# The Rotation Matrix

• March 28th 2008, 07:51 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.
• March 28th 2008, 08:37 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.

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

\end{bmatrix}$

Is a counter clockwise rotation of angle theta

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

so to rotate clockwise try negative theta

$\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