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Homework Help: X an y components of a vector

  1. Sep 8, 2010 #1
    1. The problem statement, all variables and given/known data

    what are the x and y components of a vector a in the xy plane if its direction is 210(degrees) counterclockwise from the positive direction of the x axis and its magnitude is 14 m.

    2. Relevant equations

    vector is in the third quadrant with an angle of 30(degrees)

    3. The attempt at a solution

    i got the angle to be 30(degrees) so i just did

    14sin30 for the x component = 7.0
    14cos30 for the y component = 12.1

    should they both be negative since there in the third quadrant or do the negatives cancel to get a positive.
     
  2. jcsd
  3. Sep 8, 2010 #2

    Char. Limit

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    Gold Member

    Negatives cancel only when you multiply them. Since you aren't multiplying here, both parts are negative.
     
  4. Sep 8, 2010 #3
    would my answers be correct then

    x = -7.0

    y= -12.1
     
  5. Sep 8, 2010 #4

    Char. Limit

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    That seems right, yes.

    Although, if significant figures were important, the y component might have to be rounded... I'm not sure how important they are here.
     
  6. Sep 8, 2010 #5
    14.cos 30=x . if it is 30 degree to x (210), x have to be bigger than y. (to correct)
     
  7. Sep 8, 2010 #6
    well if its 210(degrees) counterclockwise then wouldnt the angle be 30(degrees) sin 210-180 = 30 degrees
     
  8. Sep 8, 2010 #7
    why would x be cos and not y. if the vector is in the third quadrant and cos is adjacent/hypotenuse then adjacent would be x so the only side left would be y which you would be solving for.
     
  9. Sep 9, 2010 #8
    anybody please
     
  10. Sep 9, 2010 #9

    Char. Limit

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    I'm not sure what you mean...

    If you mean that the x component should correspond to the cosine, this is because the cosine of the angle measures the length of the adjacent side to the angle, in this case, the x-axis.
     
  11. Sep 9, 2010 #10
    ok i got it thanks.

    14cos30 = -12.1 x-component
    14sin30 = -7.0 y-component
     
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