A few years ago, I was working with equirectangular projections of spherical data (mostly spherical panoramas and spherical depth maps) for a 3D reconstruction research project. For a reason I can’t remember, I started wondering what a great circle would look like in an equirectangular projection. A great circle is the intersection between a plane and a sphere if the plane intersects the center of the sphere.
To get a quick answer, I drew a rough sketch of a great circle on a sphere. On the sphere, I marked the meridians and parallels at 45° intervals. Then, I sampled the great circle where it intersects with the meridians and parallels and mapped those points on an equirectangular map. Finally, I drew a curve between the sampled points to get the results shown in figure 1.