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…

This article presents a task providing college students opportunities to build on their high school knowledge of trigonometry to explore parametric equations and inverse trigonometric relationships within a contextual learning ladder problem.

This study analysed first-year preservice teachers' understanding of trigonometric equations at a South African university in the Eastern Cape province. We employed the Action-Process-Object-Schema (APOS) framework to analyse the mental constructions made by preservice teachers in solving trigonometric equations. A qualitative case study design…

The aim of the exploratory method research centered on the presence of mathematical tools in STEM through three main questions: Is mathematics an essential tool in the field of STEM? Can mathematics complete projects solely with mathematical and digital tools? Does understanding mathematical modeling affect STEM teaching? A better understanding of…

If using different instruments obtained a different analogical reasoning component. With use people-piece analogies, verbal analogies, and geometric analogies, have analogical reasoning component consists of encoding, inferring, mapping, and application. Meanwhile, with use analogical problems (algebra, source problem and target problem is equal),…

Purpose: Analogical reasoning has been studied using a variety of tasks that generally required consideration of the relationship between the object and its integration to conclude an analog schema. The aim of this study was to describe the model of analogical reasoning schema based on some analogical problems. Research Method: In this study used…

"Media Clips" appears in every issue of "Mathematics Teacher," offering readers contemporary, authentic applications of quantitative reasoning based on print or electronic media. Based on "In All the Light We Cannot See" (2014), by Anthony Doerr, this article provides a brief trigonometry problem that was solved by…

The discrete Fourier series is a valuable tool developed and used by mathematicians and engineers alike. One of the most prominent applications is signal processing. Usually, it is important that the signals be transmitted fast, for example, when transmitting images over large distances such as between the moon and the earth or when generating…

Pythagoras Theorem is an old mathematical treatise that has traversed the school curricula from secondary to tertiary levels. The patterns it produced are quite interesting that many researchers have tried to generate a kind of predictive approach to identifying triples. Two attempts, namely Diophantine equation and Brahmagupta trapezium presented…

The answers offered by computer algebra systems (CAS) can sometimes differ from those expected by the students or teachers. The comparison of the students' answers and CAS answers could provide ground for discussion about equivalence and correctness. Investigating the students' comparison of the answers gives the possibility to study different…

Pythagoras' theorem in two and three dimensions appears in General Mathematics, Units 1-2, section 6 (Geometry and trigonometry: Shape and measurement) in the Victorian Certificate of Education Mathematics Study Design (Victorian Curriculum Assessment Authority, 2010). It also comes in Further Mathematics, Units 3-4 (Applications: Geometry and…

This article focuses on a simple trigonometric problem that generates a strange phenomenon when different methods are applied to tackling it. A series of problem-solving activities are discussed, so that students can be alerted that the precision of diagrams is important when solving geometric problems. In addition, the problem-solving plan was…

A closed form solution for the trigonometric integral [integral]sec[superscript 2k+1]xdx, k=0,1,2,..., is presented in this article. The result will fill the gap in another trigonometric integral [integral]sec[superscript 2m+1] x tan[superscript 2n]xdx, which is neglected by most of the calculus textbooks due to its foreseeable unorthodox solution…

To find the point between two massive spherical bodies at which their gravitational fields cancel is an apparently simple problem usually found in introductory physics textbooks. However, by noting that such a point does not exist when the distance between the spheres is small and one of the masses is much smaller than the other--e.g., between the…

We discuss a class of trigonometric functions whose corresponding Fourier series, on a conveniently chosen interval, can be used to calculate several numerical series. Particular cases are presented and two recent results involving numerical series are recovered. (Contains 1 note.)