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:
\[ y = -3 \]