# Math Help - Develop a formula for cosine

1. ## Develop a formula for cosine

How to you develop a formula for sin(11theta) as a degree- 11 polynomial in cos(theta).

2. Originally Posted by christenc05
How to you develop a formula for sin(11theta) as a degree- 11 polynomial in cos(theta).
$\sin (11\theta) = \sin (10\theta + \theta) = \sin(10\theta)\cos(\theta) + \sin(\theta)\cos(10\theta)$

$= 2\sin(5\theta)\cos(5\theta)\cos(\theta) + \sin(\theta)[2\cos^2(5\theta) - 1]$

just continue the process of using the identities until the angle is $\theta$ only and in terms of $\cos \theta$