Answer
The amplitude of the function is $\frac{1}{4}$.
Work Step by Step
We have the trigonometric function
$y=\frac{1}{4}\sin x$
The amplitude is the maximum value of $y$. The maximum value of the given trigonometric function is $\frac{1}{4}$. So, the amplitude of the trigonometric function is $\frac{1}{4}$.
The period of the trigonometric function is $2\pi $.
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
$\begin{align}
& {{x}_{5}}=\frac{3\pi }{2}+\frac{\pi }{2} \\
& =2\pi
\end{align}$
