Trigonometry is an important section in mathematics that links algebraic, geometric and graphical reasoning. Many secondary school learners are not familiar with these types of reasoning; thus, trigonometry presents a challenge for these learners. The traditional 'chalk and talk' method of teaching trigonometry is used by many teachers; however,…

Participants were pretrained and tested on mutually entailed trigonometric relations and combinatorially entailed relations as they pertained to positive and negative forms of sine, cosine, secant, and cosecant. Experiment 1 focused on training and testing transformations of these mathematical functions in terms of amplitude and frequency followed…

In this article we consider an example suitable for investigation in many mid and upper level undergraduate mathematics courses. Fourier series provide an excellent example of the differences between uniform and non-uniform convergence. We use Dirichlet's test to investigate the convergence of the Fourier series for a simple periodic saw tooth…

This paper presents a derivation of all five Lagrange points by methods accessible to sixth-form students, and provides a further opportunity to match Newtonian gravity with centripetal force. The predictive powers of good scientific theories are also discussed with regard to the philosophy of science. Methods for calculating the positions of the…

In light of evidence indicating that errors in making accurate pie charts are prevalent, an alternative method for constructing pie charts is proposed. It involves the use of a simple trigonometric formula to compute a factor of the length of the chord that defines a given percentage sector. This factor is multiplied by the radius of the circle to…

Discusses a method of graphing polar equations using information from the Cartesian graphs of trigonometric functions. (MKR)

Presents an activity which focuses on the graph of sine and cosine functions and other properties that can easily be inferred from the graph. (ASK)

Using MAPLE enables students to consider many examples which would be very tedious to work out by hand. This applies to graph plotting as well as to algebraic manipulation. The challenge is to use these observations to develop the students' understanding of mathematical concepts. In this note an interesting relationship arising from inverse…

The graph of this function is analyzed by using calculus methods and the computer. The graph in most texts is shown to be misleading. (MP)

A computer program is presented that generates problem sets involving sketching graphs of trigonometric functions using graphical addition. The students use calculators to sketch the graphs and a computer solution is used to check it. (MP)

An integral, either definite or improper, cannot always be computed by elementary methods, such as reversed usage of differentiation formulae. Graphical properties, in particular symmetries, can be useful to compute the integral, via an auxiliary computation. We present graded examples, then prove a general result. (Contains 4 figures.)

Theorems about the hyperbola which are ordinarily introduced in calculus courses can be proved without using the calculus. (SD)