Question

graph the given function. state the period, amplitude, phase shift, and vertical shift of the function.
$y = 4\sin(x)$

Explanation:

Step1: Recall the general form of sine function

The general form of a sine function is \(y = A\sin(B(x - C))+D\), where \(A\) is the amplitude, \(B\) affects the period (\(T=\frac{2\pi}{|B|}\)), \(C\) is the phase - shift, and \(D\) is the vertical shift. For the function \(y = 4\sin(x)\), we can rewrite it as \(y=4\sin(1\times(x - 0))+0\).

Step2: Calculate the period

Using the formula \(T=\frac{2\pi}{|B|}\), with \(B = 1\), we have \(T=\frac{2\pi}{|1|}=2\pi\).

Step3: Calculate the amplitude

The amplitude is given by \(|A|\). Here, \(A = 4\), so the amplitude is \(|4| = 4\).

Step4: Determine the phase - shift

The phase - shift is \(C\). Since \(C = 0\), the phase - shift is \(0\).

Step5: Determine the vertical shift

The vertical shift is \(D\). Since \(D = 0\), the vertical shift is \(0\).

Answer:

Period: \(2\pi\)
Amplitude: \(4\)
Phase Shift: \(0\)
Vertical Shift: \(0\)