Question

One day in march in Jilton Head ,South Caolina, the first high tide occurred at 6:18am.THe hight tide was 7.05 feet ,and the low tide was -0.30 feet .The period for the oscillation of the tides is 12 hours and 24 minutes .

Answer 1

a) Determine what time the next hight will occur
b) Write the period of the oscillation as a decimal
c) What is the amplitude of the sinusoidal function that models the tide?
d) If t=0 represents midnight, write a sinusoidal function that models the tide.
e) At what time will the tides be at 6 feet for the first time that day?

Answer 2

my answer is
a) amplitude = (7.05-0.3)/2=3.675
period = 2pi/12.24=6.24
6.18+12.24=6 hours 42 minutes

b) = 12.4 hours
\[c) \pm 3.675 feet\]
i can get answer a,b,c, I need help d and e only

Answer 3

the key for d) is
\[y= 3.375+3.675 \sin( \frac{\pi }{6.2}t-1.62)\]

d) is 4:46 AM