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Primitive Function 3(sin(3t) + cos(3t))

  1. May 26, 2014 #1
    1. The problem statement, all variables and given/known data
    Find the primitive function s(t) for v(t)=3(sin(3t) + cos(3t)) for which s(0)=0

    3. The attempt at a solution

    v(t) =3(sin(3t) + cos(3t)) = 3sin3t +3cos3t

    s(t) =cos3t -sin3t + C

    0 = cos3(0) - sin3(0) + C
    0= 1 + C
    such that my primitive function is cos3t - sin3t - 1

    My teacher got another answer:
    s(t) = -cos(3t) + sin(3t) + C
    and s(0) = 0 = -1 + 0 + C such that C= 1 and the primitive function is sin3t -cos3t + 1

    has he made a mistake? or am I confused?
  2. jcsd
  3. May 26, 2014 #2
    You've made mistakes. What is the primitive function of cos and sin?
  4. May 26, 2014 #3
    the primitive function is the anti-derivative. so cosx becomes sinx and sinx becomes -cosx?
    s(t)=-cos3t+sin3t + C

    Now I got it. I´d gotten confused between the derivative and the anti-derivative. Thanks for confirming that I´d made the mistake!
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