Fun with HP 12C Part II
Sine Approximation
Source: Ted’s Math
World, Calculator Magic #4
Retrieved 2014-10-13
sin x ≈ (((x^2/72 – 1)*x^2/42 + 1)*x^/20 – 1)*x^2/6 +
1)*x
|
STEP
|
KEY
|
CODE
|
STEP
|
KEY
|
CODE
|
|
01
|
STO 0
|
44, 0
|
21
|
0
|
0
|
|
02
|
2
|
2
|
22
|
÷
|
10
|
|
03
|
y^x
|
21
|
23
|
*
|
20
|
|
04
|
ENTER
|
36
|
24
|
1
|
1
|
|
05
|
ENTER
|
36
|
25
|
-
|
30
|
|
06
|
ENTER
|
36
|
26
|
X<>Y
|
34
|
|
07
|
7
|
7
|
27
|
6
|
6
|
|
08
|
2
|
2
|
28
|
÷
|
10
|
|
09
|
÷
|
10
|
29
|
*
|
20
|
|
10
|
1
|
1
|
30
|
1
|
1
|
|
11
|
-
|
30
|
31
|
+
|
40
|
|
12
|
X<>Y
|
34
|
32
|
RCL 0
|
45, 0
|
|
13
|
4
|
4
|
33
|
*
|
20
|
|
14
|
2
|
2
|
34
|
STO 1
|
44, 1
|
|
15
|
÷
|
10
|
35
|
GTO 00
|
43, 33, 00
|
|
16
|
*
|
20
|
|
|
|
|
17
|
1
|
1
|
|
|
|
|
18
|
+
|
40
|
|
|
|
|
19
|
X<>Y
|
34
|
|
|
|
|
20
|
2
|
2
|
|
|
|
Examples:
sin 0.25 ≈ 0.2474
sin -1.82 ≈ -0.9691
Cosine Approximation
Source: Ted’s Math
World, Calculator Magic #4
Retrieved 2014-10-13
cos x ≈ (((x^2/56 – 1)*x^2/30 + 1)*x^2/12 – 1)*x^2/2 + 1
Registers: R0 = x
in radians, R1 = cos x
|
STEP
|
KEY
|
CODE
|
STEP
|
KEY
|
CODE
|
|
1
|
STO 0
|
44, 0
|
17
|
1
|
1
|
|
2
|
2
|
2
|
18
|
+
|
40
|
|
3
|
Y^X
|
21
|
19
|
X<>Y
|
34
|
|
4
|
ENTER
|
36
|
20
|
1
|
1
|
|
5
|
ENTER
|
36
|
21
|
2
|
2
|
|
6
|
ENTER
|
36
|
22
|
÷
|
10
|
|
7
|
5
|
5
|
23
|
*
|
20
|
|
8
|
6
|
6
|
24
|
1
|
1
|
|
9
|
÷
|
10
|
25
|
-
|
30
|
|
10
|
1
|
1
|
26
|
X<>Y
|
34
|
|
11
|
-
|
30
|
27
|
2
|
2
|
|
12
|
X<>y
|
34
|
28
|
÷
|
10
|
|
13
|
3
|
3
|
29
|
*
|
20
|
|
14
|
0
|
0
|
30
|
1
|
1
|
|
15
|
÷
|
10
|
31
|
+
|
40
|
|
16
|
*
|
20
|
32
|
STO 1
|
44, 1
|
|
|
|
|
33
|
GTO 00
|
43,33,0
|
|
|
|
|
|
|
|
cos 0.33 ≈ 0.23847605343
cos -0.58 ≈ 0.83646264991
Rough Approximation for erf(x)
If x ≤ 1, accuracy is at least 3 digits. Method: 3/8 Integration Rule
Source: Ball, John
A. “Algorithms for RPN Calculators” John Wiley
& Sons: 1978.
|
STEP
|
KEY
|
CODE
|
STEP
|
KEY
|
CODE
|
|
1
|
STO 0
|
44, 0
|
26
|
CHS
|
16
|
|
2
|
3
|
3
|
27
|
e^x
|
43, 22
|
|
3
|
÷
|
10
|
28
|
+
|
40
|
|
4
|
2
|
2
|
29
|
8
|
8
|
|
5
|
Y^X
|
21
|
30
|
÷
|
10
|
|
6
|
CHS
|
16
|
31
|
3
|
3
|
|
7
|
e^x
|
43, 22
|
32
|
*
|
20
|
|
8
|
ENTER
|
36
|
33
|
RCL 0
|
45, 0
|
|
9
|
RCL 0
|
45, 0
|
34
|
*
|
20
|
|
10
|
2
|
2
|
35
|
3
|
3
|
|
11
|
*
|
20
|
36
|
÷
|
10
|
|
12
|
3
|
3
|
37
|
1
|
1
|
|
13
|
÷
|
10
|
38
|
.
|
48
|
|
14
|
2
|
2
|
39
|
1
|
1
|
|
15
|
Y^X
|
21
|
40
|
2
|
2
|
|
16
|
CHS
|
16
|
41
|
8
|
8
|
|
17
|
e^x
|
43, 22
|
42
|
3
|
3
|
|
18
|
+
|
30
|
43
|
7
|
7
|
|
19
|
3
|
3
|
44
|
9
|
9
|
|
20
|
*
|
20
|
45
|
7
|
7
|
|
21
|
1
|
1
|
46
|
*
|
20
|
|
22
|
+
|
40
|
47
|
GTO 00
|
43,33,00
|
|
23
|
RCL 0
|
45, 0
|
|
|
|
|
24
|
2
|
2
|
|
|
|
|
25
|
Y^X
|
21
|
|
|
|
Examples:
x = .15; Result ≈
0.1680
x = .50; Result ≈
0.5205
x = 1.25; Result ≈ 0.9220
(actual ≈ 0.9229)
This blog is property of Edward Shore, 2014.
