Which equation correctly relates reduced latitude β to geodetic latitude Φ?

• A. tan β = (b / a) tan Φ
• B. tan β = (a / b) tan Φ
• C. tan Φ = (b / a) tan β
• D. tan Φ = (a / b) tan β

Answer: (A)

Reduced latitude is what you get when you map the ellipsoid onto a sphere by scaling the polar axis. In that transformed view, the angle from the equatorial plane to the radius toward the point has its tangent scaled by the axis ratio b over a. That means the relation between the two latitudes is tan β = (b/a) tan Φ. Since the polar radius b is smaller than the equatorial radius a, this factor reduces the tangent, so β is smaller than Φ for the same location—consistent with the way the ellipsoid’s flattening affects angles when you move to the spherical representation. The other forms would imply the opposite scaling or swapping a and b, which doesn’t fit the defining transformation.