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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Sight Reduction Formula Question
From: Trevor Kenchington
Date: 2005 Jan 8, 14:51 -0400
From: Trevor Kenchington
Date: 2005 Jan 8, 14:51 -0400
Could someone either explain how the expressions for the sine, cosine and tangent of Z (as discussed on this thread) are derived or else point me to a published explanation? I have been trying to equate the three expressions but the trig I was taught as a 16 year-old is far too rusty for me to make sense of them. Nor can I find an explanation in any of the texts I have to hand. Any guesses as to why each textbook seemingly offers only one way of calculating Z? Any observer must be well aware of whether each of his sights is close to his meridian or to his prime vertical. So why are we not told to find Z from its cosine when the body lies to east or west and from its sine when it lies north or south? That way, ambiguities would be avoided and we would be working with trigonometric values which change swiftly with changing azimuth. (And without the complications of "ATAN2" calculator buttons or other ways of applying George's tangent approach.) Trevor Kenchington -- Trevor J. Kenchington PhD Gadus@iStar.ca Gadus Associates, Office(902) 889-9250 R.R.#1, Musquodoboit Harbour, Fax (902) 889-9251 Nova Scotia B0J 2L0, CANADA Home (902) 889-3555 Science Serving the Fisheries http://home.istar.ca/~gadus