Given the X, Y, and Z coordinates of a point, determine the equivalent longitude.

• A. λ = tan^-1 (Y/X)
• B. λ = tan^-1 (X/Y)
• C. φ = tan^-1 (Y/X)
• D. λ = arccos (Y/X)

Answer: (A)

Longitude is the angle around the Z-axis in the X–Y plane, measured from the X-axis toward the Y-axis. For a point with Cartesian coordinates, its projection onto the equatorial plane is (X, Y), and the tangent of the longitude equals Y divided by X. So the longitude is λ = arctan(Y/X). In practice you’d use atan2(Y, X) to get the correct quadrant for all signs of X and Y, but the basic relationship shown is tan(λ) = Y/X, which matches the chosen expression. The other forms don’t represent longitude: using X/Y would give tan(λ) = X/Y, φ denotes latitude, and arccos(Y/X) does not produce the longitude angle.