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Different rotation matrix, with cosine?

  1. Sep 10, 2011 #1
    I know that a proper orthogonal rotation matrix in [itex]R^{2}[/itex] has the form

    [cos [itex]\theta[/itex] sin [itex]\theta[/itex]
    -sin [itex]\theta[/itex] cos [itex]\theta[/itex]]

    which would rotate a vector by the angle [itex]\theta[/itex]. However, I have also seen the matrix

    [sin [itex]\theta[/itex] cos [itex]\theta[/itex]
    -cos [itex]\theta[/itex] sin [itex]\theta[/itex]]

    What type of rotation is this? Is it even a rotation matrix? Thank you in advance.
  2. jcsd
  3. Sep 10, 2011 #2
    Recall that [itex]\cos(\frac{\pi}{2}-\theta)=\sin(\theta)[/itex] and [itex]\sin(\frac{\pi}{2}-\theta)=\cos(\theta)[/itex]. So by these identities, your matrix turns into a standard rotation matrix.
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