This topic is part of the HSC Mathematics Extention 1 syllabus under the topic Trigonometric Functions.

When doing harder trigonometric questions, it’s handy to know double and even triple angle formulae and how they are derived. Here is an example on how to derive triple angle formulae.

The formulae are the following:

sin(3 \theta) = 3 sin(\theta)-4sin^3(\theta) cos(3 \theta) = 4 cos^3(\theta)-3 cos(\theta) tan(3 \theta) = \frac{3 tan(\theta)-tan^3(\theta)}{1-3 tan^2(\theta)}

### Triple angle formulae