3. Consider the line element of the sphere of radius a: ds² = a² (do² + sin² 0 do²). The only non-vanishing Christoffel symbols are re 00 = - sin cos 0, ГФ 00 = = rø фо 1 tan O' c) The geodesics of the sphere are great circles. Thinking of 0 = 0 as the North pole and = πT as the South pole, find a set a solutions to the geodesic equation corresponding to meridians, and also the solution corresponding to the equator.

3. Consider the line element of the sphere of radius a: ds² = a² (do² + sin² 0 do²). The only non-vanishing Christoffel symbols are re 00 = - sin cos 0, ГФ 00 = = rø фо 1 tan O' c) The geodesics of the sphere are great circles. Thinking of 0 = 0 as the North pole and = πT as the South pole, find a set a solutions to the geodesic equation corresponding to meridians, and also the solution corresponding to the equator.