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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: Degree Calculator
From: Paul Hirose
Date: 2018 Dec 2, 22:10 -0800

```On 2018-11-27 19:01, David C wrote:
> My starting point is the expression
>
> 2x3  +  6x5
>
> A quick bit of mental arithmetic gives the answer 36.
>
> On the fx-82-AU 8 keystrokes are required:
>
> 2x3  +  6x5 =
>
> Next I tried Realcalc in non-rpn mode. 12 keystrokes gave me the answer:
>
> 2 x 3 = STO 6 x 5 = + RCL =

If the key sequence 2 × 3 + 6 × 5 = won't work in Realcalc I would find
that intolerably deficient.

The inexpensive TI-36X Pro even gets the correct answer to the more
complex expression 1 + 3 × 2 ^ 4. A naive solution is 1 + 3 is 4, times
2 is 8, to the 4th power is 4096. But a calculator sophisticated enough
to understand operator precedence defers the addition when you press the
× key, and defers the multiplication when you press ^ since each
successive operator is of higher precedence. Thus it applies the
operators right to left: 2 to the 4th, times 3, plus 1 equals 49.

> Because I had successfully rediscovered RPN I decided to compute Hc with RPN.
>
> The equation is
>
> arc sin (sinA SinB + CosA*CosB*CosC)
>
> After some playing around I came up with
>
> A DMS  Sto 0
> B DMS  STO 1
> C DMS  cos
> x<->y  cos  X  x<->y
> cos X                     /* part 2 of expression complete */
>
> rcl 0  sin
> rcl 1 sin
> X                         /* part 1 of expression complete */
>
> +
> arc sin
> DMS

But note that later HP calculators (even the 49G, long out of
production) delete the number from the stack when you store it. On the
other hand, they have case sensitive named variables so you can store
the parts of the triangle in variables A, b, and c.

One weakness of HP calculators is that sexagesimals must be entered in a
ddd.mmsss... format for conversion to decimal. This is no problem with
decimal minutes to tenths, since the seconds equivalents are easy to
remember. But with decimal minutes at higher precision it's simplest to
perform the conversion by hand: divide minutes by 60, then add degrees.

On the other hand, the Ti-36X Pro lets you enter sin(0°1.23′) for
instance. But all is not happiness since 1) degrees must be entered even
if zero, and 2) it takes four keystrokes to get each angle symbol.

My old Casio FX-7400G+ can get the angle symbol with a single press of
the F1 key if you select the applicable option. Confusingly, 1.23′ so
entered appears as 0°1.23°. But it's quick and it works.
```
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