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What's the best (shortest meant here) way you can devise to program a solution to this problem in HP-41 RPN?

Enter an angle in degrees mode and press A to return the answer.

Equation T = ...

What can you come up with ?

Gene
I hope this is not completely stupid, but I'll try (without testing):

lbl A
xeq deg
sto 01
sqrt
1
+
sto 02
sin
2,5
*
sto 03
pi
/
rcl 02
cos
rcl 01
sin
/
+
rcl 03
/
Assuming angle mode is DEG:

Code:
  01 LBL A  02 SIN  03 LASTX  04 SQRT  05 1  06 +  07 TAN  08 *  09 5  10 *  11 1/X  12 ST+ X  13 PI  14 1/X  15 +  16 END
I can shave off one byte:

Code:
 01 LBL A  02 SIN  03 LASTX  04 SQRT  05 1  06 +  07 TAN  08 *  09 .4  10 X<>Y  11 /  12 PI  13 1/X  14 +  15 END

Cheers, Werner
(10-27-2021 08:03 PM)Gene Wrote: [ -> ]What's the best (shortest meant here) way you can devise to program a solution to this problem in HP-41 RPN?

Enter an angle in degrees mode and press A to return the answer.

Equation T = ...

What can you come up with ?

Gene
First I draw it in my preferred graphical calculator https://www.desmos.com/calculator/pop31xijnj?lang=de
And in the time I was drawing (took 5min), smarter ones has give to you some solutions.
I was not quick enough ;-)
Great job Werner!

I was curious and comparing it to an algebraic (AOS) version. That was 39 steps/bytes.
(10-28-2021 08:39 AM)floppy Wrote: [ -> ]First I draw it in my preferred graphical calculator https://www.desmos.com/calculator/pop31xijnj?lang=de

Nice plotter, except that it is missing the important fact that x have to be in degrees (not radians nor Bogenmaßen).

(10-29-2021 05:27 PM)Gene Wrote: [ -> ]I was curious and comparing it to an algebraic (AOS) version. That was 39 steps/bytes.

Let's have a try.

Assuming that the complicated function can be simplify as W.Barbosa and Werner have done:

$$f(x)=\frac{\frac{2.5\times sin(\sqrt{x}+1)}{\pi}+\frac{cos(\sqrt{x}+1)}{sin(x)}}{2.5\times sin(\sqrt{x}+1)}=\frac{1}{\pi}+\frac{.4}{sin(x)\times tan(\sqrt{x}+1)}$$

And using a blue TI-57 LCD using certified AOS technology:

STO0 .4 ÷ ( RCL0 sin × ( 1 + RCL0 √x ) tan ) + ∏ 1/x = R/S RST

The last too steps are optional but useful in program; so this function can be recorded using 22 steps (or bytes) in LRN mode.
(10-31-2021 12:58 PM)C.Ret Wrote: [ -> ]And using a blue TI-57 LCD using certified AOS technology:

STO0 .4 ÷ ( RCL0 sin × ( 1 + RCL0 √x ) tan ) + ∏ 1/x = R/S RST

The last too steps are optional but useful in program; so this function can be recorded using 22 steps (or bytes) in LRN mode.

Perhaps you can save one byte by eliminating the parentheses:

STO0 √x + 1 = tan × RCL0 sin × 2.5 = 1/x + ∏ 1/x = R/S RST
(10-31-2021 05:43 PM)Gerson W. Barbosa Wrote: [ -> ]Perhaps you can save one byte by eliminating the parentheses:

Good suggestion :
STO0 √x + 1 = tan × RCL0 sin ÷ .4 = 1/x + ∏ 1/x = R/S RST (one Werner's step spare here)

STO0 √x + 1 = tan 1/x EXC0 sin STO÷0 .4 STO×0 ∏ 1/x STO+0 RCL0 R/S RST (two more steps spare , but, is this still AOS logic ?)
If it can be keyed on a TI-57 or TI-58C, then we will call it AOS. :-)

Gene
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