Question

The graph of the sine curve below is of electromagnetic energy that represents indigo light:  What function accurately represents the sine curve for indigo light?

Answer 1

The graph indicates that
A = 2, the amplitude
T = 2π, the period
k = 2, the y-intercept

Therefore the curve is modeled by
y = 2 cos(x)

Because cos(x) = sin(x + π/2), therefore
y = 2 sin(x + π/2)

The graph of the function confirms that the model is correct.