• 대한수학회논문집
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• 제21권2호
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• pp.385-395
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• 2006

We study the exponential fuzzy probability for quadratic fuzzy number and trigonometric fuzzy number defined by quadratic function and trigonometric function, respectively. And we calculate the exponential fuzzy probabilities for fuzzy numbers driven by operations.

• 한국멀티미디어학회논문지
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• 제20권12호
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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.

• Advances in aircraft and spacecraft science
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• 제6권5호
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• pp.409-426
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• 2019

The aim of the present work is to study the nonlinear behavior of the laminated composite plates under transverse sinusoidal loading using a new inverse trigonometric shear deformation theory, where geometric nonlinearity in the Von-Karman sense is taken into account. In the present theory, in-plane displacements use an inverse trigonometric shape function to account the effect of transverse shear deformation. The theory satisfies the traction free boundary conditions and violates the need of shear correction factor. The governing equations of equilibrium and boundary conditions associated with present theory are obtained by using the principle of minimum potential energy. These governing equations are solved by eight nodded serendipity element having five degree of freedom per node. A square laminated composite plate is considered for the geometrically linear and nonlinear formulation. The numerical results are obtained for central deflections, in-plane stresses and transverse shear stresses. Finite element Codes are developed using MATLAB. The present results are compared with previously published results. It is concluded that the geometrically linear and nonlinear response of laminated composite plates predicted by using the present inverse trigonometric shape function is in excellent agreement with previously published results.

• Korean Journal of Mathematics
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• 제29권1호
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• pp.137-167
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• 2021

Spherical fuzzy set (SFS) is also one of the fundamental concepts for address more uncertainties in decision problems than the existing structures of fuzzy sets, and thus its implementation was more substantial. The well-known sine trigonometric function maintains the periodicity and symmetry of the origin in nature and thus satisfies the expectations of the experts over the multi parameters. Taking this feature and the significance of the SFSs into the consideration, the main objective of the article is to describe some reliable sine trigonometric laws (ST L) for SFSs. Associated with these laws, we develop new average and geometric aggregation operators to aggregate the Spherical fuzzy numbers (SFNs). Then, we presented a group decision- making (DM) strategy to address the multi-attribute group decision making (MAGDM) problem using the developed aggregation operators. In order to verify the value of the defined operators, a MAGDM strategy is provided along with an application for the selection of laptop. Moreover, a comparative study is also performed to present the effectiveness of the developed approach.

• 한국수학교육학회지시리즈A:수학교육
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• 제49권3호
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• pp.353-373
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• 2010

This research was to help slow learners to be motivated and to make their outcome productive, using GSP based on the mathematization theory for learning mathematics, as a way of encouraging the learner-centered approach. With 2 of the second graders in a high school, who had not yet understood trigonometric functions in their first grade period, 7 units of lesson plans were designed for the research. The results showed that first, understanding real life contexts and analyzing properties by observation, and experiment using GSP, to build the concept of trigonometric functions could be a foothold on which learner's organization and outcome from a horizontal mathematization led to vertical mathematization. Despite the delay during the level-up-stage for a while, the learners could attain the vertical mathematization stage and moreover the applicative mathematization through effective use of GSP and the interaction between the learners or a teacher and the learners. Second, using GSP was a vertical tool of connecting horizontal mathematization with vertical mathematization in forming the concept of trigonometric functions and its meaning could be understood by their verbalizing and presenting the outcomes through their active performance. Using GSP is helpful for slow learners to overcome learning difficulties, based on the instructional materials designed by Realistic Mathematics Education.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제33권3호
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• pp.319-334
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• 2019

본 연구는 삼각함수와 관련된 과제를 통해 고등학교 학생들의 함수 개념 이해 정도를 Hitt(1998)의 층위 분석을 통해 살펴보았다. 우선 학생들의 함수 이해 정도를 층위 분석을 통해 단계를 구분한 후 이해 관점을 과정과 대상 관점으로 다시 분류하였다. 그 결과 고등학교 학생들의 함수 개념 이해의 정도 층위는 3단계에서 불완전성을 보였다. 그리고 함수의 이해의 관점은 그래프 해석에서 과정 관점이 주를 이루고 있으며 대수적 표상의 조작이 중요시되고 있음을 알 수 있었다. 이러한 결과를 바탕으로 삼각함수를 다양한 관점으로 이해할 수 있는 교수-학습 방법에 대한 연구와 함께 문제 해결과 그에 따른 표상 체계 사이의 일관성이 유지되는 함수 개념 이해 층위 5단계에 도달할 수 있는 수업모델의 연구가 필요할 것으로 보인다.

• 정보학연구
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• 제8권3호
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• pp.1-10
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• 2005

Cosine and Sine function is widely used for the arithmetic, translation, object drawing, Simulation and etc. of Computer Graphics in Natural Science and Engineering. In general, Cordic Algorithm is effective method since it has relatively small size and simple architecture on trigonometric function generation. However profitably it has those merits, the problem of operation speed is occurred. In graphic display system, the operation result of object drawing is quantized and has the condition that is satisfied with rms error less than 1. So in this paper, the proposed generator is composed of partition operation at each ${\pi}/4$ and basic Cosine, Sine function generator in the range of $0{\sim}{\pi}/4$ using the lower order of Tayler's series in an acceptable error range, that enlarge the range of $0{\sim}2{\pi}$ according to a definition of the trigonometric function for the purpose of having a high speed Cosine, Sine function generation. And, division operator using code partition for divisor three is proposed, the proposed function generator has high speed operation, but it has the problems in the other application parts with accurate results, is need to increase the speed of the multiplication.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제11권3호
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• pp.21-28
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• 2007

The symmetric dual filters are essential for the construction of biorthogonal multiresolution an analyses and wavelets. We propose an algorithm to seek for dual symmetric trigonometric filters $\tilde{m}_0$ for for the given symmetric trigonometric filter $m_0$ and illustrate our algorithm by examples.

• Korean Journal of Mathematics
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• 제29권4호
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• pp.765-774
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• 2021

In this paper, we solve and investigate the superstability of the p-radical functional equations $$f(\sqrt[p]{x^p+y^p})-f(\sqrt[p]{x^p-y^p})={\lambda}f(x)g(y),\\f(\sqrt[p]{x^p+y^p})-f(\sqrt[p]{x^p-y^p})={\lambda}g(x)f(y),$$ which is related to the trigonometric(Kim's type) functional equations, where p is an odd positive integer and f is a complex valued function. Furthermore, the results are extended to Banach algebras.

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 2010년도 추계학술대회
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• pp.641-642
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• 2010

삼각함수는 직각삼각형에서 한 각의 크기가 일정하면, 이들 변의 비의 값은 삼각형의 크기에는 관계없이 일정하다는 가장 단순하고 독특한 성질에 기초를 둔 학문이다. 직삼각형의 밑변의 길이와 건물을 올려다본 각이 있다면 건물의 높이를 삼각함수를 이용하여 구할 수 있다. 이는 차를 타고 이동하면서 건물의 높이를 가늠할 수 있는 좋은 방법이라고 볼 수 있다.