Answer
The variable k in the equation $y = k + \sin x$ determines the vertical shift from the origin.
$y = 0 + \sin x$ -> no vertical shift
$y = \frac{1}{2} + \sin x$ -> $\frac{1}{2}$ units vertical shift from the original position
$y = -\frac{1}{2} + \sin x$ -> $-\frac{1}{2}$ units vertical shift from the original position
Work Step by Step
See below graph for reference: