Learning Resources
Outcomes
In this lesson you will learn
- how to find the period of the resulting function when two trigonometric functions are added together
By the end of this section students will be able to:
- model problem situations with combinations and compositions of functions
- investigate and interpret combinations and compositions of functions
Introduction
Some applications and problem situations require a combination of two or more functions to make a realistic model. For example, to reproduce an instrumental sound accurately on an electronic synthesizer, the relative strength of each sound and pitch must be analyzed for understanding. Each pitch can be represented by a sine function, and the addition of these sine functions creates a desired effect.
The activities in this section will have you analyzing musical notes to gain an understanding of how to combine trigonometric functions so that the same note can be synthesized and replayed in different pitches.
Obviously to be successful with this section, you will need to have a solid understanding of the work done in chapter 2 on combinations of functions. Although this section is a short one, do not under estimate its importance. The exploration of patterns and the prediction of the shape of the graph for any given function or function combination is a critical concept.
This unit of work should take about 1.5 to 2 hours to complete.
Prerequisites
To be successful in this lesson, it would be helpful to know the following:
- radian measure
- periodic of a trigonometric function
- amplitude of a trigonometric function
- how to find the sum and product of polynomial functions
- how to find the lowest common multiple of a set of numbers