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Where Do We Use This:

  1. Oct 26, 2010 #1
    1. The problem statement, all variables and given/known data
    I have an assignment that is based on the forumal

    A sin x + B cos x = K sin(x+ φ).

    I need to: 1.Explain why we might need such a formula
    2. Show proof or dervivation of this formula on which you add in english the
    reasons for each step. (I know how to go from A sin x + B cos x to K sin(x+ φ))
    3.Describe a real application of this formula


    2. Relevant equations

    A sin x + B cos x = K (sin x cos φ + cos x sin φ) = K sin(x+ φ).

    3. The attempt at a solution

    I have done a lot of searching and have come up with nothing...
    Any help is appreciated

    Thanks
     
  2. jcsd
  3. Oct 26, 2010 #2
    You probably ought to explicitly say the relation between A and B to K and Phi.

    This kind of formula is mostly used for simple harmonic motion: if you have a mass on a spring or a pendulum swinging at small angles. It's actually more typical to see the formula as a cos argument rather than a sine.
     
  4. Oct 26, 2010 #3
    Could you explain to me what relation they hold ???
     
  5. Oct 27, 2010 #4
    A = K cos φ
    B = K sin φ

    comes directly from your second equation, the one with the trig identity.
     
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