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.

So start with LBL A and evaluate:

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.

So start with LBL A and evaluate:

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