NavList:

Hanno,

I think Weems used secants cosecants for the convenience of adding rather than subtracting logs. Fewer mistakes are made when adding vs. subtraction.

Greg Rudzinski

[NavList] Re: Longitude by Time Sight...good enough at sea?
From: Hanno Ix
Date: 20 Dec 2012 15:41

Question:

As you know it is a simple arithmetic to write his [cos(t/2)]^2- formula (pg15)
in terms of sine, cosine. And since he uses logarithms anyway, there is
effectively no difference at all:

log10(sec(70deg)) = + 0.46595 and log10(cos(70deg)) = - 0.46595.

So, when ignoring the minus sign his table is a log10(cos())
and a log10(sin()) anyway.

He even transfers sin^2 into cosec^2 which complicates things.

Is there a particuler reason why Weems uses cosecants, secants
rather than the more familiar sine, cosine?

h

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