Question

Use the table to answer the question I will describe the table x on top 0 next to it pie/2 next to 0 next to pie/2 is pie and next to that is 3pie/2 and next to that is 2pie then under x is y next to it is -3 then next to that is -2 next to that is -3 next to that is -4 then next to that is -3 the equation of the midline is y=

Answer 1

To find the midline of the given data, we first need to understand what the midline represents in this context. The midline of a sinusoidal function is the horizontal line that runs exactly halfway between the maximum and minimum values of the function.

From the data provided, we have the following \( y \) values corresponding to the \( x \) values:

- \( y = -3 \) at \( x = 0 \)
- \( y = -2 \) at \( x = \frac{\pi}{2} \)
- \( y = -3 \) at \( x = \pi \)
- \( y = -4 \) at \( x = \frac{3\pi}{2} \)
- \( y = -3 \) at \( x = 2\pi \)

Now, let's identify the maximum and minimum values:

- Maximum value: \( -2 \) (at \( x = \frac{\pi}{2} \))
- Minimum value: \( -4 \) (at \( x = \frac{3\pi}{2} \))

Next, we find the midline by calculating the average of the maximum and minimum values:

\[
\text{Midline} = \frac{\text{Maximum} + \text{Minimum}}{2} = \frac{-2 + (-4)}{2} = \frac{-6}{2} = -3
\]

Therefore, the equation of the midline is:

\[
y = -3
\]