Question

Review the table of values to determine the minimum, maximum, and midline for the cosine function.

x 0, pi/2, pi, 3pi/2, 2pi
y 0, -1, -2, -1, 0

(3 points)
The maximum value is y =

The minimum value is y =

The value of the midline is d =

Answer 1

To analyze the cosine function based on the values provided in the table:

- The values of \( y \) are: 0, -1, -2, -1, 0.

Let's determine:

1. **Maximum Value**:
The highest value of \( y \) in the list is 0.
- **Maximum value is \( y = 0 \)**.

2. **Minimum Value**:
The lowest value of \( y \) in the list is -2.
- **Minimum value is \( y = -2 \)**.

3. **Midline**:
The midline can be found by calculating the average of the maximum and minimum values. The formula for the midline \( d \) is:
\[
d = \frac{\text{max} + \text{min}}{2}
\]
Substituting the maximum (0) and minimum (-2):
\[
d = \frac{0 + (-2)}{2} = \frac{-2}{2} = -1
\]
- **Value of the midline is \( d = -1 \)**.

In summary:
- The maximum value is \( y = 0 \).
- The minimum value is \( y = -2 \).
- The value of the midline is \( d = -1 \).