Sinusoidal equation problem

May 2010
5
0
I was wondering if anyone can help me out with the following problem;

Young Tovy lives next to the ocean. He likes to wade to a small island very close to shore, but can wade to the island only when the depth of the water is 1.2 metres or less. The depth of the water is determined by the tide.

Tovy and a few of his friends want to go to the island for a picnic on Tuesday, and so they need to know when it is safe to wade across to the island. They measure the water depths on Monday (the day before the picnic), and the results are as follows:
Time
5:30
7:15
8:15
10:45
12:00
18:30
19:30

Depth(m)
2.10
0.73
0.43
1.62
2.77
1.49
0.77

The time is in hours and minutes, and so 5:30 is the same as 5.5 hours.

A. Write a sinusoidal equation that represents the data. Round the parameters to two decimal places.

B. Draw a graph using IT that shows the water depths for two days (Monday and Tuesday).

C. Calculate the depth of the water at noon on Tuesday. Show how you arrive at your answer.

D. What are the maximum and minimum water depths?

E. They want to go on the picnic as close to the middle of the day (on Tuesday) as possible. When can they go to the island, and by when do they have to return? Explain how you arrive at your answer.
 

skeeter

MHF Helper
Jun 2008
16,216
6,764
North Texas
I was wondering if anyone can help me out with the following problem;

Young Tovy lives next to the ocean. He likes to wade to a small island very close to shore, but can wade to the island only when the depth of the water is 1.2 metres or less. The depth of the water is determined by the tide.

Tovy and a few of his friends want to go to the island for a picnic on Tuesday, and so they need to know when it is safe to wade across to the island. They measure the water depths on Monday (the day before the picnic), and the results are as follows:
Time
5:30
7:15
8:15
10:45
12:00
18:30
19:30

Depth(m)
2.10
0.73
0.43
1.62
2.77
1.49
0.77

The time is in hours and minutes, and so 5:30 is the same as 5.5 hours.

A. Write a sinusoidal equation that represents the data. Round the parameters to two decimal places.

B. Draw a graph using IT that shows the water depths for two days (Monday and Tuesday).

C. Calculate the depth of the water at noon on Tuesday. Show how you arrive at your answer.

D. What are the maximum and minimum water depths?

E. They want to go on the picnic as close to the middle of the day (on Tuesday) as possible. When can they go to the island, and by when do they have to return? Explain how you arrive at your answer.
I recommend you use technology to perform a sinusoidal regression. TI graphing calculators do a nice job of this.
 
May 2010
5
0
It would help if I had one (Worried)
any other suggestions or help??
Anything at all is appreciated.
 

skeeter

MHF Helper
Jun 2008
16,216
6,764
North Texas
It would help if I had one
any other suggestions or help??
Anything at all is appreciated.
My advice to you is to purchase/borrow a graphing calculator, or look for software that will do the job.