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Answer:
(a)
(b) 7.5ft above the low tide.
Step-by-step explanation:
(a) To find the function that computes the height of the tide, you need to select the form of the sinusoidal function. For example, use the form:
Where A is the amplitude, B the frequency, C the phase shift and D the vertical shift.
The amplitude is half the distance between the highest and the lowest tide:
The frequency is related to the period T by:
The period is 12 hours, then
The high tide is at 1:00 a.m. and 1:00 p.m. , this is the moment when , if
then
must be equal to
when
:
The vertical shift is the sum of the lowest value, the height of the low tide () and the amplitude:
The function is:
Because the function must be the height above low tide height, subtract this heigh from the function:
(b) Use x=11 in the function
above the low tide.