in some countries, the electricity running to a home oscillates between -240 volts to 240 volts, with a…

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

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

Answer

Explanation:

Step1: Recall the general form of a sine - wave function

The general form of a sine - wave function for an oscillating quantity is $y = A\sin(Bx)$, where $A$ is the amplitude and $B$ is related to the frequency $f$. The amplitude is half the difference between the maximum and minimum values of the oscillating quantity.

Step2: Calculate the amplitude

The electricity oscillates between - 240 volts and 240 volts. The amplitude $A=\frac{240 - (-240)}{2}=240$.

Step3: Relate the frequency to the coefficient $B$

The frequency $f$ of a sine - wave $y = A\sin(Bx)$ is given by $f=\frac{B}{2\pi}$. We are given that $f = 90$ cycles per second. Rearranging the formula $f=\frac{B}{2\pi}$ for $B$, we get $B = 2\pi f$. Substituting $f = 90$ into the formula, we have $B=2\pi\times90 = 180\pi$.

Step4: Write the function

The function representing the electricity voltage is $y = 240\sin(180\pi x)$.

Answer:

$y = 240\sin(180\pi x)$