Respuesta :
The cosine function [tex]\rm x(t) = -1.5cos\left ( \dfrac{2\pi t}{12.5} \right )+t[/tex] for the depth is a function of time.
Given
Low tides occur at a depth of 2.5 m at 12:00 am and 12:30 pm, separated by a period of T = 12.5 hours.
Likewise, high tides occur at a depth of 5.5 m at 6:15 am and 6:45 pm, separated by a period of T = 12.5 hours.
What is the cosine model?
A cosine function would be a simpler model for the situation.
Use a time coordinate of t hours.
The amplitude is (1/2)*(5.5 - 2.5) = 1.5 m.
Use x(t) to denote depth at time t.
Because x(0)=2.5 and x(T/2) = 5.5,, use the periodic function;
[tex]\rm x(t) = -1.5cos\left ( \dfrac{2\pi t}{12.5} \right )+t[/tex]
Verify the model.
x(0) = -1.5 + 4 = 2.5
x(6.25) = 1.5 + 4 = 5.5
x(12.5) = -1.5 + 4 = 2.5
Hence, the cosine function [tex]\rm x(t) = -1.5cos\left ( \dfrac{2\pi t}{12.5} \right )+t[/tex] for the depth is a function of time.
To know more about the Cosine function click the link given below.
https://brainly.com/question/17281973
