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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Spherical Law of Cosines
From: Dan Allen
Date: 2002 Oct 18, 14:44 -0700

```Thanks to Bill Arden who pointed out yet another mistake of mine...

I have been writing these things while being very involved in other
matters and my memory has not been what it used to be...

sin(c) = sin(a)*sin(b) + cos(a)*cos(b)*cos(ab)

is what I should have written as the alternative version.

With apologies,

Dan

Begin forwarded message:

> From: ARDENW714@aol.com
> Date: Fri Oct 18, 2002  12:22:00 PM US/Pacific
> To: danallen46@ATTBI.COM
> Subject: law of cosines
>
> Hi, Dan -
>
> You wrote recently ...
>
> "Note too that there are equivalent ways of writing the spherical law
> of cosines.  One can write it as
>
> cos(c) = sin(a)*sin(b) + cos(a)*cos(b)*cos(ab)
>
> where the pairs of sin/cos of a/b are switched."
>
> Isn't the left side of that equation SIN(c)? Or is that another
> substitution that I didn't know enough to make?
>
> I hope I haven't been doing that wrong - I've been using
> sin(Hc) = sin(lat)*sin(dec) + cos(lat)*cos(dec)*cos(LHA) and it seems
> to work correctly.
>
> Regards,
> Bill Arden
>

```
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