Respuesta :
Answer:
The sinusoidal function that model the depth in terms of time, 'x', is presented here as follows;
f(x) = 39·sin((π/3)·x - π) + 5
Step-by-step explanation:
A sinusoidal function is given by the general function as follows;
y = A·sin(B·x + C) + D
Where;
A = The amplitude = ([tex]y_{max}[/tex] - [tex]y_{min}[/tex])/2 = (The high tide - The low tide)/2 = (83 ft. - 5 ft.)/2 = 39 ft.
The period, T = 2·π/b = 6 hours
∴ B = 2·π/T = 2·π/6 = π/3
D = The vertical shift = The low tide = 5 ft.
The horizontal phase shift, 'C', is given as follows;
3 hrs = -C/B = -C/(π/(3 hr))
C = 3 hrs × -(π/(3 hr)) = -π
∴ C = -π
y = 39·sin((π/3)·x - π) + 5
The sinusoidal function that model the depth in terms of time, 'x', is therefore given as follows;
f(x) = 39·sin((π/3)·x - π) + 5
