# NavList:

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

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Re: Z tangent formula
From: George Huxtable
Date: 2005 Feb 19, 09:00 +0000

```Bill asked, a few days ago-

>Regarding a formula you gave for finding azimuth:
>
>"This formula is-
>
>Tan Z = sin (hour-angle) / (cos (hour-angle) sin lat - cos lat tan dec)
>
>and the rules for putting Z into the right quadrant, 0 to 360, clockwise
>fron North, are-
>
>If tan Z was negative, add 180 deg to Z. If hour-angle was less than 180
>deg, add another 180 deg to Z."
>
>By hour-angle I assume you mean local hour angle?
>
>I was also having trouble sporting out the parenthesis.  Should the formula
>look like the following, if I let ha= (hour-angle)?
>
>Tan Z =              sine ha
>        _________________________________________
>
>        (cos ha * sin lat) - (cos lat * tan dec)

==================

Yes, and yes. You've got it.

Remember that for this purpose ha is measured Westwards, so is always
increasing. (To my mind, this is sensible, though some authorities define
it the opposite way, always decreasing). Before local meridian passage, ha
is negative and increasing toward zero, or else a positive angle increasing
toward 360, which amounts to exactly the same thing.

And lat and dec are both North-positive, South-negative

And then Z will be an angle measured 0 to 360 degrees, clockwise from North.

By the way, in that earlier posting I missed out on something, that's so
obvious it hardly needed saying. But if those additions of 180 degrees
happen to take the end result over 360 degrees, then (of course) you should
subtract 360 degrees to bring it back into range, if that matters.

George.

================================================================
contact George Huxtable by email at george@huxtable.u-net.com, by phone at
01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
================================================================

```
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