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Dimensional anaylsis problem involving trigonometry

  1. Aug 24, 2013 #1
    1. The problem statement, all variables and given/known data

    Dimensional Analysis:

    A displacement is related to time as:

    x = A sin (2∏ft), where A and f are constants.

    Find the dimensions of A. (Hint: a trigonometric function appearing in an equation must be dimensionless.)

    2. Relevant equations

    t = seconds
    The domain of a sine must be an angle.

    3. The attempt at a solution

    x = A sin (2∏ft), where A and f are constants.

    m = A sin (2∏fs)

    A = m/[sin (2∏fs)]

    Therefore, f, a constant, must be in terms of s-1, in order to cancel out the s next to it, as the input of sine in an equation must be dimensionless.

    Therefore, A = m

    Thanks for any help!
     
  2. jcsd
  3. Aug 24, 2013 #2

    rock.freak667

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    Homework Helper

    Yes that would be correct.
     
  4. Aug 24, 2013 #3
    Correct
     
  5. Aug 24, 2013 #4
    I am absolutely stunned that I got the question correct (other than failing to use base dimensions instead of units in the SI system, as Emilyjoint posted in my other thread here!).

    Thank you!
     
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