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Decomposing vectors

  1. Aug 30, 2015 #1
    1. The problem statement, all variables and given/known data
    The magnitude of the vector is 6 m, and points 35 degrees north of west. Find the x component of the vector.

    2. Relevant equations

    x = |R|cos(theta)

    3. The attempt at a solution

    I am confused about what degrees to input into the cosine function. I know that the vector is pointing 35 degrees north of west, which means that the x component will be negative, but there are two ways I could do it am I am not sure which one I should do. First, I could tack on a negative and calculate -(6 m)cos35 = -4.9 m. Another way is not tack on a negative and calculate (6 m)cos145 = -4.9 m. Which method is better, and which one should I use on a regular basis?
     
  2. jcsd
  3. Aug 30, 2015 #2

    Geofleur

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    Both ways are fine, as long as you don't try to memorize a rule and blindly apply it. Personally, I like the first approach, and just tack on the negative sign when I know there should be one.
     
  4. Aug 30, 2015 #3

    SteamKing

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    Well, you could learn the angles for the cardinal points of the compass, but why do that when you can just make something up?

    East = 0°
    North = 90°
    West = 180°
    South = 270°
     
  5. Aug 30, 2015 #4
    Huh?
     
  6. Aug 31, 2015 #5

    SteamKing

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    You've never seen the following diagram (or a similar one)?:



    ucad.gif


    It should have been used when you studied trigonometry.

    After all,
    cos (0°) = 1.0
    sin (0°) = 0.0

    cos (90°) = 0.0
    sin (90°) = 1.0

    cos (180°) = -1.0
    sin (180°) = 0.0

    cos (270°) = 0.0
    sin (270°)= -1.0

    etc., etc.
     
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