A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Lars Bergman
Date: 2021 Nov 4, 14:43 -0700
Those formulas are for great circle sailing, where you ideally constantly change your course, in practice change the course at certain time or distance intervals. If you are keeping a fixed course you practice rhumb line sailing and then another set of formulas are used. For short and medium range distances they typically look like
Lat2 = Lat1 + Dist · cos(Course)
Long2 = Long1 + Dist · sin(Course) / cos((Lat1 + Lat2) / 2)
In other words you use plane trigonometry but have to take care of the fact that the meridians converge towards the poles so the longitude difference is a function of your latitude.
These different sailings are covered in any text book on navigation. For the daily dead reckoning job onboard ships Traverse Tables were used (prior to electronic calculators). Those tables are (or were at least) included in all Nautical Tables.