# Rewriting cos

• Jan 25th 2011, 01:30 PM
abc10
Rewriting cos
How would I rewrite cos3theta in terms of costheta any help would be much appreciated!
• Jan 25th 2011, 01:32 PM
dwsmith
Quote:

Originally Posted by abc10
How would I rewrite cos3theta in terms of costheta any help would be much appreciated!

$\displaystyle \cos(2x+x)=\cos(2x)\cos(x) - \sin(2x)\sin(x)=\cdots$
• Jan 25th 2011, 01:47 PM
Quote:

Originally Posted by abc10
How would I rewrite $\displaystyle cos3\theta$ in terms of $\displaystyle cos\theta$ any help would be much appreciated!

$\displaystyle Cos3\theta=Cos(2\theta+\theta)$

$\displaystyle Cos(A+B)=CosACosB-SinASinB$

$\displaystyle \Rightarrow\ Cos3\theta=Cos2\theta\ Cos\theta-Sin2\theta\ Sin\theta$

$\displaystyle Cos2A=Cos^2A-Sin^2A$

$\displaystyle Sin2A=2SinACosA$

$\displaystyle Sin^2A=1-Cos^2A$

$\displaystyle \Rightarrow\ Cos3\theta=\left[Cos^2\theta-Sin^2\theta\right]Cos\theta-2Sin\theta\ Cos\theta\ Sin\theta$

$\displaystyle =Cos^3\theta-\left(1-Cos^2\theta\right)Cos\theta-2\left(1-Cos^2\theta\right)Cos\theta$
• Jan 25th 2011, 01:52 PM
abc10
You guys rock!