---### Analyzing Tidal Patterns Using Trigonometric FunctionsA gauge at the end of a pier measures and tracks the water depth \( d \) (in feet) over time. Regression analysis was performed to fit a trigonometric function to the data. The function \( d(t) \) models the depth of the water over time,\[d(t) = 11 \sin(0.406t) + 21\]where \( t \) represents the number of hours past midnight and \( 0 \leq t \leq 24 \).**Problem:**High tide occurs twice in a day. After how many hours will the second high tide occur?**Options:**- [ ] 3.87 hours- [ ] 15.48 hours- [ ] 19.35 hours- [ ] 23.21 hoursThe correct choice is **highlighted**:- [x] **3.87 hours**---This function and question are a typical example of how trigonometric functions can be used to model periodic natural phenomena, such as tide patterns. The function describes a sine wave with an amplitude of 11 feet and a vertical shift of 21 feet, indicating the average water depth. Therefore, the water depth oscillates between 10 feet (21-11) and 32 feet (21+11) over the 24-hour period. The coefficient of \( t \) inside the sine function determines the period of the oscillations.

Answered: Image /qna-images/answer/d873159d-779d-460b-bbf8-e9a410458c30.jpg

A gauge at the end of a pier measures and tracks the water depth d (in feet) over time. Regression analysis was performed to fit a trigonometric function to the data. The function d(t) models the depth of the water over time, d(t) 11 sin(0.406t) + 21 where t represents the number of hours past midnight and 0 ≤ t ≤ 24. High tide occurs twice in a day. After how many hours will the second high tide occur? O 3.87 hours O 15. 48 hours O 19.35 hours 23. 21 hours

A gauge at the end of a pier measures and tracks the water depth d (in feet) over time. Regression analysis was performed to fit a trigonometric function to the data. The function d(t) models the depth of the water over time, d(t) 11 sin(0.406t) + 21 where t represents the number of hours past midnight and 0 ≤ t ≤ 24. High tide occurs twice in a day. After how many hours will the second high tide occur? O 3.87 hours O 15. 48 hours O 19.35 hours 23. 21 hours

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

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### Analyzing Tidal Patterns Using Trigonometric Functions

A gauge at the end of a pier measures and tracks the water depth \( d \) (in feet) over time. Regression analysis was performed to fit a trigonometric function to the data.

The function \( d(t) \) models the depth of the water over time,
\[
d(t) = 11 \sin(0.406t) + 21
\]
where \( t \) represents the number of hours past midnight and \( 0 \leq t \leq 24 \).

**Problem:**

High tide occurs twice in a day. After how many hours will the second high tide occur?

**Options:**

- [ ] 3.87 hours
- [ ] 15.48 hours
- [ ] 19.35 hours
- [ ] 23.21 hours

The correct choice is **highlighted**:
- [x] **3.87 hours**

---

This function and question are a typical example of how trigonometric functions can be used to model periodic natural phenomena, such as tide patterns. The function describes a sine wave with an amplitude of 11 feet and a vertical shift of 21 feet, indicating the average water depth. Therefore, the water depth oscillates between 10 feet (21-11) and 32 feet (21+11) over the 24-hour period. The coefficient of \( t \) inside the sine function determines the period of the oscillations.

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