Answer
The amplitude of the function is $2$, period is $2\pi $, and phase shift is $\pi $.
Work Step by Step
The given equation is in the form of $y=A\sin \left( Bx-C \right)$.
Here, $A=2,\text{ }B=1\text{ and }C=\pi $
So, the amplitude is:
$\begin{align}
& \text{Amplitude=}\left| A \right| \\
& =\left| 2 \right| \\
& =2
\end{align}$
The period is given below:
$\begin{align}
& \text{Period = }\frac{2\pi }{B} \\
& =\frac{2\pi }{1} \\
& =2\pi
\end{align}$
The phase shift is:
$\begin{align}
& \text{Phase shift = }\frac{C}{B} \\
& =\frac{\pi }{1} \\
& =\pi
\end{align}$
And the quarter period is as follows:
$\begin{align}
& \text{Quarter-period}=\frac{2\pi }{4} \\
& =\frac{\pi }{2}
\end{align}$
Now, add quarter periods starting from $x=\pi $ to generate x-values for the key points. The x-value for the first key point is as follows:
$x=\pi $
And the x-value for the second key point is:
$\begin{align}
& x=\pi +\frac{\pi }{2} \\
& =\frac{3\pi }{2}
\end{align}$
And the x-value for the third key point is:
$\begin{align}
& x=\frac{3\pi }{2}+\frac{\pi }{2} \\
& =2\pi
\end{align}$
And the x-value for the fourth key point is:
$\begin{align}
& x=2\pi +\frac{\pi }{2} \\
& =\frac{5\pi }{2}
\end{align}$
And the x-value for the fifth key point is:
$\begin{align}
& x=\frac{5\pi }{2}+\frac{\pi }{2} \\
& =3\pi
\end{align}$
