https://file.aiquickdraw.com/mathbot/file/1740338004955l0ozmrtu.jpg

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.

Find the amplitude and period of y = 4 cos(2x + \u03C0/2).

Learn how to find the amplitude and period of the cosine function y = 4 cos(2x + \u03C0/2) with detailed steps. This problem demonstrates the process for determining the amplitude, which is 4, and the period, which is \u03C0, from the given trigonometric equation. Suitable for students in Grades 9-12.

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