as in textbooks.
Keywords: Cognitive Functions. Praxeologies. Types of Math Tasks.
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Iyanda, Falade Kazeen, Ismail Baoku, and Gwanda Yusuf Ibrahim. "COMPUTATIONAL SOLUTION OF TEMPERATURE DISTRIBUTION IN A THIN ROD OVER A GIVEN INTERVAL I={x├|0." FUDMA JOURNAL OF SCIENCES 5, no. 1 (August 17, 2021): 608–18. http://dx.doi.org/10.33003/fjs-2021-0501-693.
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In this paper, two analytical–numerical algorithms are formulated based on homotopy perturbation method and new iterative method to obtain numerical solution for temperature distribution in a thin rod over a given finite interval. The effects of different parameters such as the coefficient which accounts for the heat loss and the diffusivity constant are examined when initial temperature distribution (trigonometry and algebraic functions) are considered. The error in both algorithms approaches to zero as the computational length increases. The proposed algorithms have been demonstrated to be quite flexible, robust and accurate. Thus, the algorithms are established as good numerical tools to solve several problems in applied mathematics and other related field of sciences
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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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Horobets, Yevhen. "Estimation of the error of the simplified algorithm of processing of functions of deflations of deformed frames of bodies of rolling stock." Technology audit and production reserves 4, no. 1(60) (June 30, 2021): 20–24. http://dx.doi.org/10.15587/2706-5448.2021.237296.
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The study is aimed at assessing the size of the error that arises when processing the results of examining the geometric characteristics of the bearing structures of rolling stock units using an algorithm without using trigonometric functions. The object of the research is a method of simplified alignment of the deflection function of body frame beams to the horizontal plane. One of the biggest problem areas is the lack of understanding by some customers of the work of the possibility of using this algorithm due to the lack of information about the errors that arise in the simplified calculation. The study was carried out by comparing the results of processing the initial data by two methods, obtained during the work on the inspection of the state of the supporting structures of the unit of the shunting diesel locomotive TGM6. One method, the algorithm of which is the subject of this study, assumes that no complex calculations are used during data processing. The second method involves the use of an algorithm for aligning the deflection functions of the body frame beams of a rolling stock unit of railways in the horizontal plane, taking into account all trigonometry tools, which will exclude the accompanying calculation errors of the simplified method. After processing the initial data, two sets of results were obtained – with the desired calculation error and without. Comparison of these datasets yielded an error value for frame tilt of 5.7. For clarity, the size of the error was compared with the expanded uncertainty values of the main sources of uncertainty in the methodology for examining the bearing structures of rolling stock. On the basis of the analysis of two methods of leveling the inclination to the horizontal plane of the deformed rolling stock body frame, the expediency of such an approach has been proved. The results obtained make it possible to reasonably use the Simplified approach to processing the data obtained during the survey of the geometric characteristics of the rolling stock. If necessary, the developed mathematical model can be used to improve the accuracy of calculating the uncertainty of measurements of geometric characteristics, as well as for use in the study of modification of existing or development of new measurement techniques
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Khairudin, Khairudin. "KEMAMPUAN AWAL KALKULUS MAHASISWA PENDIDIKAN MATEMATIKA." Edukasi: Jurnal Pendidikan 18, no. 1 (June 7, 2020): 50. http://dx.doi.org/10.31571/edukasi.v18i1.1679.
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<p class="StyleAuthorBold"><strong>Abstrak</strong></p><p>Penelitian bertujuan untuk mendeskripsikan tingkat kemampuan awal Kalkulus mahasiswa Pendidikan Matematika FKIP Universitas Bung Hatta tahun pertama. Metode penelitian menggunakan metode deskriptif. Subjek penelitian adalah mahasiswa yang mengambil mata kuliah Kalkulus Diferensial pada semester kedua. Instrumen penelitian menggunakan tes <em>diagnostic</em> yang dikembangkan oleh Stewart dengan materi aljabar, Geometri, Trigonometri, dan Fungsi serta wawancara terhadap peserta. Tenik analisis data menggunakan analisis dekriptif. Berdasarkan hasil penelitian, terlihat bahwa kemampuan awal mahasiswa berada pada tingkat sangat rendah, yaitu 8,6%. Hasil wawancara terhadap 6 orang mahasiswa yang mempunyai kemampuan skor tinggi, sedang, dan rendah menyatakan bahwa mahasiswa memerlukan tambahan pengetahuan tentang konsep bilangan serta sifat-sifatnya, operasi aljabar, visualisasi dengan teknologi serta konsep fungsi. Berdasarkan hasil tersebut, diperlukan strategi pembelajaran pada mata kuliah Kalkulus yang berbasis teknologi untuk memberi pemahaman konsep Kalkulus.</p><p> </p><p class="StyleAuthorBold"><strong><em>Abstract</em></strong></p><p><em>The research aimed to describe the initial ability level of Mathematics Education in the first year of the Mathematics Education Faculty of Bung Hatta University. The research method used descriptive. The research subjects were students who took Differential Calculus courses in the second semester. The research instrument used diagnostic tests developed by Stewart with algebraic material, Geometry, Trigonometry, and Functions as well as interviews with participants. Data analysis techniques used descriptive analysis. Based on the results of the research, it appeared that the initial ability of students is at a very low level, which is 8.6%. The results of interviews with 6 students who have the ability to score high, medium, and low stated that students need additional knowledge about the concept of numbers and their properties, algebraic operations, visualization with technology and the concept of functions. Based on these results, a learning strategy for technology-based Calculus is needed to provide an understanding of the Calculus concept.</em></p>
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Girg, Petr, and Lukáš Kotrla. "Generalized trigonometric functions in complex domain." Mathematica Bohemica 140, no. 2 (2015): 223–39. http://dx.doi.org/10.21136/mb.2015.144328.
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Bhayo, B. A., and J. Sandor. "Inequalities connecting generalized trigonometric functions with their inverses." Issues of Analysis 20, no. 2 (December 2013): 82–90. http://dx.doi.org/10.15393/j3.art.2013.2385.
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Meisel, David D., Kenneth F. Kinsey, and Charles H. Recchia. "Microcomputers in an Introductory College Astronomy Laboratory: A Software Development Project." International Astronomical Union Colloquium 105 (1990): 175–76. http://dx.doi.org/10.1017/s0252921100086656.
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We have developed software for the Apple IIe series of microcomputers for use in labs in an introductory astronomy course. This software emphasizes a toolkit approach to data analysis; it has been class tested with over 170 students and was a resounding success as a replacement for previously used graphical approximations. A unique feature of this software is the incorporation of image-processing techniques into a course designed for non-science majors.The five software packages are:(a)Datasheet - A six-column spreadsheet with columnwise operations, statistical functions, and double-high-resolution graphics.(b)Image-Processor Program - Allows 37 × 27 pixel × 8 bit video captured images to be manipulated using standard image-processing techniques such as low pass/high pass filtering and histogram equalization.(c)Picture-Processor Program - Allows 256 × 192 bilevel pictures to be manipulated and measured with functions that include calipers, odometer, planimeter, and protractor.(d)Orrery Program - Simulates planet configurations along the ecliptic. A movable cursor allows selection of specific configurations. Since both relative times and angular positions are given, students can deduce the scale of the solar system using simple trigonometry.(e)Plot Program - Allows orbital positions as observed from above the pole to be plotted on the screen. By entering trial values of elliptical orbit parameters, students obtain and the program plots the best fitting ellipse to the data. The sum of the squares of the residuals in the radial coordinate is given after each trial so that students can discover convergence more easily than by simple visual examination of a plot comparing the trial theoretical points with the raw data points.
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Titaley, Jullia, Tohap Manurung, and Henriette D. Titaley. "CUBIC AND QUADRATIC POLYNOMIAL ON JULIA SET WITH TRIGONOMETRIC FUNCTION." JURNAL ILMIAH SAINS 18, no. 2 (November 12, 2018): 103. http://dx.doi.org/10.35799/jis.18.2.2018.21555.
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CUBIC AND QUADRATIC POLYNOMIAL ON JULIA SET WITH TRIGONOMETRIC FUNCTIONABSTRACTJulia set are defined by iterating a function of a complex number and is generated from the iterated function . We investigate in this paper the complex dynamics of different functions and applied iteration function system to generate an entire new class of julia set. The purpose of this research is to make variation of Cubic and Quadratic polynomial on Julia Set and the two obvious to investigate from julia set are Sine and Cosine function. The results thus obtained are innovative and studies about different behavior of two basic trigonometry.Keywords : Julia Set, trigonometric function, polynomial function POLINOMIAL KUBIK DAN KUADRATIK PADA HIMPUNAN JULIA DENGAN FUNGSI TRIGONOMETRI ABSTRAKHimpunan Julia didefiniskan oleh fungsi iterasi dari bilangan kompleks dan dibangkitkan dari fungsi iterasi . Kami melakukan penelitian dalam penulisan ini tentang sistem dinamik kompleks dari fungsi yang berbeda dengan iterasi yang diterapkan untuk menghasilkan kelas baru dari himpunan Julia. Tujuan dari penelitian ini adalah untuk membuah kelas baru himpunan Julia dengan fungsi polinomial kubik dan kuadratik dengan fungsi sinus dan kosinus. Hasil akhir dari penelitian ini ada menemukan inovatif baru dari himpunan Julia dengan menggunakan dua fungsi trigonometri.Kata kunci: Julia set, fungsi trigonometri, fungsi polinomial
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Akniyev, G. G. "Discrete least squares approximation of piecewise-linear functions by trigonometric polynomials." Issues of Analysis 24, no. 2 (December 2017): 3–24. http://dx.doi.org/10.15393/j3.art.2017.4070.
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Nazarkevych, M. A. "DEVELOPMENT OF BIOMETRIC IDENTIFICATION METHODS BASED ON NEW FILTRATION METHODS." Ukrainian Journal of Information Technology 3, no. 1 (2021): 106–13. http://dx.doi.org/10.23939/ujit2021.03.106.
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The article is devoted to the development of biometric identification methods based on new filtration methods. Biometric identification systems need constant improvement, because they often work slowly and give the wrong result. To increase the reliability of biometric image recognition, the method is formed, which is formed from the stages: segmentation, normalization, local orientation estimation, local estimation, spine frequency estimation, Gabor filter implementation, binarization, thinning. A new filtering method is proposed, which is based on a new type of function – Ateb-functions, which are used next to the Gabor filter. The local orientation can be calculated from local gradients using the arctangent function. The normalization process is performed to evenly redistribute the values of image intensity. When segmenting, the foreground areas in the image are separated from the background areas. A new method of wavelet conversion of biometric image filtering based on Ateb-Gabor has been developed. The Gabor filter is used for linear filtering and improves the quality of the converted image. Symmetry and wavelet transform operations are also used to reduce the number of required multiplication and addition operations. The method is based on the well-known Gabor filter and allows you to rearrange the image with clearer contours. Therefore, this method is applicable to biometric images, where the creation of clear contours is particularly relevant. When Gabor filtering, the image is reconstructed by multiplying the harmonic function by the Gaussian function. Ateb functions are a generalization of elementary trigonometry, and, accordingly, have greater functionality. Ateb-Gabor filtering allows you to change the intensity of the whole image, as well as the intensity in certain ranges, and thus make certain areas of the image more contrasting. Filtering with Ateb functions allows you to change the image from two rational parameters. This allows you to more flexibly manage filtering and choose the best options. When you perform a thinning, the foreground pixels are erased until there is one pixel wide. A standard thinning algorithm is used, or the thinning developed by the authors in other studies. This filtering will provide more accurate characteristics, as it allows you to get more sloping shapes and allows you to organize a wider range of curves. Numerous experimental studies indicate the effectiveness of the proposed method.
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Romero Díaz, Tonys, and José Eligio Guzmán Contreras. "Evaluación a profesores en las competencias matemáticas de Educación Media, Juigalpa, 2014." Ciencia e Interculturalidad 18, no. 1 (December 16, 2016): 22–32. http://dx.doi.org/10.5377/rci.v18i1.3047.
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Este artículo fue producto de un diagnóstico, obtenido al aplicar una prueba de matemática, que consistió en el examen de admisión para el nuevo ingreso 2014 que aplica la Universidad Nacional Autónoma de Nicaragua, Managua. Se utilizó una muestra de veinte profesores del municipio de Juigalpa, Chontales, quienes de manera voluntaria aplicaron al examen. Se realizó un análisis de discriminación a cada uno de los ítems que componían la prueba, así como a todo el examen. Paralelamente al análisis cuantitativo, se identificó una serie de problemas en la resolución del examen a través de un análisis cualitativo de cada uno de los ejercicios planteados. Los resultados reflejaron que los profesores de secundaria del municipio de Juigalpa presentan dificultades en la resolución de ejercicios que son evaluados en los exámenes de admisión de la UNAN-Managua. Las áreas de estudio más afectadas en el examen fueron: la geometría euclidiana, los logaritmos, la teoría de conjuntos, la estadística, funciones reales y la trigonometría. Se recomienda establecer una estrategia de trabajo en conjunto UNAN-Managua y el Ministerio de Educación que refuerce la competencia de los docentes en pro de beneficiar al estudiantado de secundaria para los futuros exámenes de admisión.SummaryThis article was the result of a diagnostic that was obtained by applying a math test, which consisted of the admission test for new students of the year 2014 that the National Autonomous University of Nicaragua (Managua) applies. We used a sample of twenty teachers from the municipality of Juigalpa, Chontales who voluntarily applied the test. The discrimination analysis was done to each of the items that made up the test, as well as the entire test. Parallel to the quantitative analysis, a series of problems were identified in resolving the test through a qualitative analysis of each of the exercises.The results showed that secondary teachers in the municipality of Juigalpa presents difficulties in resolving the exercises that are evaluated in the admission test of the UNAN-Managua. The study areas that are most affected in the test were: Euclidean geometry, logarithms, set theory, statistics, real functions and trigonometry. Therefore, based on the results, it is recommended to establish a strategy of working together UNAN-Managua and the Ministry of Education to strengthen the teacher’s competence in order to benefit secondary students for future admissions tests.
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Stavek, Jiri. "Trigonometric Functions at a Crossroads." Applied Physics Research 9, no. 3 (May 31, 2017): 40. http://dx.doi.org/10.5539/apr.v9n3p40.
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In the history of physics trigonometric functions played several times a very critical role at crossroads. This time we are at a crossroads with the interpretation of correlation events of entangled particles. In this approach we propose to describe the experimental data of Alice and Bob using not so known trigonometric functions. Claudius Theorem (based on the trigonometric family of Sagitta and Cosagitta) evalutes the probabilistic occurrence of correlated and anticorrelated events. David Theorem (based on the trigonometric family of Hacoversine) describes the probability of the following identical events and gaps between the following identical events. In this trigonometric concept the Team of Alice, Bob, Claudius and David formulated a camouflage legend for Eve – “spooky action at a distance”. Merlin (with unbounded computational ability) should verify the truth of this statement. Trent (a trusted arbitrator, who acts as a neutral third party) should analyze these data and this trigonometric concept. Victor (a verifier) should make his decision which way we should continue in our future research: either through the Niels Bohr avenue or through the Albert Einstein sidewalk.