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Math Help - rotations of points

  1. #1
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    rotations of points

    Hi Can anyone explain this following example to me? I have no idea how they obtained those new coordinates. How exactly do I multiply the point A by the rotation matrix?
    Thanksrotations of points-capture.jpg
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  2. #2
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    Quote Originally Posted by srose34 View Post
    Hi Can anyone explain this following example to me? I have no idea how they obtained those new coordinates. How exactly do I multiply the point A by the rotation matrix?
    Here is the result without matrices.
    \left( {x,y} \right) \to \left( {x',y'} \right) by the system:
    \left\{ \begin{gathered}<br />
  x' = x\cos (\varphi ) - y\sin (\varphi ) \hfill \\<br />
  y' = x\sin (\varphi ) + y\cos (\varphi ) \hfill \\ <br />
\end{gathered}  \right..
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  3. #3
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    Hi
    I tried that method but my numbers are the wrong way around e.g (root(2), 0) instead of (0, root(2))
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  4. #4
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    Quote Originally Posted by srose34 View Post
    Hi
    I tried that method but my numbers are the wrong way around e.g (root(2), 0) instead of (0, root(2))
    Check your algebra.
    \left\{ \begin{gathered}<br />
  x' = 1\frac{{\sqrt 2 }}<br />
{2} - 1\frac{{\sqrt 2 }}<br />
{2} = 0 \hfill \\<br />
  y' = 1\frac{{\sqrt 2 }}<br />
{2} + 1\frac{{\sqrt 2 }}<br />
{2} = \sqrt 2  \hfill \\ <br />
\end{gathered}  \right.<br />
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  5. #5
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    ok, thanks I see what I was doing wrong
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