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    Re: S Tables Question
    From: Herbert Prinz
    Date: 2002 Oct 23, 03:54 +0000

    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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