Question

According to the US National Oceanic and Atmospheric administration, on Saturday, June 28, 1997, on a certain beach, high tide occurred at 7:45 (7.75 decimal hours) and low tide occurred at 14:15 (14.25 decimal hours). Water heights are measured as the amounts above or below the mean lower low water. The height of the water at high tide was 8.8 feet and the height of the water at low tide was -0.7 feet. Assume that the height of the water can be represented by a sinusoidal function of the form
y = Asin(ωt - phi) + B,
where y represents the height of the tide , and t
y=sin^(-1)(ω t-ϕ)+B

Answer 1

What to calculate ?

Answer 2

(a) Approximately when will the next high tide occur? Give your answer using the 24-hour clock.

Answer 3

so you want to use math to model your tide, just plug in

Answer 4

we can go step by step , ok?

Answer 5

we are given two points on the curve of the sine function.
Using (time, height of water) the points are: (7.75, 8.85) and (14.25, -0.7)

Answer 6

yes

Answer 7

A = ( max - min) / 2
B = ( max + min)/2

Answer 8

A = ( y max - y min) / 2
B = ( y max + y min)/2
w = 2*Pi/period
phi =

Answer 9

i have a question, why did you write in your question
"where y represents the height of the tide , and t y=sin^(-1)(ω t-ϕ)+B
"

Answer 10

the time from low tide to high tide is actually half a full period (full cycle). half the period is given as (14.24 - 7.75) = 6.5 hours

Answer 11

so the next tide occurs in 13 hours?

Answer 12

sorry i just saw i didnt right the question properly, represents the time in decimal hours since midnight at the start of June 28, 1997

Answer 13

thanks

Answer 14

right so the period is 13 hours. we now we just need to find phi

Answer 15

what does B represent?

Answer 16

B is the midline