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To solve question 2, we need to analyze each graph and determine the period, amplitude, and midline (mean line) of the trigonometric functions represented in graphs A, B, and C.

Let's go through each part individually:

1. **Graph A**:
   - **Period**: The period is the length of one complete cycle. Based on the graph, it appears that one cycle completes from \( x = -\pi \) to \( x = \pi \), so the period is \( 2\pi \).
   - **Amplitude**: The amplitude is the maximum displacement from the midline. It seems the maximum height is 2, so the amplitude is 2.
   - **Midline**: The midline is the average of the maximum and minimum values. Here, it is \( y = 0 \).

2. **Graph B**:
   - **Period**: This graph completes a cycle from \( x = -\pi \) to \( x = \pi \), which means the period is \( 2\pi \).
   - **Amplitude**: The amplitude is the maximum distance from the midline. The maximum value here is 3, so the amplitude is 3.
   - **Midline**: This graph's midline is at \( y = 1 \).

3. **Graph C**:
   - **Period**: Observing the graph, one cycle completes from \( x = -2\pi \) to \( x = 2\pi \), making the period \( 4\pi \).
   - **Amplitude**: The amplitude here is 1, as the maximum displacement from the midline is 1.
   - **Midline**: The midline is at \( y = -1 \).

Would you like further details on any of these calculations or have specific questions?

Here are 5 additional questions you might explore based on this:

1. How can we determine the phase shift if the graphs were shifted horizontally?
2. How does a change in amplitude affect the appearance of trigonometric graphs?
3. What transformation would we need to adjust the midline of these graphs?
4. How would we calculate the frequency of each function based on the period?
5. Can you explain how the vertical shift affects the midline of a trigonometric function?

**Tip:** For trigonometric functions, remember that the amplitude is always the absolute value of the coefficient in front of the sine or cosine term.

Explore how to determine the period, amplitude, and midline of trigonometric functions with detailed analysis of each graph. This solution covers key trigonometric concepts suitable for high school students, including periodicity, amplitude, and identifying midline values in graphs.

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