Question

A student observes the water level of the Atlantic on Tybee Island. Starting with a low tide, the student notices it takes 10 hours for the ocean to return to a low tide. If the water rises 15ft above sea level at high tide and recedes 15 ft below sea level at low tide, write the sinusoidal function representing the water level on Tybee Island.

Answer 1

Do you think that the amplitude is 15 and the period is 10? I'm just wondering about this.

Answer 2

i think so i'm not really sure

Answer 3

Yeah, I agree with that. The period is how long it takes for the function to return to the same state. So in this case, from low tide to low tide means that it's returned to the same state. That took 10 hours. The amplitude is the highest and lowest the function gets. In this case it goes from -15 to 15. There's no vertical shift to worry about, since between 15 and -15 is 0 exactly.

A*sin((P/2pi)*x)
Where A is the amplitude and P is the period.

Answer 4

I'm looking at y = 15 sin [ (2 pi) / 10 ) x ] + some constant

Answer 5

thats what i got from it

Answer 6

Ah, yes. (2pi/P), not (P/2pi) as I said originally.

Answer 7

We need low tide at x = 0 if that is when the student starts watching.

>Starting with a low tide, the student notices..

Answer 8

thx ^^

Answer 9

I'm thinking this equation may be the one. Props to @Callisto

y = 15 sin [( (2 pi) / 10 ) x - pi/2 ]