# NavList:

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

**Re: Spherical Law of Cosines**

**From:**Herbert Prinz

**Date:**2002 Oct 28, 10:46 +0000

Hello Trevor, You wrote: > Just for the record, I meant nothing of the kind and did mean exactly > what I wrote. I apologize for second guessing you. I honestly thought it was a mechanical error, when in fact it seems to have been a logical one. Your statement "And so we would have to suppose that sin(a)=cos(a)" is simply wrong. However, Dan's equations do imply cos(a+b) = 0, if angle(ab) > 0, from which a + b = 90deg, which can be translated to sin(a) = cos(b); So, it was natural for me to assume that this was what you had in mind. Once again, my apologies. You wrote further: > Herbert has, however, pointed out that the two equations for cos(c) > could be simultaneously true if sin(a) was equal to cos(b), as well as > if sin(a) was equal to cos(a). I had missed the one while noting the > other. This is missing the point. You had tried to give a reductio ad absurdum of Dan's equations, but you failed, because the inference that you tried to make (namely sin(a) = cos(a)) cannot be made. ONLY the one I have given can be made. It goes without saying that I fully agree with the final result of your analysis that we have to reject one of Dan's equations. I only had a small problem with the way how you got there. Best regards Herbert