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

Question

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 \( d = -1 \).