In a geocentric and geodetic coordinate system, how is geodetic longitude denoted?

In a geocentric and geodetic coordinate system, geodetic longitude is defined based on the relationship between the Cartesian coordinates (X, Y) of a point in three-dimensional space. Specifically, geodetic longitude corresponds to the angle measured from a reference direction (usually the positive X-axis) in the XY-plane.

To compute this angle, the arctangent function is used, and the correct formulation for geodetic longitude is the arctangent of the ratio of the Y-coordinate to the X-coordinate. This is mathematically represented as arc tan (Y/X). This computation effectively allows the determination of the angle in the XY plane, which corresponds to the geodetic longitude.

The other options involve different trigonometric functions or incorrect ratios that do not appropriately represent the calculation needed for determining geodetic longitude.