• Journal of Educational Research in Mathematics
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• v.19 no.3
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• pp.443-459
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• 2009

Despite the many discussions of mathematics education, there are a lot of controversy of the Radian. Generally, Radian is taken to have two properties. One property is an angular property and other is a property of fore numbers. For this reason, both Students and teachers are hard to understand the radian. This study is to provide a base of the radian understand. In essence, radian has only angular property, and other property is a derived property. So radian is to be understood in an angle.

• 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.

• School Mathematics
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• v.17 no.2
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• pp.309-329
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• 2015

This study is to provide didactical implications for teaching and learning of radian through a analysis of investigation result about pre-service teachers' understanding of radian. The results of this study are as follows. First, pre-service teachers understood the radian as ${\frac{180^{\circ}}{\pi}}$, rather than as the definition. Secondly, the definition style of radian affected the problem solving strategy for the measurement of the angle. Thirdly, pre-service teachers had insufficient content knowledge about properties of measurement as a pure number of radian. Lastly, They failed to describe the usefulness of circular measure. We suggested the definition of radian in textbooks should be changed from ${\frac{180^{\circ}}{\pi}}$ to mathematical definition of radian. And the general angle should be stated as the reason why the domain of trigonometric function is real numbers.

• Structural Engineering and Mechanics
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• v.78 no.5
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• pp.637-649
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• 2021

Great efforts have been conducted to investigate the seismic performances of the arch and rectangular underground structures, however, the differences between seismic responses of these two types of underground structures, especially the vault radian influencing the seismic responses of arch structures are not clarified. This paper presents a detailed numerical investigation on the seismic responses of arch underground structures with different vault radians, and aims to illustrate the rule that vault radian affects the seismic responses of underground structures. Five arch underground structures are built for nonlinear soil-structure interaction analysis. The internal forces of the structural components of the underground structures only under gravity are discussed detailedly, and an optimum vault radian for perfect load-carrying functionality of arch underground structures is suggested. Then the structures are analyzed under seven scaled ground motions, amounting to a total of 35 dynamic calculations. The numerical results show that the vault radian can have beneficial effects on the seismic response of the arch structure, compared to the rectangular underground structures, causing the central columns to suffer smaller axial force and horizontal deformation. The conclusions provide some directive suggestions for the seismic design of the arch underground structures.

• Journal of Educational Research in Mathematics
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• v.27 no.4
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• pp.833-855
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• 2017

This study aims to reinvestigate the reason for introducing radian as a new unit to express the size of angles, what is the meaning of radian measures to use arc lengths as angle measures, and why is the domain of trigonometric functions expanded to real numbers for expressing general angles. For this purpose, it was conducted historical, mathematical and applied mathematical analyzes in order to research at multidisciplinary analysis of the radian concept. As a result, the following were revealed. First, radian measure is intrinsic essence in angle measure. The radian is itself, and theoretical absolute unit. The radian makes trigonometric functions as real functions. Second, radians should be aware of invariance through covariance of ratios and proportions in concentric circles. The orthogonality between cosine and sine gives a crucial inevitability to the radian. It should be aware that radian is the simplest standards for measuring the length of arcs by the length of radius. It can find the connection with sexadecimal method using the division strategy. Third, I revealed the necessity by distinction between angle and angle measure. It needs justification for omission of radians and multiplication relationship strategy between arc and radius. The didactical suggestions derived by these can reveal the usefulness and value of the radian concept and can contribute to the substantive teaching of radian measure.

• Korean Journal of Remote Sensing
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• v.28 no.2
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• pp.237-243
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• 2012

In this paper, an atmospheric effect of repetitive measurements of X-band (9.65 GHz) arc-rail type GB-SAR (ArcSAR) system was quantitatively analyzed. Four artificial triangular trihedral corner reflectors as stationary targets for getting stable back scattered signal during 43 hours continually. The results of the analysis showed that the phase of those stationary targets had changed maximum of 5 radian (12.4 mm) and total RMS error had was 1.62 radian (4 mm) during 65 repeated measuring time. The refractive index of air which was calculated using the temperature;humidity and pressure of atmosphere showed very close relationship with the phase difference. We could check the atmospheric correction was fulfilled by the correction of an atmospheric effect using refractive index during the selected 16 hours period showed that RMS error was dropped from 1.74 radian (4.3 mm) to 0.10 radian (0.24 mm).

• Journal of Educational Research in Mathematics
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• v.18 no.2
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• pp.263-281
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• 2008

This study is to provide a base for discussions on teaching and teaming of radian through a theoretical analysis of it. Radian possesses two-fold comprehensive properties of measurement as a magnitude and a pure number. As a magnitude of an angle, it has some theoretical advantages in mathematics and in physics, in spite of its non-superiority to other angular measures in practical sense. As a pure number, it has some advantages in that it simplifies theoretical developments of trigonometric functions and justifies omitting the unit in the calculations and final expressions in physics. Radian should be taught and learnt with an appreciation of the advantages of the two-fold properties. Activities to measure angles from various viewpoints may be helpful for this. Students' awareness of the advantages of radian needs to be stimulated and deepened repeatedly as related content appears.

• Journal of the Korean Institute of Telematics and Electronics
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• v.17 no.5
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• pp.48-55
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• 1980

For the purpose of composing an anti-ghost antenna system, 2 antennas, which have the identical radiation pattern, are fixed parallel to each other with a constant separation. In view of the fact that the phase differnce between the added power and the subtracted power of the two undesired signal which is recieved from all direction except from the real front one becomes radian, now It is Possible to make the amplitude of each Power become equal and the phase of the subtracted power become out of phase with that of the added power, by adjusting the amplitude of the subtracted power and shifting its phase by + or radian. Therefore the sum of the added power and the above modified subtracted power will be able to become zero. According to the above study, a hybrid circuit is designed and through operation of this circuit , the undesired wave can be seen to be reduced by 20 dB.

• School Mathematics
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• v.17 no.3
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• pp.447-467
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• 2015

The purpose of this study is to examine how the learning experience understanding degree and radian as the measurement of arc affects the conceptual understanding of radian and measuring angle. For this purpose, we investigated pre-service teachers' understanding about measurement of angle using a length of arc, and then conducted a teaching experiment with two middle school students. The results of analyzing pre-service teachers' and students' response are as follows. Students' experience interpreting the concept of degree into measurement of arc had a positive effect on understanding of radian and students' learning process in which they got measurement of angle as measurement of arc enabled conceptual understanding of 'linear measuring'. Also a circle context and a strategy dividing by arc operated as effective strategies for solving various problems about an angle. Finally, we confirmed that providing direct manipulative activities as a chance to explore relationships between an angle and arc measure can help students' conceptual understanding of measuring angle.

• Earthquakes and Structures
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• v.10 no.1
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• pp.73-89
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• 2016

The seismic performance of moment frames could vary according to the rotation capacity of their connections. The minimum rotation capacity of moment connections for steel intermediate moment frames (IMF) was defined as 0.02 radian in AISC 341-10. This study evaluated the seismic performance of IMF frames with connections having a rotation capacity of 0.02 radian. For this purpose, thirty IMFs were designed according to current seismic design provisions considering different design parameters such as the number of stories, span length, and seismic design categories. The procedure specified in FEMA P695 was used for conducting seismic performance evaluation. It was observed that the rotation capacity of 0.02 radian could not guarantee the satisfactory seismic performance of IMFs. This study also conducted seismic performance evaluation for IMFs with connections having the rotation capacity of 3% and ductile connections for proposing the minimum rotation capacity of IMF connections.