A

Step 1: Analyze the Graph: The graph shows a sinusoidal wave that fluctuates between -5 and 5, indicating an amplitude of 5.
Step 2: Determine the Midline: The midline of the graph is at y = 0, meaning there is no vertical shift.
Step 3: Identify the Period: The graph completes one full cycle from 0 to 2π, indicating a period of 2π.
Step 4: Write the General Equation: The standard form of the sinusoidal function is given by:
$$ y = A \sin(B(x - C)) + D $$
where:
- A is the amplitude
- B determines the period
- C indicates the horizontal shift
- D is the vertical shift.
Step 5: Substitute Values:
- Amplitude (A) = 5
- Period = 2π, thus B = 1 (since period = \frac{2\pi}{B})
- No horizontal shift (C = 0) and no vertical shift (D = 0).
Therefore, the equation of the sinusoidal graph is:
$$ y = 5 \sin(x) $$
Hence, the correct answer is option A.