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Math Help - Angle of rotation in a matrix

  1. #1
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    Angle of rotation in a matrix

    The matrix [-0.8 -0.6
    0.6 -0.8] (a 2x2 matrix)

    represents a rotation. Find the angle of rotation (in radians).

    This one has me stumped, any help would be appreciated. The answer is 2.5 radians but the approach is where I am lost.
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  2. #2
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    You are probably expected to know that a rotation \theta can be represented by the matrix
    \left[\begin{array}{cc} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{array}\right]
    This does not, however, give 2.5 radians so I suspect you have either copied this out wrong or the source is incorrect.
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  3. #3
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    I understand that is the rotation matrix, what I don't understand is how you come up with the final angle of rotation. Do you plug in the numbers into the corresponding thetas? Thanks again for the help. I would be more specific but I have to head to work. Any help would be appreciated.
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  4. #4
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    Quote Originally Posted by badgerigar View Post
    You are probably expected to know that a rotation \theta can be represented by the matrix
    \left[\begin{array}{cc} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{array}\right]
    This does not, however, give 2.5 radians so I suspect you have either copied this out wrong or the source is incorrect.
    I think it does give 2.5 radians (to 2 significant figures). If \cos\theta is negative and \sin\theta is positive then \pi/2<\theta<\pi. The angle in that interval with \cos\theta = -0.8 is \pi - \arccos0.8 \approx 3.14 - 0.64 = 2.5.
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  5. #5
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    Opalg is right, sorry to have confused you
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