watch the video and then solve the problem given below. click here to watch the video. determine the…

watch the video and then solve the problem given below. click here to watch the video. determine the amplitude, period, and phase shift (if any) of the given function. also, find its graph. y = 2 sin (1/4 x)

watch the video and then solve the problem given below. click here to watch the video. determine the amplitude, period, and phase shift (if any) of the given function. also, find its graph. y = 2 sin (1/4 x)

Answer

Explanation:

Step1: Recall amplitude formula

For $y = A\sin(Bx - C)+D$, amplitude is $|A|$. Here $A = 2$, so amplitude $=|2| = 2$.

Step2: Recall period formula

The period of $y=\sin(Bx)$ is $T=\frac{2\pi}{|B|}$. Here $B=\frac{1}{4}$, so $T=\frac{2\pi}{\left|\frac{1}{4}\right|}=8\pi$.

Step3: Recall phase - shift formula

For $y = A\sin(Bx - C)+D$, phase - shift is $\frac{C}{B}$. Here $C = 0$, so phase - shift is $\frac{0}{\frac{1}{4}}=0$.

Answer:

Amplitude: 2; Period: $8\pi$; Phase - shift: 0