Fun with the HP 12C

I used the classic HP 12C, with the 99 step capacity.  Even without the trig functions, we can do a lot.

Eddie

 

Calculating f(x) = p * ∑(a^k, k=1 to n) using the TVM Keys

 

Input:

[ n ] = n
R0 = a
R1 = p

Program:

STEP	KEY	CODE
01	BEGIN	43 7
02	RCL 0	45 0
03	1	1
04	-	30
05	EEX	26
06	2	2
07	*	20
08	[i]	12
09	RCL 1	45 1
10	CHS	16
11	[PMT]	14
12	[FV]	15
13	END	43 8
14	GTO 00	43 33 00

 

Examples:

n = 60, R0 = 1.01, R1 = 350.  Result:  28,870.2283

n = 5, R0 = 2, R1 = 10.05.   Result:  623.1

 

Heron’s Formula

Area of a Triangle with side lengths a, b, and c.

Area = √(s*(s-a)*(s-b)*(s-c)) where s = (a+b+c)/2

Input:

R1 = a
R2 = b
R3 = c

Program:

STEP	KEY	CODE
01	RCL 1	45 1
02	RCL 2	45 2
03	+	40
04	RCL 3	45 3
05	+	40
06	2	2
07	÷	10
08	STO 4	44 4
09	RCL 4	45 4
10	RCL 1	45 1
11	-	30
12	RCL 4	45 4
13	RCL 2	45 2
14	-	30
15	*	20
16	RCL 4	45 4
17	RCL 3	45 3
18	-	30
19	*	20
20	RCL 4	45 4
21	*	20
22	√	43 21
23	GTO 00	43

 

Example:   a = 5, b = 5, c = 6.  Result:  12

Projectile Motion without Air Resistance:  With the projectile being launched at 45° at velocity V.  The maximum distance will be achieved at these conditions.

Theoretical Maximum Distance:

R_max = v^2/g (in feet)

Theoretical Height of the Projectile (at x = R_max/2)

H = v^2/(4g)  (in feet)

Where g = 32.17404 ft/s^2

If you desire meters, substitute g = 9.80665 m/s^2 instead.

Run the program with V in the display.  The velocity is assumed to be feet/second.  The maximum distance is calculated, then the projectile’s theoretical height.

Program:

STEP	KEY	CODE
01	2	2
02	Y^X	21
03	3	3
04	2	2
05	.	48
06	1	1
07	7	7
08	4	4
09	0	0
10	4	4
11	÷	40
12	R/S	31  (display R)
13	4	4
14	÷	40
15	GTO 00	43 33 00 (display H)

 Example:  V = 40  ft/s

Results:  R = 49.7295 ft,  H = 12.4324 ft
 

Factorials of Large Integers

N! =  N * (N-1) * (N-2) * … * 1

**For large n, this program will take time if you have an HP 12C that was manufactured in the 1980s.

Input n, press R/S. 

The mantissa is displayed.  Press R/S
The exponent is displayed (10^exponent).

 Program:

STEP	KEY	CODE
01	STO 0	44 0
02	0	0
03	STO 1	44 1
04	RCL 0	45 0
05	LN	43 23   // loop begins
06	STO+ 1	44 40 1
07	1	1
08	STO- 0	44 30 0
09	RCL 0	45 0
10	1	1
11	-	30
12	X=0	43 35
13	GTO 15	43 33 15   // end of loop
14	GTO 04	43 33 04
15	RCL 1	45 1
16	1	1
17	0	0
18	LN	43 23
19	÷	10
20	STO 1	44 1
21	ENTER	36
22	FRAC	43 24
23	1	1
24	0	0
25	X<>Y	34
26	Y^X	21
27	R/S	31  // mantissa
28	X<>Y	34
29	INTG	43 25 // exponent
30	GTO 00	43 33 00

 

Example: 

50! » 3.0414 * 10^64

50 R/S
Result:  3.0414 R/S 64

76! » 1.8855 * 10^111

76 R/S
Result:  1.8855 R/S 111

Degrees Minutes Seconds to Decimal Degrees

2°51’32.4” -> 2.859

Type input as DD.MMSSSS (degrees, minutes, seconds). For our example, the input would be 2.51324.

 Program:

STEP	KEY	CODE
01	STO 0	44 0
02	INTG	43 25
03	STO 1	44 1
04	RCL 0	45 0
05	FRAC	43 24
06	EEX	26
07	2	2
08	*	20
09	INTG	43 25
10	6	6
11	0	0
12	÷	10
13	STO+ 1	44 40 1
14	RCL 0	45 0
15	EEX	26
16	2	2
17	*	20
18	FRAC	43 24
19	3	3
20	6	6
21	÷	10
22	STO+ 1	44 40 1
23	RCL 1	45 1
24	GTO 00	43 33 00

Decimal Degrees to Degrees Minutes Seconds

 2.859 -> 2°51’32.4”

Answer displayed as DD.MMSSSS (degrees minutes seconds)

Program:

01	STO 0	44 0
02	INTG	43 25
03	STO 1	44 1
04	RCL 0	45 0
05	FRAC	43 24
06	6	6
07	0	0
08	*	20
09	ENTER	36
10	INTG	43 25
11	EEX	26
12	2	2
13	÷	10
14	STO+ 1	44 40 1
15	R-Down	33
16	FRAC	43 24
17	6	6
18	0	0
19	*	20
20	EEX	26
21	4	4
22	÷	10
23	STO+ 1	44 40 1
24	RCL 1	45 1
25	GTO 00	43 33 00

 

This blog is property of Edward Shore - 2014