A common question is to express cos3θ in terms of cosθ and sin3θ in terms of sinθ.
Here is how you do it using the addition and double angle identities.

cos 3θ in terms of cos θ

Example:

  1. \text{Express } \cos{3} \theta \text{ in terms of } \cos \theta

sin 3θ in terms of sin θ

Example:

  1. \text{Express } \sin{3} \theta \text{ in terms of } \sin \theta