The sinusoidal graph shown resembles the form of a sine or cosine function. To write its equation, let's identify key components of the sinusoid, specifically its amplitude, period, and vertical shift:

1. Amplitude: The maximum value of the wave is $5$, and the minimum value is $-5$, giving an amplitude of: $A = 5$

2. Period: The wave completes one full cycle between $-2\pi$ and $2\pi$, so the period $T$ is $4\pi$.

   The formula for the period of a sine or cosine function is $T = \frac{2\pi}{B}$, where $B$ is the horizontal stretch factor. Solving for $B$: $4\pi = \frac{2\pi}{B} \Rightarrow B = \frac{1}{2}$

3. Vertical Shift: Since the sinusoid oscillates symmetrically around the x-axis (no vertical shift), $D = 0$.

Since the wave appears to start at the origin, this function aligns with the sine function format. Thus, the equation of the sinusoid is: $y = 5 \sin\left(\frac{1}{2}x\right)$

Let me know if you would like further details or have any questions!

Related Questions:

1. How do you determine the equation of a cosine function from a graph?
2. What changes in the equation if the sinusoid has a phase shift?
3. How would a vertical shift affect the sinusoidal equation?
4. Can the amplitude ever be negative, and what would that indicate?
5. How does the period of a sinusoidal function affect its graph?

Tip: Always check the starting point of the wave to decide if it's a sine or cosine function.