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

Brief Explanations:

The cosine function is a simpler model here. At (t = 0) (12:00 am), we have a low - tide which is a minimum point of the periodic function. The cosine function (y = A\cos(Bt - C)+D) starts at its maximum or minimum value (when (t = 0) and (C = 0)). A sine function (y=A\sin(Bt - C)+D) starts at its mid - value when (t = 0) and (C = 0). Since the situation starts at a minimum (low - tide at (t = 0)), cosine is more appropriate.

Answer:

Cosine. The function starts at a minimum (low - tide at (t = 0)), and cosine starts at a maximum or minimum value when there is no phase shift, while sine starts at its mid - value with no phase shift.