Consider a sine wave having $4$ cycles wrapped around a circle of radius 1 unit (its center needs not be the origin of a Cartesian coordinate system). Assume that the length of axis of the sine wave is as same as the circumference of the circle.
The circumference of circle is assumed to be mapped to $2\pi $ $rad$. Therefore, the sine wave represents the equation along the x-axis:
$$ y = sin(4x) $$
To find the equation of the sine wave with the circumference of circle acting as the x-axis, one approach is to consider the sine wave along a rotated line like aligned $ \pi/4 $ $rad$ to x-axis. But it doesn't suffice for the circular path. This is where the problem of finding the equation is stuck. A hint/help taking to a right answer would be appreciated.
Update: From comments, it appears that the question is not clear. So, for more clarity, a rough image is uploaded at http://imgur.com/l0cY9. In the image, four lines are drawn to clearly distinguish between crests and troughs. Look at it and read the above question once again. Thanks.