Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Different rotation matrix, with cosine?
  1. Matrix in Rotation (Replies: 2)

  2. Rotational Matrix (Replies: 5)

  3. Rotation matrix (Replies: 4)

Loading...