In this paper, Richard Ollerton presents two alternative approaches to proving the six standard trigonometric angle sum and difference identities. They are suitable for students who have an understanding of rotation matrices.

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…

This article introduces a trigonometric field (TF) that extends the field of real numbers by adding two new elements: sin and cos--satisfying an axiom sin[superscript 2] + cos[superscript 2] = 1. It is shown that by assigning meaningful names to particular elements of the field, all known trigonometric identities may be introduced and proved. Two…

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)

Argues that the derivation of the area of a circle using integral calculus is invalid. Describes the derivation of the area of a circle when the formula is not known by inscribing and circumscribing the circle with regular polygons whose areas converge to the same number. (MDH)

Discusses solutions to the problem of maximizing the range of a projectile. Presents three references that solve the problem with and without the use of calculus. Offers a fourth solution suitable for introductory physics courses that relies more on trigonometry and the geometry of the problem. (MDH)

Presents three teaching ideas involving (1) results of participation in the annual American Statistical Association's poster contest for students in grades K-12; (2) a variation on an annuity problem in which the contribution each year is increased by a given percentage; and (3) concrete activities to help students understand the meaning of radian…

Presents a teaching model as an activity to introduce preservice secondary mathematics teachers to the law of cosines. The activity is student-centered in which students construct figures; measure angles and segments; calculate areas; investigate relationships; and communicate their results. (MDH)

Methods use to reconstruct traffic accidents provide settings for real life applications for students in precalculus, mathematical analysis, or trigonometry. Described is the investigation of an accident in conjunction with the local Highway Patrol Academy integrating physics, vector, and trigonometry. Class findings were compared with those of…