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,…

Studies incorporating technology into the teaching of trigonometry, although sparse, have demonstrated positive effects on student achievement. The optimal sequence for integrating technology with teacher-led mathematics instruction has not been determined. Our research investigated whether technology has a greater impact on student achievement…

In the year 1837 mathematical proof was set forth authoritatively stating that it is impossible to trisect an arbitrary angle with a compass and an unmarked straightedge in the classical sense. The famous proof depends on an incompatible cubic equation having the cosine of an angle of 60 and the cube of the cosine of one-third of an angle of 60 as…

In this pedagogical article, I explore a unified approach in obtaining the derivatives of functions and their inverses by adopting a guided self-discovery approach. I begin by finding the derivative of the exponential functions and the derivative of their inverses, the logarithmic functions. I extend this approach to generate formulae for the…

This paper reports upon particular aspects of a study carried out by Delice in 2003, the main aim of which was to compare the performance of students in the 16-19 age group from Turkey and England on trigonometry of "A-level standard" and then to compare the curriculum and assessment provision in each country to seek possible…

Herring in the ocean between Iceland and Norway was one of the largest fish stocks in the world until the fishery crashed in the late 1960s. The catch in 1971 was only 20 thousand metric tons in contrast with the record of 2 million tons in 1966 and the spawning stock declined from 10 million tons to 10 thousand tons in 20 years. After 25 years of…

The analysis and simulation of spiral growth in plants integrates algebra and trigonometry in a botanical setting. When the ideas presented here are used in a mathematics classroom/computer lab, students can better understand how basic assumptions about plant growth lead to the golden ratio and how the use of circular functions leads to accurate…