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Rotation of Vectors

  1. Jun 24, 2015 #1
    < Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >

    Hello,

    I have a problem with rotation matrices, its just a comparison problem. Θ must be 240 or -120, I don't know how the book show the answer like that, these are the two matrices

    \begin{array}--1/2&\sqrt{(3)}/2\\-\sqrt{(3)}/2&-1/2\end{array}

    with

    \begin{array}ccosΘ&-sinΘ\\sinΘ&cosΘ\end{array}

    - I tried to take element 1,1 and 2,1 , it gives 120 & -60. How is that suppose to be 240 or -120?
     
    Last edited by a moderator: Jun 24, 2015
  2. jcsd
  3. Jun 24, 2015 #2

    Fredrik

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    When you match the 11 and 21 components, you get two equations. Each of these equations has two solutions in the interval [0,360). Only one of the two solutions to the first equation will be a solution to the second equation as well.
     
  4. Jun 25, 2015 #3

    Ray Vickson

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    Look at the first column of your matrix: you have ##\cos(\theta) = -1/2## and ##\sin(\theta) = -\sqrt{3}/2##. Since both ##\sin(\theta)## and ##\cos(\theta)## are ##< 0##, in what quadrant must ##\theta## lie? Just draw a picture of you need more insight.
     
  5. Jun 26, 2015 #4
    -120 and 240 is the same angle.
     
  6. Jun 26, 2015 #5

    Fredrik

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    Nitpick: They're equivalent, but not the same. (cos 240,sin 240) and (cos(-120),sin(-120)) are however the same point in ##\mathbb R^2##.
     
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