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
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