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

**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.