the depth of the water at the end of a pier changes periodically along with the movement of tides. on a…

the depth of the water at the end of a pier changes periodically along with the movement of tides. on a particular day, low tides occur at 12:00 am and 12:30 pm, with a depth of 2.5 m, while high tides occur at 6:15 am and 6:45 pm, with a depth of 5.5 m. let t = 0 be 12:00 am. which periodic function, sine or cosine, would be a simpler model for the situation? explain.

the depth of the water at the end of a pier changes periodically along with the movement of tides. on a particular day, low tides occur at 12:00 am and 12:30 pm, with a depth of 2.5 m, while high tides occur at 6:15 am and 6:45 pm, with a depth of 5.5 m. let t = 0 be 12:00 am. which periodic function, sine or cosine, would be a simpler model for the situation? explain.

Answer

Answer:

Cosine

Brief Explanation:

At $t = 0$ (12:00 am) which is a low - tide time, the cosine function $y = A\cos(Bt)+C$ has its minimum or maximum value at $t = 0$ (depending on the sign of $A$). Since we start at a low - tide (a minimum value situation for water depth), a cosine function is a simpler model as it can start at its minimum value without a phase shift compared to a sine function which starts at $y = 0$ in its basic form $y=\sin(Bt)$.