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Subject: Re: S Tables Question
From: Herbert Prinz (hprinz@XXX.XXX)
Date: Tue Oct 22 2002 - 23:54:39 EDT
Arthur,
If Sin and Cos do not work, try Secans for S, and Cosecans for C.
I have not seen the particular tables that you are referring to and I am
shooting from the hip. Apologies, if this leads into the wrong
direction, but I would be surprised if this were the case.
There is an uncounted number of tables out there that are all variants
based on the Ageton method. The basic idea behind this method is to
split the navigational triangle into two rectangular triangles. Each of
them can be solved with a formula that contains just multiplicative
terms (as opposed to the cosine theorem that involves the addition of
two such terms), the advantage being that they can be solved with
logarithms without having to find the anti-logarithm of intermediate
results. For details look up Bowditch for formulas of the rectangular
spherical triangle. One can always use sin instead of cosec, and cos
instead of secans, as they are reciprocal. Instead of adding the
logarithms, you would subtract. I don't know why one function is given
preference over the other; I am sure there are procedural advantages.
Obviously, one tries to device a method that can use either sin/cos
functions, or sec/cosec only, as in each pair each function is the
co-function of the other (as their names suggest) and therefore, space
for tabulation is cut in half. You can check this out in your tables: If
it folds at 45 deg and S(x) = C(90-x) and vice versa, we are on the
right track.
Herbert Prinz
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