A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Robert Pearson
Date: 2017 Mar 29, 21:41 -0700
KInd of cut my self off when I hit the submit button on the last post. But continuing on:
In the table of sine and cosines the delta value is the change in the sine or cosine for a 1' in the angle. The value listed has to be multiplied by some constant depending on the number of places in the table in order to get an actual value. If you check other tables of natural trig functions that have delta listed you can see the same type values. Bowditch table 31 for instance.
Since the values are tabulated at 30' (half deg) intervals it may be using an average value for that interval. but say you check the cosine of 6°. In Bowditch Table 31 cos 6° = 0.99452 and cos 6°01' = 0.99449. The difference for a change in 1' is 0.00003 which is listed as 3 in the table. So multiple 3 by 1x10e-5 you get the correct value. In Doniol the same value is listed for the cosine but for the delta it lists 3.0 (zero is implied to reduce ink clutter I guess). In order to get the extra 1 decimal place in those delta figures you need to use natural trig values to 6 places.