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Math Help - The Rotation Matrix

  1. #1
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    Question 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.
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by checky123 View Post
    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}<br />
\cos(\theta) && -\sin(\theta) \\<br />
\sin(\theta) && \cos(\theta) \\<br /> <br />
\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}<br />
\cos(-\theta) && -\sin(-\theta) \\<br />
\sin(-\theta) && \cos(-\theta) \\<br /> <br />
\end{bmatrix} = \begin{bmatrix}<br />
\cos(\theta) && \sin(\theta) \\<br />
-\sin(\theta) && \cos(\theta) \\<br /> <br />
\end{bmatrix}

    I hope this helps

    Good luck
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