For a given rational number r, a classical theorem of Niven asserts that if cos(rp) is rational, then cos(rp) [element-of] {0,±1,±1/2}. In this note, we extend Niven's theorem to quadratic irrationalities and present an elementary proof of that.

This literature review covers 42 years and has two main objectives: to identify the obstacles to learning the polar coordinate system and to explore the teaching proposals suggested to overcome them. These questions are answered by locating and analysing articles related to the topic published in research and practitioner journals specialising in…

Students' competence in solving trigonometry has been in doubt but little attention has been given in the area of research. An assessment of students' answers to trigonometry problems is crucial to dealing with their conceptual challenges. This study employed a descriptive qualitative research design, with the goal of evaluating errors made by…

Music provides an excellent setting for students to explore trigonometric functions in a setting which is independent of their utility in resolving triangles. In this paper, we present several investigations using trigonometric functions to model musical phenomena. From a mathematical technology point of view, most examples require only function…

For integrals consisting of rational functions of sine and cosine a set of little known rules known as the Bioche rules are considered. The rules, which consist of testing the differential form of the integral for invariance under one of three simple substitutions x [right arrow] -- x, [pi] -- x, and [pi] + x, allow one to decide which of the…

The purpose of this study was to investigate the types of errors grade 10 students make in solving selected trigonometry problems. Another aim was to understand the origins of these errors that Students make when solving trigonometry problems. Another central purpose of the study was to provide instructional recommendations for addressing the…

The present educational intervention study focused on addressing some areas of improvement in the teaching and learning of trigonometric ratios in high school students. A diagnostic evaluation was performed that revealed an instrumental understanding of trigonometric concepts by the students. Subsequently, a didactic sequence was implemented that…

This qualitative case study investigates challenges faced by educators teaching trigonometry in Grade 12 within the Alfred Nzo West Education District, where persistent underperformance is linked to socioeconomic and resource limitations. Using a constructivist paradigm, six educators from diverse backgrounds participated in semi-structured…

The present study aims to explore the effect of using dynamic mathematics software in a distance education environment on students' understanding of trigonometric functions. The sample of the study consists of 45 first-year students enrolled in two associate degree programs of a state university. In the research, the lessons in the experimental…

Trigonometry is an area of mathematics that students believe to be particularly difficult and/or abstract compared to other areas of mathematics. It is introduced as the concept in the right-angled triangle from the basic level, but the curriculum of Nepal introduced it from grade nine onwards as a separate chapter. Its content area has a…

Achieving meaningful educational outcomes requires scalable strategies for mastering mathematical concepts and skills, with student engagement at the core. This paper examines the use of comprehensive, technology-enhanced activities designed to promote active learning and deeper conceptual understanding. Specifically, it focuses on the integration…

The mode of assessment is one of the most important factors influencing learning. E-assessment usually includes only checking the final answer, thus limiting teacher's ability to check the complete solution, and it does not allow inclusion of math proofs problems that constitute an important part of math content. The e-assessment module of Halomda…

This study investigates the interplay between student reasoning and instructional strategies in trigonometry education. A qualitative case study was conducted to examine how Grade 10 students employ various reasoning approaches -- deductive, inductive, abductive, analogical, and algorithmic -- when solving trigonometry problems. Each approach…

In each educational curriculum, trigonometry is an important subject at upper secondary schools and pre university level that apply in many other subjects such as algebra, calculus, geometry and physics. Many of students have serious problem in learning the trigonometric materials because usually mathematics educators transfer the trigonometric…

This paper provides some insights into the use of example-generating tasks in the design of a technology-rich learning environment to enhance students' mathematical thinking. The paper reports on an early stage of a design-based research project concerning the design of tasks and associated feedback utilising the affordances provided by a combined…