Answer
The amplitude and period of the function are $1$ and $\frac{\pi }{2}$, respectively.
Work Step by Step
We have the trigonometric function
$y=\sin 4x$
The amplitude is the maximum value of $y$. The maximum value of the given trigonometric function is $1$. So, the amplitude of the trigonometric function is $1$.
The function after a certain interval starts repeating itself, and this interval is known as the period of the function.
The period $\left( B \right)$ of the trigonometric function is
$\begin{align}
& B=\frac{2\pi }{4} \\
& =\frac{\pi }{2}
\end{align}$
And the quarter period is $\frac{\left( \frac{\pi }{2} \right)}{\left( 4 \right)}$ or $\frac{\pi }{8}$. 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
$\begin{align}
& {{x}_{2}}=0+\frac{\pi }{8} \\
& =\frac{\pi }{8}
\end{align}$
Third key point is
$\begin{align}
& {{x}_{3}}=\frac{\pi }{8}+\frac{\pi }{8} \\
& =\frac{\pi }{4}
\end{align}$
Fourth key point is
$\begin{align}
& {{x}_{4}}=\frac{\pi }{4}+\frac{\pi }{8} \\
& =\frac{3\pi }{8}
\end{align}$
Fifth key point is
$\begin{align}
& {{x}_{5}}=\frac{3\pi }{8}+\frac{\pi }{8} \\
& =\frac{\pi }{2}
\end{align}$
