Question

in some countries, the electricity coming to a home oscillates between - 240 volts and 240 volts, with a frequency of 90 cycles per second. which function represents this scenario? y = 240sin(\frac{90x}{180}) y = 240sin(\frac{90x}{90}) y = 240sin(90\pi x) y = 240sin(180\pi x)

Explanation:

Step1: Recall the general form of a sinusoidal function

The general form of a sinusoidal function for an alternating - current voltage is $y = A\sin(2\pi ft)$, where $A$ is the amplitude and $f$ is the frequency.

Step2: Identify the amplitude and frequency

The voltage oscillates between - 240 volts and 240 volts, so the amplitude $A = 240$. The frequency $f=90$ cycles per second.

Step3: Substitute values into the formula

Substitute $A = 240$ and $f = 90$ into $y = A\sin(2\pi ft)$. We get $y=240\sin(2\pi\times90t)=240\sin(180\pi t)$.

Answer:

There is no correct option provided among the ones shown in the problem - statement. If we assume there was a typo in the options and we consider the general form of an AC - voltage function $y = A\sin(\omega t)$ where $\omega=2\pi f$, with $A = 240$ and $f = 90$, the correct function should be $y = 240\sin(180\pi t)$.