Sinusoidal Pre-cal Problem:?
If someone could please help me with this sinusoidal story problem..thanks!
The jack on an oil well goes up and down, pumping oil out of the ground. As it does so, the distance varies sinusoidally with time. At time = 1 sec, the distance is at its maximum, 3.7 meters. At time = 4 sec, the distance is at its minimum 1.5m.
A) Sketch a graph- I've completed this!
B.)Write an equation- not completed!
C.) Find the distance when time = 5.5sec
D.) Find the first time when distance= 1.78m
THANK YOU!! PLEASE HELP!
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Verified answer
B)
The equation is y = A cos[b(x-c)] + d
A= amplitude = (max-min) /2 = (3.7-1.5)/2 = 1.1
d = vertical displacement = (max+min)/2 = 2.6
Period = 2(4-1)= 6
2PI/b = 6
b = 2PI/6 = PI/3
y = 1.1 cos[ PI/3(x-c)] +2.6
when t=4, the function is maximum
cos is maximum when its argument is 0 since cos(0)=1
PI/3(4-c) = 0
c=4
y(t) = 1.1 cos[PI/3(t-4)] +2.6
C)
plug t=5.5 into 1.1 cos[PI/3(t-4)] +2.6
D)
plug t=1.78 into 1.1 cos[PI/3(t-4)] +2.6