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NastyAccident
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Homework Statement
The voltage V in a power cable varies sinusoidally with time t. At t = 1, the voltage is 12 volts. The voltage rises to its maximum level of 20 volts by t = 6. At t = 11, the voltage returns to 12 volts and then begins to fall. The minimum voltage is 4 volts.
Homework Equations
y = (+/-)A*cos(Bx (+/-) C)+D or y = (+/-)A * sin(Bx (+/-) C)+D
The Attempt at a Solution
Finding A:
The use of (M-m) / 2 yields the amplitude, which is (20-4)/2 = 8.
So, A = 8.
Finding B:
The use of 2pi / B yields the period. So, assuming that the period of the average voltage function is 10 (11-1=10), I have 2pi / B = 10.
2pi=10B
2pi/10 = B
pi/5 = B
So the period is pi/5.
Finding C:
Unsure of how to proceed in this step, please advise.
Finding D:
The use of (M+m)/2 yields the vertical shift, which is (20+4)/2 = 12.
So, D or vertical shift in this case is 12.
My guess at the equation of this sinusoid is y = -8cos((pi/5)*x + C) + 12.
Any assistance is helping me understand how to obtain C would be invaluable to me.