[math-fun] Stupid Mercator map question

Yes, I know this question is 400 years old, but what is the shape of the image of a great circle on a Mercator projection map? I've seen it described as "sinusoid" shaped, but that can't be right, can it? (Yes, we've all seen those satellite location maps on TV, and they look pretty sinusoidal, but are they really?) I'm not trying to measure lengths or angles, but am simply interested in the mathematical shapes of these great circle on the flat Mercator map. I'm also not interested in the images of non-great circles.