SOLUTION: Can somebody please help me out with this?? Coastal areas experience tides which is where the ocean periodically gets to high and low points. Tides can be modeled with a sinusoi

Question 1179523: Can somebody please help me out with this??
Coastal areas experience tides which is where the ocean periodically gets to high and low points. Tides can be modeled with a sinusoidal (sine or cosine) function. At one beach, the high tide is 5 feet above mean sea level and the low tide is 5 feet below see level. The length of time between high and low tide is 6.5 hours.
If high tide is at time t=0 hours, give the function H(t) that describes the height of the tide relative to sea level t hours after the high tide.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the basic form of the sine wave function is:
y = a * sin(b * (x-c)) + d

a is the amplitude which, in this case, is 5 feet above the mean sea level and 5 feet below the mean seas level.
the amplitude is therefore equal to 5.

b is the frequency.
the frequency is equal to 360 degrees divided by the period.
since the period is 6.5 hours, the frequency is equal to 360 / 13 which is equal to 27.69230769 rounded to 8 decimal places.

c is the horizontal displacement.
this shifts the graph right or left.
since you want the graph to shift 90 degrees to the left, then do the following.
90/360 = 1/4 of a full cycle.
when the full cycle is 13, then 1/4 of the full cycle is 13/4 = 3.25.
if you want the shift to the left, then c must be negative which menns that, instead of x - c, you need x + c, because x - (-c) = x + c).
the (x-c) part of the formula is therefore equal to x + 3.25).

d is the vertical displacement.
this the value midpoint between the high and the low tides.\
if d = 0, then the center line of the y value of the graph is y = 0.
since this is where we want to be, then d = 0 and is therefore omitted because the default value of d is 0.

a word about default values.
default value of a is 1.
default value of c is 0
default velus of b is 1
default of value of d is 0.
if all of these values are at default, then the equation becoms y = sin(x).
that means a = 1, b = 1, c = 0 and d = 0.

your equation is y = 5 * sin(360/13) * (x + 3.25)
the decimal version is y = 5 * sin(27.69230769 * (x + 3.25))

this is what the graph looks liike.

the graphing formula is y = 5 * sin(360/13 * (x + 3.25).

the h(t) formula is:

h(t) = 5 * sin(360/13 * (t + 3.25).

t is the amount of hours from t = 0.
h(t) is the height of the tide at t hours from 0.

any questions, give me a shout.

theo
RELATED QUESTIONS
Can somebody help me with this problem? The directions is find the hydrogen ion... (answered by KMST)

Let {{{h(x)=36^(4x-1)}}} can somebody help me with... (answered by richard1234)

in a time of t hours, a particle moves a distance of s kilometers from its starting... (answered by rothauserc)

can somebody please help me? i dont really understand this problem.. it says: write an (answered by hokies,Alan3354,richwmiller)

The yearly production of a 4 foot orange tree is 26 pounds of oranges. A 15 foot tree... (answered by josgarithmetic)

please can somebody help with this I'm stuck x-2/3 = 2x/7 if you can help please show (answered by John10)

I'm having a very hard time with this question, can somebody please help me! The... (answered by stanbon,Alan3354)

(G&H)>(J<>L) G<>H (H&~L)v(H&K) Conclusion: J>K Can somebody please help me with... (answered by Edwin McCravy)

Please help me with this problem. The directions from my professor are as follows: Using... (answered by stanbon)