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Sinusoidal functions

  1. Apr 16, 2009 #1
    1. The problem statement, all variables and given/known data

    The voltage, V(t), in volts, of a power supply can be modelled by the function V(t) = 110sin5t+15, where t is the time, in seconds. Find the maximum and minimum voltages, within the first second, and the times they occur.


    2. Relevant equations



    3. The attempt at a solution

    well, i think since the period is 5? that means there are 5 cycles, which means there will be 5 maximums, and 5 minimums, how do i figure out where the exact points are maximum?

    v'(t)=550cos5t

    but how do i solve t there?
     
  2. jcsd
  3. Apr 16, 2009 #2

    Pengwuino

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    You are correct to think that there will be 5 cycles. However, that is 5 cycles per 2[tex] \pi[/tex] radians. In order to find the zeros for your derivative, think about when does Cos(5t) = 0? It is equal to 0 whenever the argument inside cosine is [tex]\frac{\pi }{2} + n\pi [/tex]. Thus you can solve for [tex] 5t = \frac{\pi }{2} + n\pi \\ [/tex] with n = 0, 1, 2, 3.... but remember, only with t<1 second.
     
  4. Apr 16, 2009 #3
    What do you mean with "n"?
     
  5. Apr 16, 2009 #4

    Pengwuino

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    n is an integer of 0,1,2,3.... etc etc. Remember, cosines and sines go on forever and they have an infinite number of zeros. The n tells you which zero you are at. For example, the n = 0 zero is at 5t = [tex]\frac{\pi }{2} [/tex]
     
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