Double Angle Research Articles

Kesulitan Belajar Matematika Siswa SMA pada Pokok Bahasan Persamaan Trigonometri di Kampung Pasanggrahan

Many factors cause the low learning ability of students in mathematics. The purpose of this study was to analyze students' difficulties in solving problems on the material of Trigonometric Equations. The type of research used is qualitative research. This research was conducted in the village of Pasanggrahan, Garut. The research subjects were four high school students of class XI who were taken randomly. The data collection techniques in this study were observation, tests, interviews, and documentation. The instruments used were test question sheets and interview guidelines. The results of this study indicate that students have difficulty in solving a basic trigonometric equation, difficulty in modeling problems related to trigonometric equations, and difficulty in determining a trigonometric equation and the set of solutions.

ANALISIS MISKONSEPSI SISWA PADA MATERI TRIGONOMETRI MENGGUNAKAN METODE CERTAINTY OF RESPONSE INDEX TERMODIFIKASI DI SMA

The research purpose is to analyze the misconceptions by using the certainty of response index modified in trigonometric equations at class XI State Senior High School 9 Pontianak. that Research method used in this research was a case study. The subjects in this research were seven students of class XI IPA 1 and IPA 2 of State Senior High School 9 Pontianak. The instruments used in this research were diagnostic tests and interview guidelines. From the result of the study, obtained 8 out of 32 students had computation misconceptions, 9 out of 32 students had generalized misconceptions, 1 out of 32 students had specialization misconceptions, and 1 out of 32 students had theoretical misconceptions. Misconceptions experienced are caused by students are students' associative thinking, incomplete reasoning, wrong intuition, stages of student cognitive development, and student abilities. Generalizing misconceptions are the most common misconceptions experienced by students, the cause of this misconception is wrong intuition and the stage of students' cognitive development.

Distribution of angle lambda and pupil offset as measured by combined Placido Scheimpflug Topography

BackgroundAngle lambda is the angle between the pupillary axis and the line of sight. It is important for accurate centration during anterior segment surgery. The purpose of this study is to identify the distribution of angle lambda and pupil center offset as measured by a combined placido disc Scheimpflug topography system.MethodsA prospective non-randomized study was performed on 2178 eyes in Eye World Hospital, Giza, Egypt. Sirius device (CSO, Costruzione Strumenti Oftalmici, Florence, Italy, version 3.2.1.60) was used to measure average keratometry (K), anterior chamber depth (ACD), central corneal thickness (CCT), horizontal visible iris diameter (HVID), pupil radius (PR), pupil center intercept x-component (PCI-x), and pupil center intercept y-component (PCI-y). Axial length (AL) was measured by immersion A-scan Eyecube Ultrasonography device (Ellex, Adelaide, South Australia, Australia). Angle lambda was calculated by a trigonometrical equation. Pearson correlation was used to analyze the correlation between angle lambda and age and refraction.ResultsAverage angle lambda in all eyes was 3.32° ± 1.99. Mean angle lambda was significantly smallest in myopia and largest in hyperopia. Age correlation to angle lambda was insignificant. Average PCI-x and PCI-y in all eyes was − 0.047 mm and + 0.091 mm, respectively.ConclusionsAngle λ is significantly larger in hyperopia than myopia, and the effect of age is insignificant. Pupil center offset was horizontally greater in hyperopia than in myopia. We therefore encourage the preoperative assessment of angle λ to avoid decentered ablation, especially when treating hyperopia.

Diagnostik Kesulitan Belajar Siswa Pada Materi Trigonometri Kelas XI Multimedia SMKN 2 Sinjai

This research was conducted at SMKN 2 Sinjai. This study aims to describe students' learning difficulties in mathematics on trigonometric material. The method applied in this research is descriptive qualitative research method. The subjects in this study were two students of class XI Multimedia at SMKN 2 Sinjai. The research techniques used in this study were observation, diagnostic tests and interviews. The results of this study indicate that the difficulties experienced by FD and SC subjects are difficulties in using the Pythagorean formula in determining one side length of a right triangle and applying the trigonometric comparison formula in solving real problems. Efforts that can be made in overcoming the difficulties experienced by students are teachers need to pay attention to the characteristics of their students and increase their interest in learning mathematics.

Rational solutions of Abel trigonometric polynomial differential equations

In this paper we deal with the trigonometric polynomial differential equations of the form Y′=A(θ)Y2+B(θ)Y3, where A and B are real trigonometric polynomials with B(θ)≢0. We first prove that these equations has at most two trigonometric polynomial solutions (which will always be constant solutions) and show that this upper bound is reached. Second we provide an upper bound on the number of rational trigonometric solutions that these equations can have and we show that under some conditions related with the degree of the trigonometric polynomials A(θ) and B(θ), the number of rational solutions is two.

Unstable Circadian Rhythm of Heart Rate of Alzheimer Dementia Based on Biological Data of Mattress Sensor.

It is important to detect daily Alzheimer dementia (AD) possibility using unconstrained mattress sensors because dementia takes time before subjective symptoms appear and the main treatment is to slow the rate of progression. Forcusing on circadian rhythm disorder which tend to occur with AD, this paper analyzes the features of unstable circadian rhythms of heart rate associated with its weakening and misalignment in AD. It is found that the external feature of heart rate of AD that of up and down changes seen frequently compared to that of healthy subjects makes the multiple types of effects on the estimation process of the AD detection method based on the circadian instability represented by the trigonometric regression equation estimated from the heart rate. So, we designed two feature values from the effects and analyzed them in an analysis experiment. An analysis experiment was conducted on the heart rate of total 72 days data of one AD patient and total 30 days data of 21 healthy people, and the result confirmed significant differences between the AD and the healthy people at from 0.01% to 0.1 % level for the first feature and at from 0.1% to 5% level for the second feature. And the result shows the possibility that differences in the heart rate features is found between AD and healthy people.

Valgus inter-trochanteric osteotomy and fixation with double angle barrel plate and Richard screw for neglected fracture neck femur in young adults – A prospective clinico-radiological cohort study

Background: Saving natural head is the primary aim of management in delayed presented intracapsular fracture neck of femur, especially in young population. Anatomical reduction of these fractures is a difficult task. Rather more difficult is to decide the method of fixation which might require additive procedure(s) and one such method is valgus osteotomy and fixation devices which are technically demanding. Aims and Objectives: Our aim is to evaluate the practicality and validity of valgus osteotomy and fixation with Richard screw and double angle barrel plate in delayed presented (more than 3 weeks) fracture neck of femur in young adults. Materials and Methods: We treated 18 patients with mean age of 39 years who presented late with valgus inter-trochanteric osteotomy and fixed with Richard screw and double angle barrel plate. The cases were evaluated radiologically and clinically for Harris hip score, limb length discrepancy, union time, neck-shaft angle and complications such as avascular necrosis and implant cut through. Results: 15 out of 18 patients (83%) united in an average period of 15 weeks (12–28 weeks) clinically as well as radiologically. In more than 70% of patients, the average Harris hip score was “Excellent to Good” (Harris hip score >80). Pre-operative Pauwel’s angle has been corrected from 72.5 to 33. All the patients with united fracture were able to walk with full weight bearing, sit cross legged, squat, and perform SLR and do one-leg stance. Conclusion: Fixation with Richard screw and120° double angle barrel plate provides rigid bony fixation and restore the limb length after valgus inter-trochanteric osteotomy. Valgus inter-trochanteric osteotomy is an effective method to achieve union in neglected fracture neck of femur, as it facilitates added compression at fracture site and stable internal fixation.

Orientation-Insensitive Chipless RFID Achieved in Multiple Rotational Degrees of Freedom

Frequency-coded chipless radio frequency identification (RFID) suffers from resonant frequency detuning caused by misaligned orientations. The literature has employed topological symmetry to prevent shape variations; however, this scheme is effective only for the orientation in roll and cannot address other rotational degrees of freedom, including pitch and yaw. This study takes the first step to cope with the orientation mismatch against arbitrary roll, pitch, and yaw angles. The proposed technique requires the design of tag and new reader architecture, eliminating complex signal processing. The tag comprises resonators with the pattern of a short dipole. Two reader antennas are placed orthogonally and fed with equal power, illuminating co-polarized electromagnetic waves toward the tag. Based on the Pythagorean trigonometric identity, the sum of the backscattering power is unvarying against the rotations in pitch or yaw. The proposed technique is experimentally validated using a 6.97 bit system. When orientation mismatch in yaw appears, the proposed scheme improves the read reliability from 54.3% to 93.5%. Moreover, when mismatch in both roll and yaw occurs, the reliability is improved from 43.8% to 91.8%. Practical aspects, including various detection zones and the loading effect, are also analyzed.

A Split-Wedge Anchorage for CFRP Cables: Numerical Model vs. Experimental Results.

Fiber-reinforced polymers (FRPs) are widely used within civil structural applications either for structural retrofitting or new constructions. This is due to their appreciable mechanical properties such as high stiffness and strength, resistance to environmental effects, as well low density. Through the years, such peculiarities have encouraged researchers to apply FRP cables within the design of prestressing systems, where steel cables are systematically adopted. However, the brittleness intrinsic to FRP materials necessitates additional efforts to design the anchorage devices. In fact, tendons are here subjected to stress peaks, which need to be controlled in order to prevent the premature failure of the cable. Following this goal, authors recently studied an optimized split-wedge anchorage, for 12 mm-diameter pultruded-carbon-fiber-reinforced polymer (PCFRP) tendons, adopting double-angle (DA) wedges, and compared its performance with a single-angle (SA) wedge configuration. Tensile tests were performed on 3 SA and 2 DA prototypes, respectively, through a universal testing machine: the DA configuration exploited the average cable capacity (257 kN) once, denoting a maximum efficiency. The obtained experimental results are utilized, in the framework of the present work, to calibrate contact parameters of nonlinear finite element models. The presented numerical results helped to assess benefits of the proposed configurations and the behavior of the anchorage components: the DA configuration turned out to satisfactorily avoid stress peak superpositions on the cable, with a reduction in pressure in the loading end of the cable with respect to the SA model.

Analysis of Initial Rotational Stiffness for Different Section of Semi-Rigid Connection

Structural frames are designed for gravity loads. For rigid connections, the entire 100% intensity of the beam section is not used, this is because the end support moment of the beam at the end is always greater than the midspan moment. The end moment value of the beam is reduced by using a semi-rigid connection. In this paper we have analyzed semi rigid connections for different sections. The results of the study indicatethat the formula in the paper appropriately stated the initial rotational stiffness of the top and seat angle connections. The type of semi-rigid connection is usually chosen based on stiffness of connection. In this paper initial connection stiffness (Rki) of an unstiffened top and set angle with double web angle semi-rigid connection of G+3 steel structure is estimated and result obtained are validated using theLiu Wei and Shu Ganping.

From monocular photograph to angle lambda: A new clinical approach for quantitative assessment

ABSTRACT Angle lambda assessment is essential in pediatric and strabismus practice. An abnormal angle lambda will modify the visual appearance of a strabismus or mimic one. Currently, angle lambda can be assessed by corneal topographs. Unfortunately, the use of these devices remains limited in the context of a strabismus clinic. Herein, we propose an easy, low cost, and reproducible method for angle lambda quantification, based on monocular photographs. Monocular pictures were taken by using a camera with a ring flash, centered by a fixation point. A digital evaluation analyzed the position of the corneal reflex on the pupil diameter. Using a trigonometric formula, the resulting ratio was converted into the value of angle lambda. This method was tested on 20 healthy eyes, on two successive couples of pictures, to evaluate its repeatability. Assessment using Pentacam was performed for comparison. The mean value of angle lambda was +2.61° ± 2.92° and 2.63° ± 2.85° in both picture series, respectively, and Lin’s repeatability coefficient was 0.99 – with a systematic deviation of −0.071° compared to Pentacam assessment. Angle lambda distribution was in range with values from the literature. This new method allows for angle lambda assessment without requiring a specific device and can be used in strabismus and pediatric clinics.

Controllable thermal radiation from twisted bilayer graphene

The presence of interlayer interactions in twisted bilayer graphene(TBG) enhances several characteristics, including the optical and electronic properties. We theoretically investigate the magic angle of TBG according to the vanishing of Fermi velocity and find double magic angles in a series. Thermal radiation from TBG can be tuned to the far infrared range by changing twist angles. The peculiar radiation spectrum is out of atmospheric window, which can be of great use in invisibility and keeping warm. The total radiation of TBG is slightly more than twice of a single layer graphene.

Tailored birdcage resonator for magnetic resonance imaging at 7 T using 3D printing

This study outlines the design, construction and characterization of a tailored low-cost linear birdcage (BC) resonator for magnetic resonance imaging at 7T. Typically, different BC designs found in literature are well described in theory but lack crucial information for practical realization. This is challenging, as theoretical and practical aspects often differ greatly from each other, especially in the field of high frequency technology. We propose a simple and open-source 3D printable design which results in a working BC if the instructions in this publication are followed. The aim is to open up the possibility of building a functioning BC with simple means and a budget below 750€, even for users without a great deal of expertise in MRI coil building. We demonstrate that the BC can achieve a good B1 field homogeneity using the double angle method. The proposed design is qualitatively compared to a commercially available resonator. Both perform equally well in terms of SNR and image quality.

Comparison of Barrett Toric Calculations Using Measured and Predicted Posterior Corneal Astigmatism in Cataract Surgery Patients.

AimTo compare residual astigmatism prediction errors across Barrett toric calculations using predicted posterior corneal astigmatism (PCA) and PCA measured using the IOL Master 700 with total keratometry (IOLM).MethodsA retrospective cohort study was undertaken on patients with corneal astigmatism and no other ocular comorbidities that underwent uneventful refractive femtosecond laser-assisted cataract surgery with toric IOL implantation between May 2019 and November 2019. Toric calculations were performed using the Barrett toric calculator and the following values: predicted PCA with anterior corneal measurements from Pentacam, IOLM standard keratometry (SK), OPD scan, and median measurements from these devices; predicted PCA with IOLM total keratometry (TK); and measured PCA with IOLM SK or IOLM TK. Residual astigmatism prediction error was calculated for each device and method of calculation at postoperative month 1 and 3 using the astigmatism double angle plot tool.ResultsA total of 24 eyes, 10 with-the-rule (WTR), 10 against-the-rule (ATR) and 4 oblique astigmatism, from 24 patients were included in this study. PCA ranged from 0.00 to 0.67 D with a mean of 0.24 ± 0.15 D in all eyes. PCA was significantly greater in WTR eyes (0.32 D) compared to ATR eyes (0.16 D; p < 0.05). In ATR eyes, calculations made using IOLM SK and measured PCA had significantly lower total corneal astigmatism and toric IOL cylinder power compared to calculations made using Pentacam and IOLM TK (p < 0.05). No significant difference in mean absolute or centroid residual astigmatism prediction error was observed across devices or calculation methods. The percentage of eyes with absolute astigmatism prediction errors ≤0.5 D was not significantly different across groups.ConclusionBarrett toric calculations using predicted PCA and PCA measured using IOLM produced comparable residual astigmatism prediction errors. The incorporation of median measurements did not significantly impact calculation accuracy.

Joint Slip Formulation for Members with Double Angle Section Based on Experimental Results in Wind Turbine Lattice Towers

Joint Slip Formulation for Members with Double Angle Section Based on Experimental Results in Wind Turbine Lattice Towers

PENERAPAN METODE DISCOVERY LEARNING SEBAGAI CARA MENINGKATKAN KEAKTIVAN SISWA UNTUK MENEMUKAN RUMUS SUDUT RANGKAP MATERI TRIGONOMETRI

The discovery learning method is a teaching method that regulates teaching so that children acquire knowledge that was previously unknown and not through notification, partially or wholly discovered by themselves. At SMAN 1 Kota Sorong, students' learning activity in class was very lacking. This study used the role model method, where the model used was the learning observed in SMA Negeri 1 Lawang to be adapted in SMA Negeri 1 Sorong City. The main objective of this role model research was to improve classroom learning practices that were used as objects at SMA Negeri 1 Sorong City by taking the model from SMA Negeri 1 Lawang. The research applied the discovery learning method by using the Student Activity Sheet to activate students in learning Trigonometry, especially the subject of Double Angles. Three main characteristics of discovery learning were carried out in research at SMAN 1 Sorong City, namely: (1) exploring and solving problems to create, combine and generalize knowledge; (2) student-centered; and (3) activities to combine new knowledge and existing knowledge. The application of the discovery method was proven to be able to make students of class XI IPA SMAN 1 Sorong City able to be actively involved in learning.

Heat transfer model and cooling performance of converter oxygen lance affected by slag sticking

The heat transfer mechanism and water-cooling effect during oxygen lance blowing changes by slag sticking at the nozzle. In order to effectively overcome this problem, in this study, the equivalent heat transfer method was applied to modify the heat transfer coefficient of the oxygen lance nozzle under different slag thicknesses and steel slag thermal conductivities. In addition, the gas–liquid two-phase heat transfer model was established by computational fluid dynamics numerical simulation, and the cooling effects for different types of oxygen lance nozzles were calculated by the improved model. The results show that the error rate between the calculated value of the modified model and the field measured value was reduced to 3.3%–4.6%. The nozzle with double angle and double flow design was found to be conducive to the improvement of the cooling system. In this study, the best cooling effect was obtained when the flow ratio of large nozzles and small nozzles is 60%/40% and the angle is 12°/17°.

The Qibla Directional Accuracy Determination Analysis Using Spherical Trigonometric Method and Google Earth

This research aims to find out the methods used to determine the direction of the qibla of mosques in Kendari City and provide solutions for mosques that are not following the direction of the qibla in Kendari City. The research method used is qualitative descriptive with an empirical normative approach. The data collection methods that researchers use are interviews, observations, documentation and data analysis, namely data reduction, presentation of data, and concluding. The results showed that, first, the majority of the direction of the mosque's qibla that was the object of the study was inaccurate. This is based on the results of calculations and direct checks using the Spherical Trigonometric Calculation Formula and Google Earth that researchers have done, where the direction of the qibla of each mosque is 21°-22° from West to North and 68°, 38° from North to West. Of the 20 mosques studied, 13 mosques were inaccurate or not precisely in the qibla direction. Of the 13 mosques, 12 mosques whose deviation or deviation angle is more minor to the North, one mosque is the corner of deviation or deviation is more to the North or less to the South. Second, for mosques that are not right in the direction of the qibla, it must be directed towards the actual qibla; by the way, the mosque building must be rehab or renovation, but this is difficult because it requires a substantial cost (large) then the most accessible step at a meager cost; namely, the mosque shaf must be directed towards the qibla which is the most accessible and straightforward solution.

ANALYSIS OF STUDENT ERRORS IN SOLVING TRIGONOMETRY PROBLEMS BASED ON THE NEWMAN PROCEDURE

This study was motivated by student errors in trigonometry. This study aimed to describe the types of student errors in solving trigonometry problems using the Newman error analysis procedure. This research is descriptive qualitative with the subjects of vocational high school students. Data collection involved written tests, depth interviews, and documentation. The results show that most students made comprehension and transformation errors. The comprehension errors consisted of not writing down what was known and asked; immediately writing down the completion process with the wrong formula and incorrect understanding of the concept of the basic trigonometric formula. The transformation errors were not being able to transform information on the problem into the mathematical model, and incorrect in mentioning the formula.

On a polynomial involving roots of unity and its applications

Let [Formula: see text] be a prime. Gauss first introduced the polynomial [Formula: see text] where [Formula: see text] and [Formula: see text] varies over all quadratic residues modulo p and [Formula: see text]. Later Dirichlet investigated this polynomial and used this to solve problems involving the Pell equations. Recently, Sun studied some trigonometric identities involving this polynomial. In this paper, we generalize their results. As applications of our result, we extend Chowla’s result on the congruence concerning the fundamental unit of [Formula: see text] and give an equivalent form of the extended Ankeny et al. conjecture.