Answer
See below:
Work Step by Step
Consider the provided function,
$ y=2\sin \left( 2x+\frac{\pi }{2} \right)$
The general sine function equation looks as follows:
$ y=A\sin \left( Bx+c \right)$
From both equations above:
$ A=2,\text{ }B=2\text{ and c}=\frac{\pi }{2}$
Therefore, amplitude is:
$\left| A \right|=\left| 2 \right|=2$
$\begin{align}
& \text{Period=}\frac{2\pi }{B} \\
& =\frac{2\pi }{2} \\
& =\pi
\end{align}$
If c is a positive real number, the graph of $ f\left( cx \right)$ is the graph of $ y=f\left( x \right)$ stretched horizontally by $ c $ units.
If h is a positive real number, the graph of $ hf\left( x \right)$ is the graph of $ y=f\left( x \right)$ stretched vertically by $ h $ units.
If c is a positive real number, then the graph of $ f\left( x+c \right)$ is the graph of $ y=f\left( x \right)$ shifted to the left c units.
Now, the provided function is:
$ y=2\sin \left( 2x+\frac{\pi }{2} \right)$
The graph of above function can be seen as transformations of the parent function $ y=\sin \left( x \right)$,
Stretch the graph of $ y=\sin \left( x \right)$ by 2 units horizontally and stretch the graph vertically by 2 units.
And also shift the graph to left by $\frac{\pi }{2}$.
