metspitzer wrote:

Does their orbit make a sine wave?

A satellite in an equatorial orbit will always remain over latitute 0
and draw a straight line around the earth.

The ISS is at a 51° inclination. From a "globe" perspective, it draws a
neat straight circle around the earth. But when you map this to a flat
map of the earth, it generates the sine wave:

Imagine the orbit path as a hullahoop. An equatorial orbit has the
hollahoop perfectly horizontal.

But give the hullahoop some inclination, and as you project its path
over the planet, you find that it crosses the equator twice. The first
time, it travels north east, and then as it nears the highest position,
its bearing slowly changes to eventually become south east (without
changing direction). It will cross the equator again, and at the
southern hemisphere, its bearing will again change again towards the
north east (repeating that cycle).

This is what generates those sine waves. But the vehicle itself never
actually changes its direction. It bearing changes because it is
relative to the north pole.