Develop a formula for cosine left parenthesis 3 theta right parenthesis as a third-degree polynomial in the variable cosine theta.
To find a third-degree polynomial for cos(3θ) in terms of cos(θ), we can use the triple angle formula for cosine:
cos(3θ) = 4cos^3(θ) - 3cos(θ)
Let x = cos(θ), then we have:
cos(3θ) = 4x^3 - 3x
Therefore, the third-degree polynomial for cos(3θ) in terms of cos(θ) is:
4x^3 - 3x