Question 1139459: Good morning! can someone help me solve this trigonometry word problem regarding tidal cycles?
Here's the following information:
"During a 12.5-hour period, the water level at
Grays Harbor, Washington, started at mean sea level, rose to
9.3 feet above sea level, dropped to 9.3 feet below sea level,
and then returned to mean sea level. Find a simple harmonic
motion equation that models the height h of the tide above or
below mean sea level for this 12.5-hour period."
Now how can I solve this problem?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the sine function starts at 0 and then goes to an amplitude of 1 and then back to 0 and then to an amplitude of -1 and than back to 0 in one full cycle.
the general form of the equation of a sine wave is y = a * sin(b * (x-c)) + d.
a is the amplitude
b is the frequency
c is the horizontal shift.
d is the vertical shift.
when c = 0 and d = 0, the function starts at 0 and returns to 0 for one full cycle and the center line of the function is y = 0.
since you don't have a vertical shift or horizontal shift, the general form of your equation is y = a * (b * x).
in your problem, y represents the height of the tides plus or minus 9.3 feet from the center line at y = 0, which represents sea level, and x represents the number of hours with one full cycle of the sine wave being completed in 12.5 hours.
your period = 12.5 hours, which is the number of hours in a full cycle.
the formula for frequency is frequency = 2pi / period when you are dealing in radians and not degrees.
that makes your frequency = 2 * pi / 12.5 = 2 / 12.5 * pi.
your amplitude is 9.3 feet above and below y = 0.
your equation is y = 9.3 * sin(2 / 12.5 * pi * x)
y represents the height of the tide relative to sea level.
x represents the number of hours.
here's the graph of your equation.
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