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.
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Find the maximum and minimum values:
- Maximum value: \( 7 \)
- Minimum value: \( 5 \)
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Calculate the midline: \[ \text{Midline} = \frac{\text{Maximum} + \text{Minimum}}{2} = \frac{7 + 5}{2} = \frac{12}{2} = 6 \]
So, the midline is \( 6 \).
- 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: \[ y = \sin x + 6 \]