What are the Max and Min Values for Tide Height?

In summary: sin(θ) is a minimum (-1) or maximum (+1) at θ = -90° or 90° respectively ... of course ± integer multiples of 360° .sin(θ) is a minimum (-1) or maximum (+1) at θ = -90° or 90° respectively ... of course ± integer multiples of 360° .sin(θ) is a minimum (-1) or maximum (+1) at θ = -90° or 90° respectively ... of course ± integer multiples of 360° .
  • #1
Veronica_Oles
142
3

Homework Statement


The height, h, in metres, of the tide in a given location on a given day at t hours after midnight can be modeled 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?

Homework Equations

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.
 
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  • #2
Veronica_Oles said:

Homework Statement


The height, h, in metres, of the tide in a given location on a given day at t hours after midnight can be modeled 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?

Homework Equations

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.
I've figured out c just really stuck on b.
 
  • #3
Veronica_Oles said:

Homework Statement


The height, h, in metres, of the tide in a given location on a given day at t hours after midnight can be modeled 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?

Homework Equations

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

... and (C) ?
 
  • #4
SammyS said:
What process did you use to get the answers to (A) ?
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
Veronica_Oles said:
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.
That's fine.

Why does that work?

By the way, what is the answer to (C) ?
 
  • #6
SammyS said:
That's fine.

Why does that work?

By the way, what is the answer to (C) ?
The answer to c is 11.3 because I just substitute 9 for t in the equation.
 
  • #7
Veronica_Oles said:
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.
That's fine.

Why does that work?
 
  • #8
SammyS said:
That's fine.

Why does that work?
It works because
SammyS said:
That's fine.

Why does that work?
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
Veronica_Oles said:
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.
What is shifted vertically?

How is this related to the sine function?
 
  • #10
SammyS said:
What is shifted vertically?

How is this related to the sine function?

The height (m) gets shifted vertically?
 
  • #11
What function is it that's shifted vertically?
 
  • #12
Maybe I should have asked something more obvious.

Can you solve ##\ 5 \sin (30 (t-5)) + 7 =12 \ ## for ##\ t\ ## ?
 
  • #13
SammyS said:
Maybe I should have asked something more obvious.

Can you solve ##\ 5 \sin (30 (t-5)) + 7 =12 \ ## for ##\ t\ ## ?
SammyS said:
Maybe I should have asked something more obvious.

Can you solve ##\ 5 \sin (30 (t-5)) + 7 =12 \ ## for ##\ t\ ## ?
yes you can. Wouldn't the answer be 5.5?
 
  • #14
Veronica_Oles said:
yes you can. Wouldn't the answer be 5.5?
What are the units of the coefficient, 30 ?
 
  • #15
SammyS said:
What are the units of the coefficient, 30 ?
Isn't the 30
SammyS said:
What are the units of the coefficient, 30 ?
not sure but is degrees? 30 is k value
 
  • #16
Veronica_Oles said:
Isn't the 30

not sure but is degrees? 30 is k value
I have figured it out I realized I calculated something incorrectly.
 
  • #17
Veronica_Oles said:
Isn't the 30

not sure but is degrees? 30 is k value
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° .
 

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