To analyze the given values, we can interpret the data as relating to the cosine function over one complete cycle from \(0\) to \(2\pi\).
Given the point pairs:
- At \(0\), \(y = 0\)
- At \(\frac{\pi}{2}\), \(y = -1\)
- At \(\pi\), \(y = -2\)
- At \(\frac{3\pi}{2}\), \(y = -1\)
- At \(2\pi\), \(y = 0\)
Minimum and Maximum Values:
- Maximum value: The highest point in this set of data is \(0\).
- Minimum value: The lowest point, which is \(y = -2\).
Midline:
The midline of a periodic function, such as cosine, is the average of the maximum and minimum values. It can be calculated with the following formula:
\[ \text{Midline} = \frac{\text{Maximum} + \text{Minimum}}{2} \]
Substituting in the values:
\[ \text{Midline} = \frac{0 + (-2)}{2} = \frac{-2}{2} = -1 \]
Summary:
- Minimum value: \( -2 \)
- Maximum value: \( 0 \)
- Midline: \( -1 \)
Thus, for the given cosine function based on the provided data points:
- Max: \(0\)
- Min: \(-2\)
- Midline: \(-1\)