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Why is this equation dimensionally correct?

  1. Feb 2, 2012 #1
    1. The problem statement, all variables and given/known data
    Show that this equation is dimensionally correct.
    y = (2m)cos(kx), where k = 2m^-1


    2. Relevant equations
    None that I know of.


    3. The attempt at a solution

    I don't know why this is correct. I have looked through the chapter and all of the dimensional analysis examples(there are only three) list what the variables represent. The only information given is what I have typed, so I am just assuming that m represents meters.

    Are trig. functions dimensionless?
     
  2. jcsd
  3. Feb 2, 2012 #2

    Pengwuino

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    Yes, trigonometric functions take arguments that are dimensionless.
     
  4. Feb 2, 2012 #3
    Thank you for answering my question.

    So, does it just boil down to the equation being correct because y and 2m are both lengths?
     
  5. Feb 3, 2012 #4

    vela

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    Were you asking if kx is dimensionless or if cos kx is dimensionless?
     
  6. Feb 3, 2012 #5
    cos(kx)
    This is my first physics class and our book doesn't mention trig. functions in the section about dimensional analysis. I am just a little confused.
     
  7. Feb 3, 2012 #6

    vela

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    OK, Pengwuino answered the other question: kx needs to be dimensionless. The value of the cosine is dimensionless as well, which is the answer to your question.

    In general, the standard mathematical functions map a unitless quantity to a unitless result. The main exception is the logarithm because you can do things like log (a/b) = log a - log b, but you should be able to combine logarithms in a way so that you have a unitless argument.
     
  8. Feb 3, 2012 #7

    HallsofIvy

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    Actually, whether this is "dimensionally correct" depends upon what dimensions x has!

    Assuming that x is a distance, measured in meters, then, since k has dimensions of "m^{-1}", kx is dimensionless. In general, mathematical functions take dimensionless variables and return dimensionless values. When you are told that [itex]f(x)= x^2[/itex] and asked "what is f(3)", you don't have to ask if it is 3 meters or 3 feet, the answer is "9"!
     
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