To write the equation of the sine wave in the form $y = A \sin(B(x - C)) + D$, let's break down each component based on the graph:

1. Amplitude ($A$): The amplitude is the distance from the middle of the wave (midline) to the maximum or minimum value. In the graph, the maximum is 3, and the midline is at $y = 1$. Therefore, the amplitude $A$ is: $A = 3 - 1 = 2$

2. Vertical shift ($D$): The midline of the wave is the horizontal line where the wave oscillates around. In this case, the midline is $y = 1$, so the vertical shift $D$ is: $D = 1$

3. Period and $B$: The period of a sine wave is the distance between two consecutive peaks or troughs. Here, one full cycle of the wave occurs between $-\pi$ and $\pi$, so the period is $2\pi$. The formula for the period is $\frac{2\pi}{B}$, so we can find $B$: $2\pi = \frac{2\pi}{B} \implies B = 1$

4. Horizontal shift ($C$): The wave appears to have a horizontal shift to the right. The maximum point is at $x = 0$ (instead of $x = -\frac{\pi}{2}$ for a standard sine wave). Since the sine wave reaches its maximum at $x = 0$, there is no horizontal shift, so $C = 0$.

Now, combining all these values into the sine equation:

$y = 2 \sin(x) + 1$

This is the equation of the sine wave.

Would you like further details or clarifications?

Here are 5 related questions:

1. How does changing the amplitude $A$ affect the graph of the sine wave?
2. What happens to the graph if the vertical shift $D$ is changed?
3. Can you explain how to calculate the period of a trigonometric function?
4. What effect does the horizontal shift $C$ have on the graph?
5. How would the graph look if $B$ were greater than 1?

Tip: When identifying the amplitude of a sine wave, always check the vertical distance from the midline to the highest point on the graph.