# Graphs of the Trigonometric Functions

By M Bourne

Where do we use this?

In the UK, electricity is supplied at 240 V, 50 Hz. The graph of this voltage has a period of 0.02 sec and an amplitude of 240 V.

### Tip

The best thing to do in this section is to learn the basic shapes of each graph. Then it is only a matter of considering what effect the variables *a*, *b* and *c* are having. You can do a table of values and join the dots, but that becomes painful very quickly.

### Trigonometry Applications

Check out lots more uses of trigonometry.

## Why study trigonometric graphs?

The graphs in this section are probably the most commonly used in all areas of science and engineering. They are used for **modelling** many different natural and mechanical phenomena (populations, waves, engines, acoustics, electronics, UV intensity, growth of plants and animals, etc).

The trigonometric graphs in this chapter are **periodic**, which means the shape repeats itself exactly after a certain amount of time. Anything that has a **regular cycle** (like the tides, temperatures, rotation of the earth, etc) can be modelled using a sine or cosine curve.

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## Overview of Trigonometric Graphs

Here's a movie that gives an overview of the concepts in this chapter.

We begin the chapter with an examination of what amplitude means and the effect of the "*a*" variable.

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Chapter Contents

- Graphs of the Trigonometric Functions
- 1. Graphs of y = a sin x and y = a cos x
- 2. Graphs of y = a sin bx and y = a cos bx
- 2a. Frequency of Music Notes
- 3. Graphs of y = a sin(bx + c) and y = a cos(bx + c)
- 4. Graphs of tan, cot, sec and csc
- 5. Applications of Trigonometric Graphs
- 6. Composite Trigonometric Graphs
- 6a. Biorhythm Graphs
- 7. Lissajous Figures