Answer:
h(t)=0.7sin(πt/6)+1.1
Step-by-step explanation:
A periodic function that models the height of the tide can be written as
[tex]h(t)=A cos(\omega t)+y_c[/tex]
where
A is the amplitude
[tex]\omega[/tex] is the angular frequency
[tex]y_c[/tex] is the central value of the tide
Here we know that:
- the hight tide is 1.8 meters
- the low tide is 0.4 meters
So, the central value of the tide is
[tex]y_c = \frac{1.8+0.4}{2}=1.1 m[/tex]
Also, the amplitude is the maximum displacement from the equilibrium position (central value of the tide), so:
[tex]A=1.8-y_c = 1.8-1.1 = 0.7 m[/tex]
Now we have to find the angular frequency, which is related to the period T by
[tex]\omega=\frac{2\pi}{T}[/tex]
Here the high tide occurs at 12 am and 12 pm: this means that the period is 12 hours, so
T = 12
[tex]\omega=\frac{2\pi}{12}=\frac{\pi}{6}[/tex]
Therefore, the correct equation is
h(t)=0.7sin(πt/6)+1.1
