We present a method to compute the power series expansions of e[superscript x] ln (1 + x), sin x, and cos x without relying on mathematical analysis. Using the properties of elementary functions, we determine the coefficients of each series through the method of undetermined coefficients. We have validated our formulae through the use of…

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…

In some secondary mathematics curricula, there is a topic called Stereometry that deals with investigating the position and finding the intersection, angle, and distance of lines and planes defined within a prism or pyramid. Coordinate system is not used. The metric tasks are solved using Pythagoras' theorem, trigonometric functions, and sine and…

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…

The telescoping sum constitutes a powerful technique for summing series. In this note, this technique is illustrated by a series of problems starting off with some simple ones in arithmetic, then some in trigonometry, famous families of numbers, Apery-like formulas, and finally ending with a class of problems that are solved by computer.

Three major techniques are employed to calculate [pi]. Namely, (i) the perimeter of polygons inscribed or circumscribed in a circle, (ii) calculus based methods using integral representations of inverse trigonometric functions, and (iii) modular identities derived from the transformation theory of elliptic integrals. This note presents a…

In this paper we have converted the Laplace transform into an integral equation of the first kind of convolution type, which is an ill-posed problem, and used a statistical regularization method to solve it. The method is applied to three examples. It gives a good approximation to the true solution and compares well with the method given by…

Non-linear second-order differential equations whose solutions are the elliptic functions "sn"("t, k"), "cn"("t, k") and "dn"("t, k") are investigated. Using "Mathematica", high precision numerical solutions are generated. From these data, Fourier coefficients are determined yielding approximate formulas for these non-elementary functions that are…

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…

Some insights are provided into techniques for removing the mystery of how calculators evaluate functions. (Author/MK)

Consideration of a definite integral in an advanced calculus class led to a great deal of mathematical thinking and to the joy of discovery. Graphing calculators allowed students to investigate quick solutions which should be regarded as stepping stones to additional investigation and rigorous proof. With slight modifications to their proofs,…

Emphasizes a real-world-problem situation using sine law and cosine law. Angles of elevation from two tracking stations located in the plane of the equator determine height of a satellite. Calculators or computers can be used. (LDR)

The fourth of four quins intended to develop computational skills with non-negative rational numbers through applications to business and industry, this guidebook on minimum course content is designed for the student who has acquired basic computational skills with non-negative rational numbers. Topics include ratio, proportion, and percentage…