Answer:
To write a trigonometric equation of the form h(t) = Acos(Bt - C) that models the tide level, we need to determine the values of A, B, and C based on the given information.
Let's begin by examining the high and low tide times and levels in the table:
| Time | Tide Level |
|------|------------|
| 12am | 1.5 |
| 1am | 2.5 |
| 2am | 3.5 |
| 3am | 4.5 |
| 4am | 5.5 |
| 5am | 5.5 |
| 6am | 5.0 |
| 7am | 4.0 |
| 8am | 3.0 |
| 9am | 2.0 |
| 10am | 1.0 |
| 11am | 0.5 |
| 12pm | 0.0 |
| 1pm | 0.5 |
| 2pm | 1.5 |
| 3pm | 2.5 |
| 4pm | 3.5 |
| 5pm | 4.5 |
| 6pm | 5.0 |
| 7pm | 4.5 |
| 8pm | 3.5 |
| 9pm | 2.5 |
| 10pm | 1.5 |
| 11pm | 1.0 |
We can see that the tide levels oscillate between a maximum of 5.5 feet and a minimum of 0 feet, with a period of approximately 12 hours. Therefore, we can set the amplitude A = (5.5 - 0)/2 = 2.75 feet and the period P = 12 hours.
The general form of a trigonometric equation of the form h(t) = Acos(Bt - C) is that the coefficient of t in the argument of the cosine function is equal to 2π divided by the period P. Therefore, we have:
B = 2π/P = 2π/12 = π/6
The value of C can be determined by finding the value of t at which the cosine
Hope this Helps! Have a Great day