Question

C: 0 pi/2 pi 3pi/2 2pi y: 0 -1 -2 -1 0

Find the minimum, maximum and midline for the cosine function

Answer 1

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: \(-1\)