# NavList:

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

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Re: Which calculator to use for "arctan(tan(269))"?
From: Bill Lionheart
Date: 2016 Nov 4, 16:39 +0000

```Another way on calculators that have complex number is to use
Arg(x+iy)  where [x,y] is the vector Stuart had. ...but I am not sure
if folks have calculators that do complex numbers but not polar
coordinates. It may be fewer keystrokes on some anyway.

On the other hand if you are 180 degrees out you are seriously lost so
maybe it does not need automating.

I was explaining polar coordinates to a class of optometry students. I
drew a diagram to show them when they needed to add 180 to the answer
from inverse tan. Half of the got it straight away  and half of them
were baffled. The baffled half just wanted to rule in terms of the
signs of x and y.  I suspect humans are fairly equally divided between
those who are dominantly geometric and those who are symbolic in the
way they view things. At least before they are trained in mathematics
where you have to be good at both.

Probably those who have taught celestial navigation observed the same?

Bill

On 4 November 2016 at 15:28, Robin Stuart  wrote:
> Tony,
>
>         I don’t have the Casio fx-85ES Plus but a look in its manual online
> indicates that it does have the capability to easily convert between
> rectangular and polar formats. If you use
>
> Zc = Pol{ [ cos(LatAP) · tan(Dec) - sin(LatAP) · cos(LHA) ] , [-sin(LHA) ] }
>
> the θ value should be in the correct quadrant. You may still have to add 360
> (or use the modulus function if there is one) when the result is negative.
>
> As far as alternative calculators for celestial navigation go the TI-36X Pro
> has received some attention on Navlist,
>
> Regards,
>
> Robin Stuart
>
> View and reply to this message

--
Professor of Applied Mathematics
http://www.maths.manchester.ac.uk/bl
```
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