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R47: Trigonometry
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R47: Trigonometry

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sine cosine   tangent A O H θ 
P1: dot
    move right 1.618
P2: dot
    move up 1
P3: dot

L1: line from P1 to P2
L2: line from P2 to P3
L3: line from P3 to P1

TRI: line from P1 to P2 to P3 close fill 0xeeffff behind P1

A: circle with .c at L1 "A" bold fit width 75% fill lightblue
O: circle with .c at L2 "O" bold same
H: circle with .c at L3 "H" bold same

SIN: line ← from H to O behind H chop "sine"     small above aligned
COS: line ← from H to A behind A chop "cosine  " small below rjust
TAN: line ← from A to O behind A chop "tangent"  small below aligned

RT: box width 0.1 height 0.1 with .se at P2 fill white
    dot at P2

ANG: arc from 0.1  between P1 and P2 to \
              0.07 between P1 and P3
     text "θ" small small at 0.07 right of ANG

Motivations

The R47 has unparalleled trig support, inclining me to go off on a tangent, then triangulate toward a more acute degree of coordination.

(Ya know, I kinda lost track in all that excitement…was that five puns packed into a single sentence, or six? Well? Are ya feelin’ φ-licitous, punk?)

Okay, okay, enough silliness. Let us attempt a measure of rectitude here. This is trig we're talkin’ ’bout here, and everyone knows you cannot have fun with math, right? 🤓

Hard Button Use

If I had told you that a new calculator was coming out with over 100 menus, several of which are multi-page, you would be justified in guessing that the trig buttons are all behind one of those menus, as was done on the HP-28C/S, with its TRIG menu.

But no! The creators of the R47 chose to dedicate six of the hotly-contested shifted function locations on its faceplate to the primary trig functions, plus one more for 🟦 TRG to access further functionality.

One wonders what else we might have surfaced by freeing up six of these seven spots for further faceplate-level menus.

Speculations aside, it stands to reason that our benefactors felt this aspect of the calculator’s functionality was important enough to justify the space they gave it.

Angle Data Types

To properly understand the deep way the R47 handles angle values, consider the near-duplicated menu items on the first two rows of the 🟦 TRG menu. (Disregard ATAN2; it is shoehorned in here for an unrelated reason.) Why does the R47 have both the common DEG ⊙ setting and also a ⇒DEG function? The short answer is “data types,” but to come to a proper understanding, we will have to do some digging.

Try this: enter 1 and then 🟧 ⇒DEG to get the value 1.° on the stack. It now includes the radix mark to indicate that this conversion changed our integer entry to a floating-point value, but more to our point here, it includes a degree sign to the right. We can demonstrate to ourselves that this is not merely cosmetic but instead a tagged attribute of the number by saying STO 00 then RCL 00 to produce a copy. We find that this also copies the degree mark. Hmm! If the R47 was instead storing the bare value 0.1, that mark would be lost on this round-trip.

Let us go further by feeding R00 into the four other 🟧-shifted functions on that menu.1 You should then see:

    0.017 … r
    1.111 … g
    1° 0' 0.00"
    0.005 555 … πr

Because these are distinct data types stored on a per-register basis, we can do things on the R47 that lesser machines cannot. The uncommon clarity we see in the display above is a solid example of this, but if you want to be truly impressed, press + four times, then 🟧 ⇒DEG. If you followed the instructions above exactly, you should get 5.°. Why? Because you have added five different representations of 1° together, then forced the result back to degrees.

If you do not see this as a grand jeté with a beautiful landing, you aren’t following the dance steps properly.

Any scientific calculator worth the name will have at least degrees and radians. Grad might be left off to simplify the user interface,2 but fine then, let us put my lowly Casio fx-260SOLAR — called the fx-82 series elsewhere — to the simplest imaginable test of angle unit arithmetic:

AC Min         ; clear memory
Mode 4         ; set DEG mode
1 °'" M+       ; put 1° into the machine’s sole memory
AC MR          ; verify that it remembers that the value is in degrees
Shift Mode 5   ; convert value to radians and enter RAD mode
M+ MR          ; WRONG!

That verification step in the middle produces 1°0°0 in the fx-260’s crude 7-segment lettering, the closest it can come to indicating 1°, zero minutes, zero seconds. Already the R47 is ahead on aesthetic points, but the important bit is the result, demonstrating that although the machine knew the units at each step, it still produced the erroneous value 1.017… which is wrong in both degrees and radians. Correct would be any of

`2° = 2/180π = π/90 = 0.0349 rad`

Failing at this level is akin to attempting a schoolchild’s single jeté and ending up face-down on the ballet mat.3

Here's the true shocker: the same occurs on much newer machines like my shiny new (2025) Casio fx-115ES Second Edition, a fair competitor to the well-regarded fx-991EX Classwiz from 2015, which also face-planted.

There are two additional angle display modes in the R47, but we cover them elsewhere.

A Peek Into the Mind Behind

I think it is fair to presume that the primary audience for this site has already recognized the diagram at the top of this page as a SOH-CAH-TOA triangle and thus needs no tutelage in what the six basic trig functions do. Let us instead examine the remainder of the R47’s TRG menu:

This is not a random assortment to fill out the space left over by all that ADM stuff covered above. Everything listed has prominent uses in electrical engineering, and it is no coincidence that the R47 project leader is an EE. Thus why relatively rare functions like sinc() and atan2() get pride of place in the first row of this menu. Had he become a civil engineer, we might have the hyperbolic trig functions in these spots instead.

Speaking of, you will have to dig those functions out of the catalog if you want them. As of this writing, the R47 does not implement the inverse hyperbolic cosecant — not yet, anyway! — but it does implement sinh, cosh, tanh, arsinh, arcosh, and artanh. Do be aware that unlike on the WP34s or the HP calculators that inspired it, these are distinct functions, not called by prefixing the regular trig ones with a HYP modifier keypress.

(You may now wish to return to my R47 article index.)

License

This work is © 2025 by Warren Young and is licensed under CC BY-NC-SA 4.0

  1. ^ We're ignoring .ms⁻¹ because it is not part of this series of ⇒ functions. The WP43 — one of the R47’s ancestors — has a sixth angle type here, the MIL — short for milliradian — which got dropped along the way for some reason.
  2. ^ Certainly not to save firmware space in today's world of mega-bytes for milli-bucks!
  3. ^ …except that in this analogy, it won’t be the wannabe dancer crying for want of sympathy, but the audience crying for want of proper angle support. 😭