Answer
The amplitude and period of the function are $3$ and $4\pi $ , respectively.
Work Step by Step
We have the trigonometric function
$y=3\sin \frac{1}{2}x$
The amplitude is the maximum value of $y$. The maximum value of the given trigonometric function is $3$. So, the amplitude of the trigonometric function is $3$.
The function after a certain interval starts repeating itself, and this interval is known as the period of the function.
And the period $\left( B \right)$ of the trigonometric function is
$\begin{align}
& B=\frac{2\pi }{\left( \frac{1}{2} \right)} \\
& =4\pi
\end{align}$
And the quarter period is $\frac{4\pi }{4}$ or $\pi $. 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
$\begin{align}
& {{x}_{2}}=0+\pi \\
& =\pi
\end{align}$
Third key point is
$\begin{align}
& {{x}_{3}}=\pi +\pi \\
& =2\pi
\end{align}$
Fourth key point is
$\begin{align}
& {{x}_{4}}=2\pi +\pi \\
& =3\pi
\end{align}$
Fifth key point is
$\begin{align}
& {{x}_{5}}=3\pi +\pi \\
& =4\pi
\end{align}$
