Sinusoidal Functions: Max/Min Volts in 1s w/ t-Values

[Draggu]

Homework Statement

The voltage, V(t), in volts, of a power supply can be modeled 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?

 

[Pengwuino]

You are correct to think that there will be 5 cycles. However, that is 5 cycles per 2$$\pi$$ 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 $$\frac{\pi }{2} + n\pi$$. Thus you can solve for $$5t = \frac{\pi }{2} + n\pi \\$$ with n = 0, 1, 2, 3... but remember, only with t<1 second.

 

[Draggu]

What do you mean with "n"?

 

[Pengwuino]

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 = $$\frac{\pi }{2}$$