To determine the equation of the sinusoidal graph shown, we need to observe a few key properties:

1. Amplitude (A): The amplitude is the distance from the midline of the graph to the peak. In this case, the maximum value on the y-axis is 2 and the minimum value is -2, so the amplitude $A$ is $2$.

2. Period (T): The period is the length of one complete cycle of the graph. From the graph, one complete cycle occurs from $0$ to $4\pi$. Thus, the period is $4\pi$.

   The period $T$ is related to the angular frequency $\omega$ by the formula $T = \frac{2\pi}{\omega}$. Using the period of $4\pi$: $T = \frac{2\pi}{\omega} = 4\pi \quad \Rightarrow \quad \omega = \frac{2\pi}{4\pi} = \frac{1}{2}$

3. Phase shift: There is no horizontal shift visible in the graph, so the phase shift is zero.

4. Midline: The midline of the graph appears to be at $y = 0$, so there is no vertical shift.

Since the graph starts at $y = 0$ and increases, it matches the form of a sine function. Therefore, the equation is:

$y = 2 \sin\left(\frac{1}{2}x\right)$

This is the equation of the graph.

Would you like more details or have further questions on this? Here are 5 questions to further explore this concept:

1. What is the relationship between amplitude and the maximum/minimum values of the graph?
2. How do you calculate the period from a sinusoidal graph?
3. What is the difference between a sine and cosine function graph?
4. How does phase shift affect the graph of a trigonometric function?
5. Can you find the equation if the graph represents a cosine function?

Tip: When determining the period of a sine or cosine function, always remember the formula $T = \frac{2\pi}{\omega}$, where $T$ is the period and $\omega$ is the angular frequency.