Question 6

Explanation

To analyze the function $H(t) = A \cos(Bt) + C$, we need to determine three parameters based on the given data.

Amplitude

Amplitude $A$ is half the difference between the maximum and minimum values of the function

Therefore, $|A| = 4$. Since the cosine function starts from the maximum value, we can take $A = 4$ (positive).

Vertical Shift

The vertical shift $C$ is the midpoint between the maximum and minimum values, or the average of the maximum and minimum values

Therefore, $C = 6$

Period and Value of B

The period of the function $\cos(Bt)$ is $\frac{2\pi}{B}$

Given that the tidal period is $12$ hours

Since the tidal period is typically positive, we take $B = \frac{\pi}{6}$ (positive).

Thus, the parameter values are $A = 4$, $B = \frac{\pi}{6}$, and $C = 6$

The most appropriate answer choice is $A = 4, B = \frac{\pi}{6}, C = 6$