APFIVE Sinusoidal Model for Tidal Data
Tidal data shows that low tide occurred at 2:15 PM with a depth of 1.5 meters, and high tide occurred at 8:15 PM with a depth of 7.5 meters. If t represents hours since midnight, which of the following models best represents the tidal pattern with the correct phase shift?
A
$$d(t) = 3·sin\left(\frac{\pi}{6}(t-17.25)\right) + 4.5$$
B
$$d(t) = 3·sin\left(\frac{\pi}{6}(t-20.25)\right) + 4.5$$
C
$$d(t) = 3·sin\left(\frac{\pi}{6}(t-14.25)\right) + 4.5$$
D
$$d(t) = 3·sin\left(\frac{\pi}{6}(t-8.25)\right) + 4.5$$
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