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:
- 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:
- Express sin3θ in terms of sin(kθ)
Expressing sinnθ in terms of cos(kθ) when n is even
Express the following:
- Express sin4θ in terms of cos(kθ)