Question

TRIG QUESTION: The height of the water in a harbor rose to a maximum height of 15 feet at 6PM and then dropped to a minimum level of 3 feet by 3AM. Assume that the water level can be modeled by the sine function. Write an equation that represents the height 'h' of the water 't' hours after noon on the first day

Answer 1

Still need help?

Answer 2

Yup

Answer 3

ok, well you want the sin function to hit a maximum of 15 and a minimum of 3. Therefore, the middle of that value is 9. So your starting point will be 9 units above the origin. And, you also want it to move down 6 units to hit 3 and up 6 units to hit 15. So the altitude will be 6.

The general form is this..

y = (altitude) sin(x)

But you want to show h in terms of t, so you switch some variables around.

h(t) = 6sin(t) + 9

Answer 4

Now, I will assume that is the answer. I don't know why they would give you times unless they want you to change the frequency, but that would be a little more complicated for your level of mathematics.

Answer 5

Not what it says at the back of the book. The given equation is: \[h = 9 + 6\sin [9(t-1.5)]\] I'm normally pretty good with trigonometric functions, but this question is one that I just couldn't answer correctly.

Answer 6

They wanted me to find the vertical shift and horizontal phase. The vertical shift was easy to find, the horizontal phase, on the other hand.. I don't know how they found "1.5"

Answer 7

**\[ h =9 + 6\sin [\pi/9(t-1.5)]\]
Made a mistake.

Answer 8

thank God cause the other one made no sense haha

Answer 9

So how did they work that one out? It's driving me crazy.

Answer 10

Simple! :)

The pi is there to cancel out the normal frequency. When you have a pi in there, the normal 2*pi frequency gets changed to whole numbers instead of multiples of pi.

The /9 is there because thats how long it takes in hours to go from 6 PM to 3 AM.

Answer 11

Yes, but what about the 1.5 phase?