Question

Over a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. The tide measures 5.15 ft at midnight, rises to a

high of 10.2 ft falls to a low of 0.1 ft, and then rises to 5.15 ft by the next midnight
What is the equation for the sine function f(x), where x represents time in hours since the beginning of the 24-hour period, that models the
situation?
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Answer 1

The equation for the sine function f(x), which models the tide in the harbor over a 24-hour period, is f(x) = 5.05 sin((2π/24) x) + 5.15.

Step-by-step explanation:

The tide in the harbor can be modeled by a sinusoidal function. Given that the tide measures 5.15 ft at midnight, rises to a high of 10.2 ft, falls to a low of 0.1 ft, and then rises back to 5.15 ft by the next midnight, we can use these key points to determine the equation for the sine function f(x).

1. The amplitude of the sinusoidal function is half the difference between the high and low tides, which is (10.2 - 0.1) / 2 = 5.05 ft.
2. The midline of the function is the average of the high and low tides, which is (10.2 + 0.1) / 2 = 5.15 ft.
3. The period of the function is 24 hours, so the frequency is 1 wave per 24 hours.

Combining these values, the equation for the sine function f(x) that models the tide in the harbor over a 24-hour period is:

f(x) = 5.05 sin((2π/24) x) + 5.15

Answer 2

f(x)=5.05 sin((pi/12)x) + 5.15

Step-by-step explanation: