The content of the modules:
It is an interesting exercise to sit back and think about how we have developed the topic of trigonometry during the earlier secondary school years.
We commenced by looking at ratios of sides in a right-angled triangle. This enabled us to find unknown sides and angles. We extended this to include non-right-angled triangles using the sine and cosine rules.
In the module Trigonometric functions and circular measure, we redefined the sine and cosine functions in terms of the coordinates of points on the unit circle. This enabled us to define the sine and cosine of angles greater than \(90^\circ\) and to plot the graphs of the trigonometric functions and discover their periodic nature.
The sine and cosine functions are used to model periodic phenomena in nature, such as waves, tides and signals. Indeed, these functions are used to model all sorts of oscillatory motion arising in a range of subjects, including economics and ecology.
In this module, we continue this development by applying the ideas and techniques of calculus to the trigonometric functions. For example, if we wish to analyse the motion of a particle modelled by a trigonometric function, we can use calculus to find its velocity and acceleration.
The simplicity of the results obtained by doing this is amazing and has wide-ranging impact in physics and electrical engineering, and indeed in any area in which periodic motion is being modelled.