ARTICLE | doi:10.20944/preprints202303.0146.v1
Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: sine; cosine; Bhaskara I’s formula
Online: 8 March 2023 (06:25:57 CET)
We approximate the trigonometric function sine and cosine on the interval . This analysis provides two formulas to approximate sine and cosine. At first, we try to derive the formula which involves a square root, and then we derive another formula that does not require any use of a square root. Nevertheless, after deriving the procedure which requires no square root, we further try to increase its accuracy and then derive another formula that approximates trigonometric functions more accurately on the interval [0, pi/2]. So, this analysis provides mainly two types of procedures. One uses square roots, whereas the other does not. We also focus on ensuring the accuracy of these trigonometric functions in the interval [0,pi/2]. This accuracy analysis is portrayed using the graph. This graph shows the difference between the values generated by the functions defined here and the actual value of these functions. So, these graphs also indicate the error of these functions on that interval. Finally, we compare our approximation with the approximation formula of the 7th-century Indian Mathematician Bhaskara I.
ARTICLE | doi:10.20944/preprints202209.0378.v1
Subject: Computer Science And Mathematics, Mathematics Keywords: Mathematics; Factors; Success; Failure; Students; Teachers;
Online: 26 September 2022 (05:35:23 CEST)
Background: Bangladeshi students from science, technology, engineering, and mathematics (STEM) often struggle with solving many mathematical problems in different pedagogic contexts. They mostly lack the considerable prior learning or strong basics required to cope with the teaching and learning materials used at the undergraduate levels, which leads many students to take readmissions every year. Objective: This research aims at investigating the factors affecting the success and deficit of university undergraduate mathematics students in Bangladesh. The mixed-method research incorporates quantitative and qualitative data analysis on the students' and teachers’ perspectives regarding the issues. The authors focus more on categorizing the reasons influencing effective mathematics pedagogies than on identifying new or unknown causes. Methodology: This study is outlined in three phases. The phases include i. Exploratory qualitative survey ii. Quantitative triangulation survey, iii. Explanatory semi-structured interviews. Findings: First, the qualitative survey exposes the important factors that highlight the student’s success and failure in mathematics. Next, the quantitative data confirm that there are some similarities and dissimilarities between students’ and teachers’ perceptions. Also, the coefficient correlation analysis shows male students lack consistency and passion for study resulting in poor performances. Conversely, female students emphasize the inability to connect mathematical theories to real-life usages, curriculum loads, and unavailable resources as the reasons for underperformance. Finally, the interview data demonstrate the students attribute their failure to inadequate practices, memorizing habits, poor teaching, low motivation, and external distractions. Also, students acknowledge the necessity of steady practice, clear understanding, regular study, and working strategies for successful mathematics education. Teachers emphasize students’ clear concepts, aptitude, motivation, and curiosity for successful learning. Conclusion: This conclusion proposes a fresh start with the local mathematics pedagogic practices by analyzing teacher-student feedback on the success and failure factors impacted by varied individual and contextual elements. The study offers inclusive feedback on the part of both stakeholders. However, an open discussion or interaction between students and teachers might be needed to enhance mutual trust and understanding between them.