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Sinusoidal functions

  • Thread starter Draggu
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  • #1
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Homework Statement



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.


Homework Equations





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?
 

Answers and Replies

  • #2
Pengwuino
Gold Member
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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.
 
  • #3
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What do you mean with "n"?
 
  • #4
Pengwuino
Gold Member
4,989
15
What do you mean with "n"?
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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