A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Robin Stuart
Date: 2016 Nov 4, 10:28 -0700
The Pol(X,Y) function computes the θ value using atan(Y/X) but also looks at the individual signs of X and Y to determine the quadrant in which the angle lies. Whereas you must not change the ratio Y/X you can adjust what you include in X and what in Y so that Pol(X,Y) picks the required quadrant. In this case we know that the azimuth measured East from North is in the 1st or 2nd quadrants when the LHA is in the range 180°to 360° which suggests using Y = -sin(LHA). In fact since cos(Dec) is always positive for navigational problems we could equally use Y = - cos(Dec) . sin(LHA).
You say: “these operands do not look like just parts of the formula I used from the SR work-sheet”
[ cos(Dec) · sin(LHA) ] / [ cos(LatEP) · sin(Dec) - sin(LatEP) · cos(Dec) · cos(LHA) ]
= [ - cos(Dec) · sin(LHA) ] / [sin(LatEP) · cos(Dec) · cos(LHA) - cos(LatEP) · sin(Dec) ]
= [ - sin(LHA) ] / [sin(LatEP) · cos(LHA) - cos(LatEP) · tan(Dec) ]