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A ship at a harbor floats up and down due to waves. The function, h(t) = 15sin(60t), represents the change in height, in centimetres, that the ship floats up and down from a reference point, where t is the time in seconds. Explain how concepts can be used to prove that at t=10.5s, the ship is at its lowest height. No calculations are required

sin is minimum 3/4 of the way through a period.

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Did you know that the concept of trigonometric functions can help explain the behavior of a ship floating up and down due to waves at a harbor? In this case, the height of the ship can be represented by the function h(t) = 15sin(60t), where t is the time in seconds. By analyzing the equation, we can deduce that the function produces a sine wave that oscillates between positive and negative values. Since the amplitude of the sine wave is 15, we know that the ship's height oscillates between a maximum of +15 centimeters and a minimum of -15 centimeters from a reference point. The important concept to understand is that the lowest point of the wave occurs when the sine function reaches its lowest value, which in this case is -1. At t=10.5s, the ship is at its lowest height because when we plug in t=10.5s into the function, h(10.5) = 15sin(60 * 10.5) = 15sin(630). Since sin(630) = -1, the height of the ship at t=10.5s is -15 centimeters, indicating that it reached its lowest point. Therefore, by using the concept of trigonometric functions, we can prove that at t=10.5s, the ship is at its lowest height.