• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.161-169
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• 1999

Generalized nonnegative trigonometric polynomials are defined as the products of nonnegative trigonometric polynomials raised to positive real powers. The generalized degree can be defined in a natural way. We improve and extend the large sieve involving pth powers of trigonometric polynomials so that it holds for generalized trigonometric polynomials.

• Communications of Mathematical Education
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• v.22 no.3
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• pp.289-310
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• 2008

The purpose of study is to propose the possibilities of finding trigonometric function values using trigonometric function graphs instead of the unit circle method. And it is to discuss how to enhance relating trigonometric function value finding to graphs construction, and students conceptual understanding of the properties of trigonometric functions. The conclusions of this study are the effectiveness of function value finding using trigonometric function graphs, the use of a precise term of function value finding given general angles, consideration of a link between function value finding and graphs, and the possibility of teaching trigonometric function graphs in advance of function value finding.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.513-520
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• 2005

We calculate the normal fuzzy probability for trigonometric fuzzy numbers defined by trigonometric functions. And we study the normal probability for some operations of two trigonometric fuzzy numbers. Furthermore, we calculate the normal fuzzy probability for some fuzzy numbers generated by operations.

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.369-378
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• 2008

The aim of this paper is to study the stability problem for the pexider type trigonometric functional equation f(x + y) − f(x−y) = 2g(x)h(y), which is related to the d'Alembert, the Wilson, the sine, and the mixed trigonometric functional equations.

• Research in Mathematical Education
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• v.17 no.1
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• pp.63-78
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• 2013

Trigonometric ratios are difficult concepts to teach and learn in middle school. One of the reasons is that the mathematical terms (sine, cosine, tangent) don't convey the idea literally. This paper deals with the understanding of a concept from the learner's standpoint, and searches the orientation of teaching that make students to have full understanding of trigonometric ratios. Such full understanding contains at least five constructs as follows: skill-algorithm, property-proof, use-application, representation-metaphor, history-culture understanding [Usiskin, Z. (2012). What does it mean to understand some mathematics? In: Proceedings of ICME12, COEX, Seoul Korea; July 8-15,2012 (pp. 502-521). Seoul, Korea: ICME-12]. Despite multi-aspects of understanding, especially, the history-culture aspect is not yet a part of the mathematics class on the trigonometric ratios. In this respect this study investigated the effect of history approach on students' understanding when the history approach focused on the mathematical terms is used to teach the concept of trigonometric ratios in Grade 9 mathematics class. As results, the experimental group obtained help in more full understanding on the trigonometric ratios through such teaching than the control group. This implies that the historical derivation of mathematical terms as well as the context of mathematical concepts should be dealt in the math class for the more full understanding of some mathematical concepts.

• Journal for History of Mathematics
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• v.19 no.1
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• pp.79-90
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• 2006

The purpose of this paper is to derive the ratios of trigonometric special angles from Euclid's by constructing regular pentagon and decagon. The intention of this paper is started from recognizing that teaching of the special angles in secondary math classroom excessively depends on algebraic approaches rather geometric approaches which are the origin of the trigonometric ratios. In this paper the method of constructing regular pentagon and decagon is reviewed and the geometric relationship between this construction and trigonometric special angles is derived. Through such geometric approach the meaning of trigonometric special angles is analyzed from a geometric perspective and pedagogical ideas of teaching these trigonometric ratios is suggested using history of mathematics.

• Honam Mathematical Journal
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• v.30 no.1
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• pp.185-195
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• 2008

We consider a system of trigonometric functional equations in the spaces of generalized functions such as Schwartz distributions and Gelfand generalized functions. As a consequence we find locally integrable solutions of the n-dimensional trigonometric functional equation.

• Communications of the Korean Mathematical Society
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• v.23 no.4
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• pp.567-575
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• 2008

In this article we prove the Hyers.Ulam stability of trigonometric functional equations.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.1
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• pp.33-37
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• 2022

In this short note, we prove an open problem for the interval (-∞, ∞), related to a reverse trigonometric Masjed-Jamei inequality presented in [2] and establish a new inequality of a similar kind.

• Journal of the Korean Society of Industry Convergence
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• v.16 no.1
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• pp.9-13
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• 2013

This paper measured some condition about differential height of two points for the comparison of measure by direct method and Geodimeter and trigonometric Leveling method. The research was compared relationship between the volue to get from three measure method and five measured man. The significance of between three measure method and five measured man has been investigated by analysis of two-way ANOVA. The result indicate that between five measured man show insignficance, and between the direct method and Geodeter method show signficance and between the direct method and trigonometric Leveling method show signficance but between the Geodeter method and trigonometric Leveling method, two method show insignficant. Therefore, when using Geodemeter leveling method and trigonometric Leveling method, you must keep particular attention when former two Leveling method about instrumental error, natural error, and personal error, two Leveling method using low precision leveling.