A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2016 Nov 3, 15:55 -0700
The quadrant ambiguity of the arctangent is a normal mathematical property of that operation. Many computer languages have math libraries that implement a separate function often called atan2 which is reasonably well described here: https://en.wikipedia.org/wiki/Atan2.
If you're doing calculator computations for lines of position, then you should consider dropping the intercept method entirely.
Conanicut Island USA