HP 41C/DM41X and HP 42S/DM42: Conversions

HP 41C/DM41X and HP 42S/DM42: Conversions

The program CONV has the "standard" conversions:

inches (IN) <-> centimeters (CM)

gallons (GAL) <-> liters (L)

pounds (LB) <-> kilograms (KG)

Fahrenheit (°F) <-> Celsius (°C)

Source: HP 67 Manual (Useful Conversion Factors, back cover). April 1977.

HP 41C/DM41: CONV41

Download raw file: CONV 41 Version

Custom menu:

Key: A (Σ+), B (1/x), C (√x), D (LOG), E (LN)

1st Level (to US): →IN, →GAL, →LB, →°F, HELP

2nd Level (to SI): →CM, →L, →KG, →°C, EXIT

(184 bytes)

01▸LBL "CONV"

02 SF 27

03 CF 01

04 RTN

05▸LBL A

06 2.54

07 FS? 01

08 1/X

09 /

10 CF 01

11 RTN

12▸LBL a

13 SF 01

14 GTO A

15▸LBL B

16 3.785411784

17 FS? 01

18 1/X

19 /

20 CF 01

21 RTN

22▸LBL b

23 SF 01

24 GTO B

25▸LBL C

26 .45359237

27 FS? 01

28 1/X

29 /

30 CF 01

31 RTN

32▸LBL c

33 SF 01

34 GTO C

35▸LBL D

36 1.8

37 *

38 32

39 +

40 RTN

41▸LBL d

42 32

43 -

44 1.8

45 /

46 RTN

47▸LBL E

48 CF 27

49 RTN

50▸LBL e

51 SF 21

52 "A >IN a >CM"

53 AVIEW

54 "B >GAL b >L"

55 AVIEW

56 "C >LB c> KG"

57 AVIEW

58 "D >F d >C"

59 AVIEW

60 CF 21

61 RTN

62 END

HP 42S/DM42/Free 42: CONV42

Download raw file:  CONV 42 Version

Custom menu:

1st Level (to US): →IN, →GAL, →LB, →°F

2nd Level (to SI): →CM, →L, →KG, →°C

The arrow keys (↓) and (↑) toggle the menu.

To exit the program, press [EXIT].

00 { 219-Byte Prgm }

01▸LBL "CONV"

02▸LBL A

03 MENU

04 "→IN"

05 KEY 1 XEQ 01

06 "→GAL"

07 KEY 2 XEQ 02

08 "→LB"

09 KEY 3 XEQ 03

10 "→°F"

11 KEY 4 XEQ 04

12 KEY 7 GTO B

13 KEY 8 GTO B

14 KEY 9 GTO 99

15▸LBL 20

16 STOP

17 GTO 20

18▸LBL B

19 MENU

20 "→CM"

21 KEY 1 XEQ 05

22 "→L"

23 KEY 2 XEQ 06

24 "→KG"

25 KEY 3 XEQ 07

26 "→°C"

27 KEY 4 XEQ 08

28 KEY 7 GTO A

29 KEY 8 GTO A

30 KEY 9 GTO 99

31▸LBL 21

32 STOP

33 GTO 21

34▸LBL 99

35 CLMENU

36 EXITALL

37 RTN

38▸LBL 01

39 2.54

40 /

41 RTN

42▸LBL 02

43 3.785411784

44 /

45 RTN

46▸LBL 03

47 0.45359237

48 /

49 RTN

50▸LBL 04

51 1.8

52 ×

53 32

54 +

55 RTN

56▸LBL 05

57 2.54

58 ×

59 RTN

60▸LBL 06

61 3.785411784

62 ×

63 RTN

64▸LBL 07

65 0.45359237

66 ×

67 RTN

68▸LBL 08

69 32

70 -

71 1.8

72 /

73 RTN

74 .END.

Eddie

All original content copyright, © 2011-2025. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

TI-60 Geometry: Intersection and Angle Between Two Lines

TI-60 Geometry: Intersection and Angle Between Two Lines

We have two lines in the standard form:

y = R1 * x + R2

y = R3 * x + R4

where R1, R3 are the slopes and R2, R4 are the y-intercepts, which are stored prior to executing the programs.

TI-60: Intersection Point

x = (R4 – R3) / (R1 – R3), y = R1 * x + R2

Step Key Code	Key	Step Key Code	Key
00 53	(	14 54	)
01 71	RCL	15 95	=
02 04	4	16 13	R/S
03 75	-	17 65	×
04 71	RCL	18 71	RCL
05 02	2	19 01	1
06 54	)	20 85	+
07 55	÷	21 71	RCL
08 53	(	22 02	2
09 71	RCL	23 95	=
10 01	1	24 13	R/S
11 75	-	25 22	RST
12 71	RCL
13 03	3

TI-60: Angle Between Two Lines

Θ = arctan(abs((R1 – R3) / (1 + R1 * R3)))

Step Key Code	Key	Step Key Code	Key
00 53	(	13 65	×
01 71	RCL	14 71	RCL
02 01	1	15 03	3
03 75	-	16 54	)
04 71	RCL	17 95	=
05 03	3	18 96	x²
06 54	)	19 86	√x
07 55	÷	20 12	R/S
08 53	(	21 34	RST
09 01	1
10 85	+
11 71	RCL
12 01	1

Examples

	Intersection Point: (x, y)	Angle: Θ (degrees)
y = -2 * x + 3 y = 3 * x + 4	(-0.2, 3.4)	45°
y = x + 8 y = 3 * x – 6	(7, 15)	26.56505118°
y = 4 * x – 6 y = 2 * x + 1	(3.5, 8)	12.52880771°

May I close with this: Happy Birthday, Susan Sarandon!

Eddie

All original content copyright, © 2011-2025. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

The author does not use AI engines and never will.

fx-991CW: Sums with a Step Not Equal to One

fx-991CW: Sums with a Step Not Equal to One

Step ≠ 1? An Adjustment is Necessary

The summation function on the Casio fx-991 CW calculator, and a lot of other advanced scientific calculators, calculates the sum of f(x) from x = a to x = b, with an increment of 1.

But what if have a sum of following:

log(2) + log(4) + log(6) + log(8): sum(f(x) from x = 2 to x = 8, step = 2)

Clearly, the increment is not 1, but 2 instead. Believe it or not, we can still use the summation function. We will need to adjust both the function and the limits to fit the requirements of the summation function.

1. Adjust f(x) to f(step * x)

2. Adjust the limits to x = a ÷ step and x = b ÷ step

For this particular problem:

1. f(x) becomes log(2 * x)

2. The limits become x = 2 ÷ 2 = 1 to x = 8 ÷ 2 = 4 (this allows the step to be 1)

Which transforms:

sum(log(x) from x = 2 to x = 8, step = 2)

to:

Σ(log(2 * x) from x = 1 to x = 4)

Sum: 2.584331224

A Couple More Examples

Example 1:

sum(x^2 from x = 0.5 to x = 2, step = 0.5), f(x) = x^2

The key here is the step (also known as the increment). The adjustments needed are:

1. f(x) becomes (0.5 * x)^2 = (x / 2)^2

2. The limits become x = 0.5/0.5 = 1 to x = 2/0.5 = 4

Sum: 15/2 = 7.5

Example 2:

sum(e^(x) from x = 1.5 to x = 2.1, step = 0.1), f(x) = e^(x)

The adjustments needed are:

1. f(x) becomes e^(0.1 * x) = e^(x / 10)

2. The limits become x = 1.5/0.1 = 15 to x = 2.1/0.1 = 21

Sum: 43.1994368

In Summary…

For the sum:

sum(f(x), x = a to x = b, step = Δx):

1. Adjust f(x) to f(Δx * x)

2. Adjust the limits: x = a/Δx to x = b/Δx

3. Summation function looks like this: Σ( f(Δx * x), x = a/Δx to x = b/Δx)

Hope you find this useful! Take care,

Eddie

All original content copyright, © 2011-2025. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

The author does not use AI engines and never will.

Trigonometric Calculus when Angles are in Degrees

Trigonometric Calculus when Angles are in Degrees

Today’s blog is a quickie.

The preferred angle measure in calculus is the radian. However, a lot of applications, including geometry, astronomy, engineering, and construction, use degrees.

An approach is to convert everything to radians before proceeding. Another approach is to remember that x radians = x° * π / 180, and use the conversion factor.

Derivatives

d/dx sin( x° )

Now all calculus calculations must have radians.

d/dx sin( x * π / 180)

= π / 180 * cos (x * π / 180)

= π / 180 * cos(x°)

Similarly – remember the angle considered is in DEGREES:

d/dx sin(x°) = π / 180 * cos(x°)	d/dx csc(x°) = - π / 180 * csc(x°) * cot(x°)
d/dx cos(x°) = - π / 180 * sin(x°)	d/dx sec(x°) = π / 180 * tan(x°) * sec(x°)
d/dx tan(x°) = π / 180 * sec(x°)^2	d/dx cot(x°) = -π / 180 * csc(x°)

Integration

Now let’s try integration.

∫( sin(x°) dx)

= ∫( sin(x * π / 180)) dx

= 180 / π * ∫(π / 180 * sin(x * π / 180)) dx

= 180 / π * -cos(x * π / 180) + C

= -180 / π * cos(x°) + C

Similarly:

∫ sin(x°) dx = -180 / π * cos(x°) + C

∫ cos(x°) dx = 180 / π * sin(x°) + C

∫ tan(x°) dx = -180 / π * ln(cos(x°)) + C

Use caution when using calculators. A lot of calculators when using calculus in degree mode get it correct but its’ always good to verify.

Eddie

All original content copyright, © 2011-2025. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

The author does not use AI engines and never will.