Question

Complete the equation of the periodic function represented by the table of values by entering the midline I will describe the table x on top next to it is 0 next to 0 is pie/2 next to that is 3pie/2 and next to that is 2pie then under x is y next to that is 6 and next to that is 7 next to that is 6 next to that is 5 and next to that is 6 y=sin x+_

Answer 1

To find the midline of the periodic function \( y = \sin x + k \) from the provided values, we need to analyze the maximum and minimum values in the table.

From your description, it appears the values of \( y \) corresponding to \( x \) values are as follows:

- \( x = 0 \): \( y = 6 \)
- \( x = \frac{\pi}{2} \): \( y = 7 \) (maximum)
- \( x = \frac{3\pi}{2} \): \( y = 6 \)
- \( x = 2\pi \): \( y = 5 \) (minimum)

Now, we need to determine the midline of the sinusoidal function.

1. **Find the maximum and minimum values**:
- Maximum value: \( 7 \)
- Minimum value: \( 5 \)

2. **Calculate the midline**:
\[
\text{Midline} = \frac{\text{Maximum} + \text{Minimum}}{2} = \frac{7 + 5}{2} = \frac{12}{2} = 6
\]

So, the midline is \( 6 \).

3. **Write the complete equation**:
Given that the midline is already aligned in your function representation, the complete equation of the sinusoidal function would be:
\[
y = \sin x + 6
\]

Thus, replacing the blank in your equation \( y = \sin x + \_ \), we fill it with **6**:
\[
y = \sin x + 6
\]