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Component form

  1. Feb 12, 2008 #1
    1. The problem statement, all variables and given/known data
    Find an expression in component form for 12.0 m and 170° (i+j)
    2. Relevant equations


    3. The attempt at a solution

    I was thinking about using one of these equations, but I don't know which one to use or if there is another way of doing it. Does it matter which one I use?

    Would it be

    12.0cos170? but I don't know where the i or the j would go

    Could someone please show me how to set this problem up?

    Thank you very much
  2. jcsd
  3. Feb 12, 2008 #2


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    Gold Member

    Yes, it matters which one you use for a particular component. Why not draw the vector on a graph? To break it up into its components: the x component (i) is the first equation you've written down, the y (j) component is the second one. You can prove this to yourself by using the graph and some trigonometry.

    As an additional check, you can go back from i and j to polar notion. The magnitude is essentially what I told you in the other thread i.e. |A|. The angle is tan^-1 (y/x) (thats the inverse tangent)

    EDIT: An important note about evaluating tan^-1() using a calculator. If your components are in quadrants one and four, your answer in degrees is correct. However if your components are in the second and third quadrants, your answer is off by 180 degrees. Therefore you have to add or subtract 180 degrees from the answer tan^-1() gives you. It does not matter if you add or subtract, as they are both correct. Your problem is a classic example of this. Try it!
    Last edited: Feb 12, 2008
  4. Feb 12, 2008 #3


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    Homework Helper

    i is usually the x direction
    j is usually the y direction
    draw a diagram, and see the projection onto the x and y axes to visualise, then use trig to determine which equation to use.
  5. Feb 13, 2008 #4
    Thank you very much

    Does 12sin10 look right for the i (x component)?

    Thank you
    Last edited: Feb 13, 2008
  6. Feb 13, 2008 #5
    Can someone please tell me if this is correct?

    Thank you
  7. Feb 13, 2008 #6


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    Homework Helper

    one thing is unclear here... is the angle measuring from the positive x-axis?
    draw a diagram if unsure what is what.
  8. Feb 13, 2008 #7
    Thank you

    Yes. Would i be 12cos10 and would j be 12sin10? Would I use 10°? (180-170)

    Thank you
    Last edited: Feb 13, 2008
  9. Feb 13, 2008 #8
    Yes, just be careful. 170° is in the 2nd quadrant, so your 'x' or 'i' value will be negative. So, it's actually -(12cos10).
  10. Feb 13, 2008 #9
    Thank you very much

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