Do you mean could a sine or cosine function describe the motion of a point on a ferris wheel if the center of the wheel moved up and down sinusoidally during the period?

As stated the answer simply cannot be determined. The answer to the one that I am guessing you meant is: not in general.

The height h of a point from the ground on a ferris wheel of radius R and angular speed and center height H can be modeled by

If the height of the center H is now varied sinusoidally, then

which is the sum of two sinusoidal functions. The only way that this is going to be a sinusoidal function is under the following conditions:

(oscillations are perfectly in phase)

or

(oscillations are perfectly out of phase.)

-Dan