It looks like you want to find the amplitude of the function given in the image. The function is:

$y = 4 \cos\left( 2x + \frac{\pi}{2} \right)$

To find the amplitude, we look at the coefficient in front of the cosine function.

Amplitude:

The amplitude of a cosine function $y = A \cos(Bx + C)$ is given by the absolute value of $A$. In this case, $A = 4$.

So, the amplitude is:

$\text{Amplitude} = |4| = 4$

Period:

The period of a cosine function is calculated as:

$\text{Period} = \frac{2\pi}{|B|}$

where $B$ is the coefficient of $x$ inside the cosine. Here, $B = 2$, so the period is:

$\text{Period} = \frac{2\pi}{2} = \pi$

Thus, the amplitude is 4 and the period is $\pi$.

Would you like more details or further explanations?

Here are some related questions you might find interesting:

1. How does the amplitude affect the graph of the cosine function?
2. What is the phase shift of the function given by $y = 4 \cos(2x + \frac{\pi}{2})$?
3. How do you determine the period of a sine function?
4. What happens if the coefficient $A$ is negative in a cosine function?
5. How does the period of the cosine function change if $B$ is larger or smaller?

Tip: When solving for the amplitude, make sure to check the coefficient directly in front of the cosine (or sine) function.