To find the cosine of a ray that has been rotated -450 degrees, we can simplify the angle by reducing it within the range of 0 to 360 degrees.
First, we can subtract multiples of 360 degrees from -450 degrees:
\[ -450 + 360 = -90 \] \[ -90 + 360 = 270 \]
So, rotating -450 degrees is equivalent to rotating 270 degrees in the positive direction.
Next, we find the cosine of 270 degrees. The coordinates of the angle 270 degrees on the unit circle are (0, -1). Therefore:
\[ \cos(270^\circ) = 0 \]
Thus, the cosine of a ray on the positive x-axis rotated -450 degrees is:
\[ \boxed{0} \]
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