# Data Collecting and Modeling

1. May 9, 2016

### Veronica_Oles

1. The problem statement, all variables and given/known data
The height, h, in metres, of the tide in a given location on a given day at t hours after midnight can be modelled using the sinusoidal function h(t)= 5 sin 30 (t-5) + 7
(A) find max and min value for depth of water.
(B) what time is high tide? What time is low tide?
(C) what is the depth of the water at 9:00am?

2. Relevant equations

3. The attempt at a solution
(A) The maximum would be 12 because 5 + 7. The minimum would be 2 because 7-5.

However when it comes to questions b and c I have no idea what to do or where to even begin.

2. May 9, 2016

### Veronica_Oles

I've figured out c just really stuck on b.

3. May 9, 2016

### SammyS

Staff Emeritus
What process did you use to get the answers to (A) ?

... and (C) ?

4. May 9, 2016

### Veronica_Oles

I added the a value and the c value to obtain my maximum and I subtracted my c and a value to get my minimum.

5. May 9, 2016

### SammyS

Staff Emeritus
That's fine.

Why does that work?

By the way, what is the answer to (C) ?

6. May 9, 2016

### Veronica_Oles

The answer to c is 11.3 because I just substitute 9 for t in the equation.

7. May 9, 2016

### SammyS

Staff Emeritus
That's fine.

Why does that work?

8. May 9, 2016

### Veronica_Oles

It works because
It works because the vertical shift is constant and the midline. Therefore you add or subtract the amplitude from it to get your answer.

9. May 9, 2016

### SammyS

Staff Emeritus
What is shifted vertically?

How is this related to the sine function?

10. May 9, 2016

### Veronica_Oles

The height (m) gets shifted vertically?

11. May 9, 2016

### SammyS

Staff Emeritus
What function is it that's shifted vertically?

12. May 9, 2016

### SammyS

Staff Emeritus
Maybe I should have asked something more obvious.

Can you solve $\ 5 \sin (30 (t-5)) + 7 =12 \$ for $\ t\$ ?

13. May 11, 2016

### Veronica_Oles

yes you can. Wouldn't the answer be 5.5?

14. May 11, 2016

### SammyS

Staff Emeritus
What are the units of the coefficient, 30 ?

15. May 11, 2016

### Veronica_Oles

Isn't the 30
not sure but is degrees? 30 is k value

16. May 11, 2016

### Veronica_Oles

I have figured it out I realized I calculated something incorrectly.

17. May 11, 2016

### SammyS

Staff Emeritus
Right. Well then, actually it's 30 degrees per hour .

sin(θ) is a minimum (-1) or maximum (+1) at θ = -90° or 90° respectively ... of course ± integer multiples of 360° .