The problem involves modifying a tidal height function, h(t) = 5 sin (30(t+3)), to align with new tidal data indicating a maximum height of 8, a minimum height of -8, and a specific high tide time of 5:30 am.
The discussion is ongoing, with participants exploring the relationship between the period and the k value in the sine function. Some guidance has been provided regarding the calculation of the k value, but clarity on the phase shift and its derivation remains a point of inquiry.
Participants note that the period is initially stated as 12, but there is a suggestion that a more accurate value might be 12.4, indicating a potential area for further exploration.
This will become clear from the resolution of the other thread, which is essentially the same question.Veronica_Oles said:Homework Statement
The function h(t) = 5 sin (30(t+3)) is used to model the height of tides. On a different day, the maximum height is the minimum height is -8 and high tide occurs at 5:30am.
Modify function so it matches new data.
Homework Equations
The Attempt at a Solution
Answer: h(t) = 8 sin (30(t-2.5))
I know how to get the 8 b/c (8-(-8))/2 = 8
But I don't understand where the 2.5 comes from?
You take 360 divide it by the period then get k value?haruspex said:This will become clear from the resolution of the other thread, which is essentially the same question.
Do you understand where the 30 comes from? (It really should be more like 29.)
Yes. What is the period in this case?Veronica_Oles said:You take 360 divide it by the period then get k value?
The period is 12.haruspex said:Yes. What is the period in this case?
Ok, but more accurate is 12.4.Veronica_Oles said:The period is 12.
Okay.haruspex said:Ok, but more accurate is 12.4.