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Vector Degrees Problem

  1. Jan 20, 2009 #1
    1. The problem statement, all variables and given/known data

    Ax= -4.00 , Ay= -8.00
    Please give your answer in the interval (0,360) degrees for theta.




    2. Relevant equations

    Theta = ______ degrees

    3. The attempt at a solution

    I tried inverse of tangent (-8/-4) = 63.4 degrees for theta, but its telling me I am wrong. Tried the degree in negative and the computer showed up wrong also. Any Ideas?
     
  2. jcsd
  3. Jan 20, 2009 #2

    gabbagabbahey

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    Hmmm... well just looking at Ax and Ay, what quadrant does A lie in? Does theta=63.4 degrees lie in that quadrant? :wink:

    The problem is that the inverse tangent of (Ay/Ax) always returns a value between 0 and 180 degrees. But the tangent function has a period of 180 degrees, so tan(theta)=tan(theta+n*180)=Ay/Ax implies that theta=ArcTan(Ay/Ax)-n*180 for some integer value of n and not just theta=ArcTan(Ay/Ax).
     
  4. Jan 20, 2009 #3
    Remember the unit circle. The angle is in the third quadrant.
     
  5. Jan 20, 2009 #4
    It is in the 3rd quadrant making it positive for tangent. Just what would the variable n be?

    Thanks for the help, appreciate it
     
  6. Jan 20, 2009 #5
    Got it now, since its int he 3rd quadrant we add 180 degrees. I knew it was something so simple. so its 243.4 degrees for theta.

    Thanks,
     
  7. Jan 20, 2009 #6
    Choose n such that your angle is in the correct quadrant. In this case, what are the limits of n?
     
  8. Jan 20, 2009 #7

    gabbagabbahey

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    Exactly; A is in the 3rd quadrant.

    The tangent is positive in both the third quadrant and the first quadrant, and the arctangent always returns a value in the first to quadrants. That is why you are getting an angle that is in the first quadrant.

    Since A is in the 3rd quadrant, 'n' will be any integer that gives a theta in between 180 degrees and 270 degrees. In this case, n=-1 should do nicely.
     
  9. Jan 20, 2009 #8

    gabbagabbahey

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    Welcome :smile:
     
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