Graphs of the Trigonometric Functions

By M Bourne

Where do we use this?


240 volt

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.


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.