Any "equation" for a geometric figure depends on how you set up the coordinates system so I am going to assume your sphere is at the origin of the coordinate system.

Any great circle? Okay, assume the great circle makes angle with the xy-plane and that the line between the two intersections with the xy-plane makes angle with the x-axis. Let be the angle a line from the center of the sphere (the origin) to intersection of the sphere with the xy-plane (the circle with ) The points on that circle are given by , , and z= 0. Now we can just "rotate" that to angle . z= r sin(\phi)[/tex] where r is : so that the parametric equations for the circle atfixedangle with the xy-plane and fixed angle with the x-axis, with parameter are

, , .