
Spherical CoordinatesThe problem for February 2002 involves spherical coordinates (or sphericalpolar coordinates) denoted by (θ, φ). These angular coordinates on the unit sphere are related to the usual Cartesian coordinates (x, y, z) as follows: z = cos θ
x = sin θ cos φ y = sin θ sin φ That is, θ is the angle between the zaxis and the line from the center of the sphere at (x, y, z) = (0,0,0) to the point on the surface of the sphere, and φ is the angle between the x direction and the perpendicular from the point to the zaxis. θ always ranges from zero to pi. φ usually ranges from zero to two pi, but may range from minus pi to pi, for example. Threedimensional spherical coordinates include a third dimension r, which is the distance from the center of the coordinate system to the point. For points on the unit sphere, r = 1. 
Send all responses to .
Thanks,
Steve