This is how you plot an orbit as a sine wave: Please Register or Log in to view the hidden image! I've done one of these myself from my own observations.

What you drew isn't a sine wave. It's a bunch of half circles. But yes, you can depict a perfectly circular orbit with a sine function. The sine function would represent the X axis of the orbit as the phase (equivalent to time in this case) changed.

It's hard to draw a sine wave with MS Paint. Just to be clear about this: what is being graphed is the projection of the orbit onto a particular axis vs. time. For example, the Sky and Telescope image above shows where Jupiter's moons are as seen from Earth, projected along one particular axis in the sky (probably the rotational axis of the planet Jupiter).

You can plot an orbit as a projection onto the major or minor axis like this graph of an orbit with an eccentricity of 0.5: Please Register or Log in to view the hidden image! Blue line plotted against minor axis. Red line plotted against major axis. Horizontal axis is time. Upper and lower horizontal lines represent semi-major axis distance. But I don't see where it is going to tell you anything new about the orbit.

Not really, you can just use a picture box in a VS app and draw with code. I was watching a youtube vid on orbits and noticed that the object in orbit would change its direction every 180degs and it reminded me of a sine wave. so I asked the question.

You can plot the orbit on a 2D graph as a periodic wave. (A circular orbit would be a regular sine wave. Janus58's plot is more accurate for an elliptical orbit.) But you're not doing any calculating; you're simply rendering the same data in a different visualization.