Expressing sinⁿθ and cosⁿθ in terms of sin(kθ) and cos(kθ)

Introduction – new identities you will need

In the next set of videos, I start to look at how we can express sinⁿθ and cosⁿθ in terms of sin(kθ) and cos(kθ). But before we can do this I need to show you some new identities which you will need to learn which are developed from de Moivre’s theorem.

Expressing cosⁿθ in terms of cos(kθ)

I now use the identities we derived in the previous video

to show you how we can express cosⁿθ in terms of cos(kθ) by using the example:
Express the following:

1. Express cos³θ in terms of cos(kθ)

Expressing sinⁿθ in terms of sin(kθ) when n is odd

I now use the identities we derived in the first video to show you how we can express sinⁿθ in terms of sin(kθ) where n is odd by using the example:

Express the following:

1. Express sin³θ in terms of sin(kθ)

Expressing sinⁿθ in terms of cos(kθ) when n is even

Express the following:

1. Express sin⁴θ in terms of cos(kθ)