Question

The current I, in amperes, flowing through an AC (alternating current) circuit at time t is I(t)=220sin(45πt−π/6), where t≥0. Find the period and the horizontal shift.

a) Period: 1/45, shift 1/135 to the left.

b) Period: 2/45, shift 1/270 to the right.

c) Period: 1/45, shift 1/135 to the right.

d) Period: 2/45, shift 1/270 to the left.

e) Period: 2/45, shift 1/540 to the right.

Answer 1

The period of the AC circuit is 2/45 and there is a horizontal shift of 1/270 to the left.

Step-by-step explanation:

The given equation for the current in the AC circuit is I(t) = 220sin(45πt−π/6), where t≥0. To find the period, we need to determine the time it takes for the function to complete one full cycle. In this case, the coefficient of t in the equation is 45π, so the period is given by T = 2π/(45π) = 2/45.

To find the horizontal shift, we need to determine the value of t that would make the argument of the sine function equal to 0. In this case, the argument of the sine function is 45πt−π/6. Setting this equal to 0, we can solve for t: 45πt−π/6 = 0, t = π/270.

Therefore, the correct answer is option d) Period: 2/45, shift 1/270 to the left.