DT6 | Deriving Trigonometry – Triple Angle Formulae

So last week we touched on using addition formulae to yield the double angle formulae. This article will explore how to obtain the triple angle formula for each trigonometric function.

We will continue using the addition formula to help us.

Using the addition formula, we can work out the following:

Notice that we used the addition formula, the Pythagorean identity and the double angle formula to eventually get our answer.

It seems like the derivation of sin3ϴ requires the knowledge of what sin2ϴ is.

Let’s do the same for cosine:

And tangent:

With that, we have the triple angle formula for the three trigonometric functions:

Next week, we will explore the possibilities of a quadruple angle formula.

Stay tuned for more! Thanks for reading my Messy Workings 😊