Question 299753: vertical distance between a wave's high point and low point is 1.8 and they cycle is repeated every 4 seconds. determine a sinusoidal equation
use your model to determine when the boat is 0.5 abovie its mean position
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! vertical distance between a wave's high point and low point is 1.8 and they cycle is repeated every 4 seconds. determine a sinusoidal equation
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h(t) = 0.9*sin(2pi*t/4) t in seconds, vertical units not specified
h(t) = 0.9*sin(pi*t/2)
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use your model to determine when the boat is 0.5 abovie its mean position
0.5 = 0.9*sin(pi*t/2)
sin(pi*t/2) = 5/9 =~ 0.55555
pi*t/2 = arcsin(0.55555) =~ 0.589, 2.5526 radians
t = 0.589*2/pi
t =~ 0.375 + 4n seconds, n = 0,1,2,3,... rising
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t = 2.5526*2/pi
t =~ 1.625 + 4n seconds, n = 0,1,2,3.... falling
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Or, t = (1 +/- 0.625) + 4n seconds, n = 0,1,2,3,...
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