Answer
The amplitude of the function is $4$.
Work Step by Step
We have the trigonometric function: $y=4\sin x$.
The amplitude is the maximum value of the function. The maximum value of the given trigonometric function is $4$. So, the amplitude of the trigonometric function is $4$.
So, the period of the trigonometric function is $2\pi $.
And the quarter period is $\frac{2\pi }{4}$ or $\frac{\pi }{2}$. The cycle begins at $x=0$. Add quarter periods to find out the key points.
First key point is
${{x}_{1}}=0$
Second key point is
$\begin{align}
& {{x}_{2}}=0+\frac{\pi }{2} \\
& =\frac{\pi }{2}
\end{align}$
Third key point is
$\begin{align}
& {{x}_{3}}=\frac{\pi }{2}+\frac{\pi }{2} \\
& =\pi
\end{align}$
Fourth key point is
$\begin{align}
& {{x}_{4}}=\pi +\frac{\pi }{2} \\
& =\frac{3\pi }{2}
\end{align}$
Fifth key point is
$\begin{align}
& {{x}_{5}}=\frac{3\pi }{2}+\frac{\pi }{2} \\
& =2\pi
\end{align}$
