# The Rotation Matrix

• Mar 28th 2008, 06:51 PM
checky123
The Rotation Matrix
The rotation matrix for an anti-clockwise rotation is
|cos -sin|
|sin cos|
Find the matrix for a rotation in a clockwise direction using matrix methods.
• Mar 28th 2008, 07:37 PM
TheEmptySet
Quote:

Originally Posted by checky123
The rotation matrix for an anti-clockwise rotation is
|cos -sin|
|sin cos|
Find the matrix for a rotation in a clockwise direction using matrix methods.

$\displaystyle \begin{bmatrix} \cos(\theta) && -\sin(\theta) \\ \sin(\theta) && \cos(\theta) \\ \end{bmatrix}$

Is a counter clockwise rotation of angle theta

note that $\displaystyle \cos(-\theta)=\cos(\theta) \mbox{ and } \sin(-\theta)=-\sin(\theta)$

so to rotate clockwise try negative theta

$\displaystyle \begin{bmatrix} \cos(-\theta) && -\sin(-\theta) \\ \sin(-\theta) && \cos(-\theta) \\ \end{bmatrix} = \begin{bmatrix} \cos(\theta) && \sin(\theta) \\ -\sin(\theta) && \cos(\theta) \\ \end{bmatrix}$

I hope this helps

Good luck