# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Cosine Method Revisited**

**From:**Gordon Talge

**Date:**1996 Dec 15, 15:53 EST

In replay to cosine method. I was not implying that there was an ambiguity problem with it, what I ment was that if you are not careful with trig, stuff like that can come up. The cosine method is not the only trig formula that will work, although it is the fundental basic one. There are many others, check Bowditch, older editions. The problem with the cosine formula with hand calculations is the logs of negative numbers. To use sin h = sin L sin d + cos L cos d cos t with a calculator is straight forward, but with trig tables it is alot of work. Log trig make it easer, but you have the problem that ( sin L sin d ) could be negative. To solve this they used the haversine formula : hav z = hav (L ~ d) + cos L cos d hav t. Since the haversine is always positive and so is the cosine, there is not any problem with the logs. Here z is zenith distance. The fundamental formula for Z is sin Z = sin t cos d sec h. Now here we have a problem with the ambiguity. This formula is fundamental also. Now there are better trig formulas for Z, such as outlined in the nautical almanac. As far the difference between a circle of position and line of position. The circle of position looks like a line of position locally. You can get away with representing circles as straight line on charts for small distances in most area of the world. This is the whole idea behind mecator charts. Godon ,,, (. .) +-----------------------ooO-(_)-Ooo----------------------+ | Gordon Talge WB6YKK e-mail: gtalge{at}XXX.XXX | | Department of Mathematics QTH: Loma Linda, CA | | Mt. San Jacinto College Lat. N 34? 03.1' | | San Jacinto, CA Long. W 117? 15.2' | +--------------------------------------------------------+