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Homework Help: Trig: Angles of Vectors

  1. May 5, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the magnitude of a and the smallest positive angle theta from the positive x-axis to the vector OP that corrosponds to a.

    a= (3,-3)

    2. Relevant equations

    a1 = ||a|| * cos theta
    a2 = ||a|| * sin theta
    3. The attempt at a solution

    ||a|| = [tex]\sqrt{}[/tex](9+9) = 3[tex]\sqrt{}[/tex]2
    a1 = 3[tex]\sqrt{}[/tex]2 * cos theta

    =1/[tex]\sqrt{}[/tex]2 =acos = 45 degrees.

    However doing the other side of the equation...

    a2= -1/[tex]\sqrt{}[/tex]2 = asin = -45 degrees = 315 degrees, which is the right answer. I thought they were supposed to be consistent...
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 5, 2010 #2

    Mark44

    Staff: Mentor

    arccos produces an angle between 0 and 180 degrees, while arcsin produces an angle between -90 and + 90 degrees. Since your vector is in the fourth quadrant, an angle of 45 degrees wouldn't be right, nor would -45 degrees, since the problem asks for a positive angle.
     
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