This study investigates the problem-solving strategies employed by ninth-grade students when addressing symbolic and real-world contextual problems involving trigonometric ratios. Conducted with 46 ninth-grade students from a Turkish public high school, this research employed a worksheet consisting of six problems aligned with the Turkish…

We study a 1-parameter family of trigonometric definite integrals, showing how the joint usage of Information and Communication Technologies and paper-and-pencil work lead to different outputs, revealing different mathematical meanings and different concrete meanings. This family of integrals is useful for describing a phenomenon in soil…

This article reports on using open-response questions to reveal the level of, and change in, conceptual understanding of a small sample of Grade 11 learners of trigonometry in a South African high school. The investigation used learner response sheets in a regular classroom with the teacher as researcher. Combining the idea of concept image and…

This paper being an extension of Bhattacharjee (2012) is very much relevant to Year 9 to Year 10A in the "Australian Curriculum: Mathematics". It also falls within the purview of class IX to class XII curriculum of Mathematics in India (Revised NCERT curriculum) for students aged 14-17 years. In Bhattacharjee (2012), the discovery of…

Some new methods of integrating composite functions of transcendental functions are presented.

This study examined the knowledge levels of prospective mathematics teachers about the concepts of degree and radian, which are among the angle measuring units that constitute the basis of trigonometry, and the relationships between those concepts. The study group consisted of 93 prospective mathematics teachers attending a state university in…

Using modern technology to examine classical mathematics problems at the high school level can reduce difficult computations and encourage generalizations. When teachers combine historical context with access to technology, they challenge advanced students to think deeply, spark interest in students whose primary interest is not mathematics, and…

Trigonometry is one of the topics in mathematics that the students in both high school and pre-undergraduate levels need to learn. Generally, the topic covers trigonometric functions, trigonometric equations, trigonometric identities and solving oblique triangles using the Laws of Sines and Cosines. However, when solving the oblique triangles,…

The standard approach to finding antiderivatives of trigonometric expressions such as sin(ax) cos(bx) is to make use of certain trigonometric identities. The disadvantage of this technique is that it gives no insight into the problem, but relies on students using a memorized formula. This note considers a technique for finding antiderivatives of…

It is very well known that the Cauchy-Schwarz inequality is an important property shared by all inner product spaces and the inner product induces a norm on the space. A proof of the Cauchy-Schwarz inequality for real inner product spaces exists, which does not employ the homogeneous property of the inner product. However, it is shown that a real…

A new trigonometric identity derived from factorizations and partial fractions is given. This identity is used to evaluate the Poisson integral via Riemann sum and to establish some trigonometric summation identities.

Presents an approach to Vieta's formula involving pi and infinite product expansions of the sine and cosine functions. Indicates how the formula could be used in computing approximations of pi. (MVL)

The Law of Sines and The Law of Cosines are of paramount importance in the field of trigonometry because these two theorems establish relationships satisfied by the three sides and the three angles of any triangle. In this article, the authors use these two laws to discover a host of other trigonometric relationships that exist within any…

Describes a five-step graphing method for various trigonometric periodic functions. Emphases is on teaching constants and functions. (YP)