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

Find the minimum, maximum and midline for the cosine function

1 answer

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: \(-1\)