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Math Help - How to find the angle and direction of a rotation matrix in 2D?

  1. #1
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    How to find the angle and direction of a rotation matrix in 2D?

    If I have a rotation matrix:
    (-0.7 0.7)
    (-0.7 -0.7)

    how can I get the angle and the direction of it?

    If I do:
    (cos-1(-0.7) -sin-1(0.7)
    (sin-1(-0.7) cos-1(-0.7)

    I get:
    (134 -44)
    (-44 134)

    which are two different angles, 135 and -44 in degrees, how do I know which one is the answer and what direction the rotation is happening?

    I couldn't find anything on the internet, so any links explaining how to get the angle and the direction would be grateful.
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  2. #2
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    Re: How to find the angle and direction of a rotation matrix in 2D?

    Quote Originally Posted by LoneWolf View Post
    If I have a rotation matrix:
    (-0.7 0.7)
    (-0.7 -0.7)

    how can I get the angle and the direction of it?

    If I do:
    (cos-1(-0.7) -sin-1(0.7) <--- typo!
    (sin-1(-0.7) cos-1(-0.7)

    I get:
    (134 -44)
    (-44 134)

    which are two different angles, 135 and -44 in degrees, how do I know which one is the answer and what direction the rotation is happening?

    I couldn't find anything on the internet, so any links explaining how to get the angle and the direction would be grateful.
    1. I assume that your matrix looks like this:

    \left(\begin{array}{cc} -\frac12 \sqrt{2}&\frac12 \sqrt{2} \\ -\frac12 \sqrt{2} & -\frac12 \sqrt{2} \end{array}\right)

    2. You should know that \sin(135^\circ) = \sin(45^\circ)

    You now have all informations to determine the angle of rotation.
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