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    Re: W.H. Simms Math Question
    From: Frank Reed
    Date: 2011 Nov 5, 23:05 -0700

    Hello Alexander.

    Welcome aboard!

    In many nineteenth century treatments of trigonometry you'll find that sin(1") factor inserted in various formulae. It is indeed related to the small angle approximation, but I would say that it was really their way in that era of saying "in radians". In modern mathematical notation, we would say:
    sin(x) = x (for x small enough),
    but they would say:
    sin(x) = sin(1")*x.
    The sine of one second of arc is extremely close to (2*pi)/(360*3600), differing at the twelfth decimal point (if I remember correctly), so it works well. You can easily convert to modern trigometric fashion by dropping sin(1") wherever you come across it in those older works.

    -FER


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