The voltage E of an alternating current electrical circuit can be represented by the sinusoidal function E = 220 cos( t), where E is the measured in volts and t is measured in seconds. How long does it take the alternating current to complete one full cycle?

2 seconds

To determine how long it takes for the alternating current to complete one full cycle, we need to find the period of the sinusoidal function. The period represents the time it takes for the function to repeat.

In this case, the given function is:

E = 220 cos(t)

The general form of a cosine function is:

y = A cos(Bx + C)

Comparing this with the given function, we can deduce that A (amplitude) = 220, B (frequency) = 1, and C (phase shift) = 0.

The period of a cosine function is given by the formula:

Period = 2π / |B|

Since B = 1 in this case, we have:

Period = 2π / |1| = 2π

Therefore, the alternating current takes 2π seconds (approximately 6.28 seconds) to complete one full cycle.