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Linear transformation rotation

  1. Feb 9, 2008 #1
    1. The problem statement, all variables and given/known data
    T: R2-->R2 first reflects points through -3pi/4 radian (clockwise) and then reflects points through the horizontal x1-axis. [Hint T(e1)= (-1/sqrt2, 1/sqrt2)



    3. The attempt at a solution
    I just don't understand why the points would be (-1/sqrt2, 1/sqrt2). If it's -3pi/4, why wouldn't it be (-(sqrt2)/2, -(sqrt2)/2)?
     
  2. jcsd
  3. Feb 9, 2008 #2

    HallsofIvy

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    Did you miss the part about the reflection or are you rotating the wrong way? Rotating (1, 0) -3pi/4 radians (clockwise as it says) gives you (-1/sqrt(2), -1/sqrt(2)) but then the reflection through the horizontal axis changes that to (-1/sqrt(2),+1/sqrt(2)).
     
  4. Feb 9, 2008 #3
    Doesn't -3pi/4 radians correlate to (-(sqrt2)/2, -(sqrt2)/2) though (on a unit circle)? Where is the sqrt2 on the bottom coming from?
     
  5. Feb 9, 2008 #4

    HallsofIvy

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    Are you aware that 2= (sqrt(2))*(sqrt(2))? 1/sqrt(2) is exactly the same as sqrt(2)/2.
     
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