Locations on a Sphere: Latitude, Longitude, and 3D Coordinates

① This example demonstrates how to locate any point on a sphere using latitude and longitude parameters, dynamically generating the point and its projections in 3D space, and visually showing the conversion between spherical and Cartesian coordinates. ② Core mathematical concepts include spherical geometry, the latitude/longitude system, the application of trigonometric functions (sine and cosine) in 3D coordinates, and the properties of intersections between planes and spheres (great/small circles). ③ Construction highlights: using GeoGebra commands such as Sphere to create the sphere, Plane and IntersectPath to construct latitude circles and longitude arcs, Rotate to change latitude/longitude by rotating planes or points, Line and OrthogonalPlane to build auxiliary reference axes and perpendicular planes, with objects O (center), a, c, b, d (axes or auxiliary lines), Latitude, Longitude (angle sliders), P, P', P'' (sphere point and its projections) linked together for an interactive model. ④ Suitable for high school or early college students learning solid geometry, spherical coordinates, and trigonometric applications; also useful for geography or astronomy lessons explaining latitude and longitude, and for teachers creating interactive courseware.