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

**Re: Which calculator to use for "arctan(tan(269))"?**

**From:**Tony Oz

**Date:**2017 Jul 6, 01:14 -0700

Robin Stuart on 2017 Feb 1, 08:40 said:

Calculate

<snip>

Pol{ [ cos(Lat) · tan(Dec) - sin(Lat) · cos(LHA) ] , [-sin(LHA) ] }

and then

Hc = cos-1( r cos(Dec) ) and θ = Zn

There is no need for a separate calculation of the altitude!!! One proviso, as Lars indicated, is that it only gives the correct answer for objects above the horizon.

I attempted to feed this formula the coordinates (Lat, λ) of my location and Singapore's: 60°N,30°E and 1°17'N, 103°50'E - to see what it gives.

To my surprise - the Hc obtained was exactly the GC distance between me and Singapore, coinsiding with the check calculation by the formula:

d = arccos[sin(Lat

_{1})·sin(Lat_{2}) + cos(λ_{1})·cos(λ_{2})·cos(Lat_{1}- Lat_{2})]

So, may be the **Pol()** calculator's function is much more usefull that I expected. I guess I must try it to see what Robin's and Lars's warning about being above the horizon means.

Regards,

Tony