In both geocentric and geodetic coordinate systems, the geodetic longitude λ is equal to which expression?

• A. arc tan (X/Y)
• B. arc tan (Y/X)
• C. arc sin (X/X)
• D. arc sin (Y/X)

Answer: (B)

Longitude is the angle around the Earth's axis measured in the equatorial plane from the prime meridian. For a point with Cartesian coordinates (X, Y, Z), its projection onto the equatorial plane is (X, Y, 0). The longitude λ satisfies tan λ = Y/X, so λ = arctan(Y/X). That makes arc tan (Y/X) the expression that matches how longitude is determined from X and Y in both geocentric and geodetic coordinate systems. In practice you’d use the two-argument arctangent to get the correct quadrant, but among the given choices this is the form that expresses the relationship. The other options don’t represent the proper Y-to-X ratio that defines the angle around the Z-axis.