• Journal of Educational Research in Mathematics
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• v.24 no.4
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• pp.607-622
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• 2014

The purpose of this paper is that it analyzes the historical development of the concept of trigonometric functions and discuss some didactical implications. The results of the study are as follows. First, the concept of trigonometric functions is developed from line segments measuring ratios to numbers representing the ratios. Geometry, arithmetic, algebra and analysis has been integrated in this process. Secondly, as a result of developing from practical calculation to theoretical function, periodicity is formalized, but 'trigonometry' is overlooked. Third, it must be taught trigonometry relationally and structurally by the principle of similarity. Fourth, the conceptual generalization of trigonometric functions must be recognized as epistemological obstacle, and it should be improved to emphasize the integration revealed in history. The results of these studies provide some useful suggestions to teaching and learning of trigonometry.

• The Mathematical Education
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• v.50 no.3
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• pp.355-365
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• 2011

The purpose of this study is to provide mathematical knowledge for supporting the didactical knowledge on circular measure and radian in the high school curriculum. We show that circular measure related to arcs can be mathematically justified as an angular measure and radian is a well defined concept to be able to reconcile the values of trigonometric functions and ones of circular functions, which are real variable functions. Radian has two-fold intrinsic attributes of angular measure and arc measure on the unit circle, in particular, the latter property plays a very important role in simplifying the trigonometric derivatives. To improve students's low academic achievement in trigonometry section, the useful advantage and the background over the introduction of radian should be preferentially taught and recognized to students. We suggest some teaching plans to practice in the class of elementary and middle school for enhancing teachers' and students' understanding of radian.

• Journal of Korea Society of Digital Industry and Information Management
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• v.9 no.1
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• pp.95-102
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• 2013

This paper covers nulling algorithm. In this algorithm, we assume that nulling points are already known. In general, nulling algorithm using matrix equation was utilized. But, this algorithm is pointed out that computational complexity is disadvantage. So, we choose gradient method to reduce the computational complexity. In order to further reduce the computational complexity, we propose approximate gradient method using characteristic of trigonometric functions. The proposed method has same performance compared with conventional method while having half the amount of computation when the number of antenna and nulling point are 20 and 1, respectively. In addition, we could virtually eliminate the trigonometric functions arithmetic. Trigonometric functions arithmetic cause a big problem in actual implementation like FPGA processor(Field Programmable gate array). By utilizing the above algorithm in a multi-cell environment, beamforming gain can be obtained and interference can be reduced at same time. By the above results, the algorithm can show excellent performance in the cell boundary.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.63-81
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• 2020

In this paper we consider certain classes of generalized level 2 Eisenstein series by simple differential calculations of trigonometric functions. In particular, we give four new transformation formulas for some level 2 Eisenstein series. We can find that these level 2 Eisenstein series are reducible to infinite series involving hyperbolic functions. Moreover, some interesting new examples are given.

• Journal of Korea Multimedia Society
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• v.20 no.12
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• pp.1992-1999
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• 2017

This study proposes a decorative typeface which is produced through the concept of trigonometric functions in an open-source programming language known as Processing. First, the theoretical background of Processing and trigonometric functions as well as previous research in this area are analyzed. Second, basic modules of 'V', 'I', 'O', and 'M' were created for use as the final alphabet typeface with the concept of a trigonometric function. Third, a decorative parabolic curve that encircles the base module was created. Finally, the modules created on Processing were edited in Adobe Illustrator to create a typeface set with characters from A to Z. Various artworks using Programming can produce an infinite number of different versions by modifying only some of the variables and codes, and this method can include multimedia features such as text, images, videos, interactive art and various forms of content and media. Therefore, with regard to expression, the possibilities are endless. In this study, I attempt to expand the field of visual culture using programming and computational methodologies. In contrast to the digital typeface production method, which relies on existing graphic tools, this study is meaningful because it expands the range of use of decorative typefaces.

• Journal of Power Electronics
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• v.17 no.1
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• pp.253-261
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• 2017

For a single-phase active power filter (APF), designing a more efficient algorithm to guarantee accurate and fast harmonics extraction with a lower computing cost is still a meaningful topic. The common idea still employs a IRPT-based Park transform, which was originally designed for 3-phase applications. Therefore, an additional virtual signal generation (VSG) link is necessary when it is used in the single-phase condition. This method, with virtual signal generation and transform, is obviously not the most efficient one. Regarding this problem, this paper proposes a novel harmonics extraction algorithm to further improve efficiency. The new algorithm is based on the principle of trigonometric orthogonal functions (TOF), and its mathematical principle and physical meaning are introduced in detail. Its implementation and superiority in terms of computation efficiency are analyzed by comparing it with conventional methods. Finally, its effectiveness is well validated through detailed simulations and laboratory experiments.

• Communications of Mathematical Education
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• v.23 no.3
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• pp.785-801
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• 2009

The education of mathematics is comprised of formal thoughts so students lose interest and they don't have a chance to have a liberal mind. To solve this problem, recently, the flow of mathematic education is changing from formal mathematics to experimental mathematics, which focuses on student's activity and experience. Experimental mathematics can improve student's interest and participation. This study is about teaching methods of trigonometric functions through experimental mathematics measuring height and width of buildings. For measuring height of buildings we use clinometer and for measuring width of buildings we developed a mathematical tool with which we can measure angle for width of buildings. Through this activity, students obtained an interest in mathematics and they gained a positive attitude for the lesson. If we use this experimental mathematics method in high school, it's possible to reduce fears of mathematics and to increase an interest for mathematics.

• Communications of Mathematical Education
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• v.33 no.3
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• pp.319-334
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• 2019

In this study, using the tasks related trigonometric functions, the degree of high school students' understanding of the function concept was examined through the level of Hitt(1998). First, the degree of the students' understanding was classified by level, then the concept understanding was reclassified by the process or the object. As a result, high school students' concept understanding showed incompleteness in three stages. It was possible to know that the process in the interpretation of the graph is the main perspective, and the operation of algebraic representation is regarded as important. Based on these results, it seems necessary to study the teaching-learning method which can understand trigonometric functions from various perspectives. It seems necessary to study a lesson model that can reach function concept's understanding level 5 that maintains consistency between problem solving and representation system.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.87-97
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• 2009

We prove the Hyers-Ulam stability of the sine and cosine functional equations in the spaces of generalized functions such as Schwartz distributions, Fourier hyperfunctions, and Gelfand generalized functions.

• Journal of Korea Multimedia Society
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• v.21 no.12
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• pp.1504-1512
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• 2018

The purpose of this study is to design and apply a simple game that can visually experience basic concepts of game mathematics in order to teach game mathematics effectively. To do this, simple games linked with game mathematical theory are to be developed by utilizing the functions provided by Unity so that students could actively learn game mathematics. To demonstrate the plausibility of this approach, "Bouncing Ball Game" was developed to understand the concept of periodicity of trigonometric functions. As a result, students were able to effectively learn how mathematical concepts related to ball movements applied to the game.