06-30-2016, 08:09 PM
Program
01- 3 3 34- 16 CHS 67- 36 ENTER
02- 44 11 STO n 35- 1 1 68- 36 ENTER
03- 10 ÷ 36- 40 + 69- 45 6 RCL 6
04- 44 14 STO PMT 37- 43 33 40 g GTO 40 70- 20 ×
05- 43 35 g x=0 38- 36 ENTER 71- 9 9
06- 43 33 13 g GTO 13 39- 20 × 72- 48 .
07- 36 ENTER 40- 22 1/x 73- 4 4
08- 20 × 41- 1 1 74- 22 1/x
09- 1 1 42- 30 − 75- 40 +
10- 24 ∆% 43- 43 21 g √x 76- 20 ×
11- 44 12 STO i 44- 43 35 g x=0 77- 45 5 RCL 5
12- 42 13 f NPV 45- 43 33 00 g GTO 00 78- 30 −
13- 45 14 RCL PMT 46- 1 1 79- 20 ×
14- 20 × 47- 34 x≷y 80- 45 4 RCL 4
15- 36 ENTER 48- 43 34 g x≤y 81- 40 +
16- 36 ENTER 49- 43 33 52 g GTO 52 82- 20 ×
17- 20 × 50- 22 1/x 83- 3 3
18- 4 4 51- 9 9 84- 22 1/x
19- 20 × 52- 0 0 85- 30 −
20- 16 CHS 53- 44 13 STO PV 86- 20 ×
21- 3 3 54- 33 R↓ 87- 1 1
22- 40 + 55- 22 1/x 88- 40 +
23- 20 × 56- 44 14 STO PMT 89- 45 14 RCL PMT
24- 36 ENTER 57- 36 ENTER 90- 20 ×
25- 36 ENTER 58- 20 × 91- 2 2
26- 20 × 59- 40 + 92- 20 ×
27- 16 CHS 60- 43 21 g √x 93- 45 0 RCL 0
28- 1 1 61- 45 14 RCL PMT 94- 10 ÷
29- 40 + 62- 30 − 95- 45 13 RCL PV
30- 43 21 g √x 63- 44 14 STO PMT 96- 43 35 g x=0
31- 43 33 00 g GTO 00 64- 36 ENTER 97- 34 x≷y
32- 36 ENTER 65- 20 × 98- 34 x≷y
33- 20 × 66- 36 ENTER 99- 30 −
Constants
R0: 1.745329252e-02
R1: -8.86096144e-07
R2: 1.3495798e-11
R3: -9.7284-17
R4: 0.199991241
R5: 0.14251795
R6: -0.0616468
These should be stored manually:
1.745329252 EEX CHS 2 STO 0
8.86096144 CHS EEX CHS 7 STO 1
1.3495798 EEX CHS 11 STO 2
9.7284 CHS EEX CHS 17 STO 3
.199991241 STO 4
.14251795 STO 5
.0616468 CHS STO 6
Take care not pressing Σ+ as this will change the contents of registers R1 through R6.
Usage
Angles in DEGREES
-90 =< x =< 90
R/S --> cos(x)
R/S x≷y --> sin(x)
R/S ÷ --> tan(x)
GTO 32 R/S --> asin(x) 0 =< x < 1
GTO 38 R/S --> acos(x) 0 < x <= 1
GTO 44 R/S --> atan(x) 1e-50 < x < 1e50, x=0
(On the HP-12C Platinum, GTO 032, GTO 038 and GTO 044, respectively)
RCL 0 ÷ --> Rad->Deg
RCL 0 × --> Deg->Rad
Examples:
30 R/S --> 0.866025404 ; cos(30 deg)
x≷y --> 0.500000000 ; sin(30 deg)
x≷y ÷ --> 0.577350270 ; tan(30 deg)
0.5 GTO 32 R/S --> 29.99999998 ; asin(0.5) = 30 deg
0.5 GTO 38 R/S --> 60.00000002 ; acos(0.5) = 60 deg
1 GTO 44 R/S --> 44.99999997 ; atan(1) = 45 deg
RCL 0 180 × --> 3.141592654 ; π
3 ÷ --> 1.047197551 ; π÷3
RCL 0 ÷ --> 59.99999999 ; π÷3 rad = 60 deg
R/S --> 0.500000001 ; cos(π÷3 rad) = 1÷2
x≷y --> 0.866025403 ; sin(π÷3 rad) = 1÷2×√3
x≷y ÷ --> 1.732050804 ; tan(π÷3 rad) = √3
5 1/x GTO 44 R/S --> 11.30993251 ; atan(1÷5) = 11.30993251 deg
RCL 0 × --> 0.197395561 ; atan(1÷5) = 0.197395561 rad
16 × STO FV --> 3.158328968
239 1/x GTO 44 R/S --> 0.239725192 ; atan(1÷239) = 0.239725192 deg
RCL 0 × --> 0.004183994 ; atan(1÷239) = 0.004183994 rad
4 × CHS RCL FV + --> 3.141592992 (3.141592652 on the HP-12C Platinum) ; π = 16×atan(1÷5) - 4×atan(1÷239)
Accuracy comparison with the HP-15C and the HP-35:
Sin(x):
x (deg) HP-12C HP-12C Platinum HP-15C (1982) HP-35 (1972)
------------------------------------------------------------------------
0.000000 0.000000000E+00 0.000000000E+00 0.000000000E+00 0.000000000E+00
0.000010 1.745329252E-07 1.745329252E-07 1.745329252E-07 1.745000000E-07
0.000110 1.919862177E-06 1.919862177E-06 1.919862177E-06 1.919800000E-06
0.022000 3.839724258E-04 3.839724261E-04 3.839724260E-04 3.839723931E-04
3.330000 5.808674960E-02 5.808674961E-02 5.808674960E-02 5.808674961E-02
14.44000 2.493660251E-01 2.493660252E-01 2.493660251E-01 2.493660250E-01
25.55000 4.312985869E-01 4.312985871E-01 4.312985870E-01 4.312985871E-01
36.66000 5.970652564E-01 5.970652564E-01 5.970652564E-01 5.970652561E-01
47.77000 7.404527823E-01 7.404527827E-01 7.404527827E-01 7.404527828E-01
58.88000 8.560867284E-01 8.560867283E-01 8.560867283E-01 8.560867285E-01
69.99000 9.396329131E-01 9.396329128E-01 9.396329127E-01 9.396329127E-01
81.11000 9.879868530E-01 9.879868529E-01 9.879868528E-01 9.879868527E-01
88.88000 9.998089502E-01 9.998089500E-01 9.998089500E-01 9.998089499E-01
89.99000 9.999999850E-01 9.999999848E-01 9.999999848E-01 9.999999848E-01
89.99900 1.000000000E+00 9.999999998E-01 9.999999998E-01 9.999999998E-01
90.00000 1.000000000E+00 1.000000000E+00 1.000000000E+00 1.000000000E+00
Tan(x):
x (deg) HP-12C HP-12C Platinum HP-15C (1982) HP-35 (1972)
------------------------------------------------------------------------
0.000000 0.000000000E+00 0.000000000E+00 0.000000000E+00 0.000000000E+00
0.000010 1.745329252E-07 1.745329252E-07 1.745329252E-07 1.745000000E-07
0.000110 1.919862177E-06 1.919862177E-06 1.919862177E-06 1.919800000E-06
0.022000 3.839724258E-04 3.839724544E-04 3.839724543E-04 3.839724542E-04
3.330000 5.818499267E-02 5.818499268E-02 5.818499267E-02 5.818499266E-02
14.44000 2.575006491E-01 2.575006492E-01 2.575006491E-01 2.575006490E-01
25.55000 4.780471796E-01 4.780471799E-01 4.780471798E-01 4.780471798E-01
36.66000 7.442915883E-01 7.442915884E-01 7.442915883E-01 7.442915880E-01
47.77000 1.101686576E+00 1.101686577E+00 1.101686578E+00 1.101686578E+00
58.88000 1.656411391E+00 1.656411391E+00 1.656411391E+00 1.656411391E+00
69.99000 2.745986127E+00 2.745986120E+00 2.745986117E+00 2.745986119E+00
81.11000 6.393166511E+00 6.393166491E+00 6.393166451E+00 6.393166426E+00
88.88000 5.115045162E+01 5.115043114E+01 5.115042993E+01 5.115042860E+01
89.99000 5.773502604E+04 5.728989416E+04 5.729577951E+05 5.729655162E+04
89.99900 Error 0 5.735393346E+05 5.729577951E+05 5.730193057E+05
90.00000 Error 0 Error 0 9.999999999E+99 9.999999999E+99
ArcTan(x):
x HP-12C HP-12C Platinum HP-15C (1982) HP-35 (1972)
-----------------------------------------------------------------------
0.00000 0.000000000E+00 0.000000000E+00 0.000000000E+00 0.000000000E+00
0.00011 6.302535741E-03 6.302535739E-03 6.302535721E-03 6.302535688E-03
0.15500 8.810733019E+00 8.810732983E+00 8.810732986E+00 8.810732984E+00
0.26795 1.500004317E+01 1.500004315E+01 1.500004317E+01 1.500004317E+01
0.41421 2.249982576E+01 2.249982574E+01 2.249982578E+01 2.249982579E+01
0.57735 2.999998843E+01 2.999998845E+01 2.999998843E+01 2.999998843E+01
0.77700 3.784720679E+01 3.784720675E+01 3.784720677E+01 3.784720676E+01
0.88800 4.160507644E+01 4.160507646E+01 4.160507646E+01 4.160507646E+01
1.00000 4.499999997E+01 4.499999999E+01 4.500000000E+01 4.500000000E+01
1.22200 5.070548705E+01 5.070548704E+01 5.070548702E+01 5.070548702E+01
1.48880 5.611145719E+01 5.611145720E+01 5.611145723E+01 5.611145722E+01
2.11100 6.465265739E+01 6.465265738E+01 6.465265735E+01 6.465265735E+01
4.88800 7.843782363E+01 7.843782359E+01 7.843782359E+01 7.843782360E+01
7.55500 8.246000676E+01 8.246000683E+01 8.246000683E+01 8.246000679E+01
99.9990 8.942705958E+01 8.942705557E+01 8.942705557E+01 8.942705555E+01
7777.77 8.999266614E+01 8.999263291E+01 8.999263339E+01 8.999263337E+01
1.0E+05 9.000000000E+01 8.999942704E+01 8.999942704E+01 8.999942704E+01
Edited to change subject line.
01- 3 3 34- 16 CHS 67- 36 ENTER
02- 44 11 STO n 35- 1 1 68- 36 ENTER
03- 10 ÷ 36- 40 + 69- 45 6 RCL 6
04- 44 14 STO PMT 37- 43 33 40 g GTO 40 70- 20 ×
05- 43 35 g x=0 38- 36 ENTER 71- 9 9
06- 43 33 13 g GTO 13 39- 20 × 72- 48 .
07- 36 ENTER 40- 22 1/x 73- 4 4
08- 20 × 41- 1 1 74- 22 1/x
09- 1 1 42- 30 − 75- 40 +
10- 24 ∆% 43- 43 21 g √x 76- 20 ×
11- 44 12 STO i 44- 43 35 g x=0 77- 45 5 RCL 5
12- 42 13 f NPV 45- 43 33 00 g GTO 00 78- 30 −
13- 45 14 RCL PMT 46- 1 1 79- 20 ×
14- 20 × 47- 34 x≷y 80- 45 4 RCL 4
15- 36 ENTER 48- 43 34 g x≤y 81- 40 +
16- 36 ENTER 49- 43 33 52 g GTO 52 82- 20 ×
17- 20 × 50- 22 1/x 83- 3 3
18- 4 4 51- 9 9 84- 22 1/x
19- 20 × 52- 0 0 85- 30 −
20- 16 CHS 53- 44 13 STO PV 86- 20 ×
21- 3 3 54- 33 R↓ 87- 1 1
22- 40 + 55- 22 1/x 88- 40 +
23- 20 × 56- 44 14 STO PMT 89- 45 14 RCL PMT
24- 36 ENTER 57- 36 ENTER 90- 20 ×
25- 36 ENTER 58- 20 × 91- 2 2
26- 20 × 59- 40 + 92- 20 ×
27- 16 CHS 60- 43 21 g √x 93- 45 0 RCL 0
28- 1 1 61- 45 14 RCL PMT 94- 10 ÷
29- 40 + 62- 30 − 95- 45 13 RCL PV
30- 43 21 g √x 63- 44 14 STO PMT 96- 43 35 g x=0
31- 43 33 00 g GTO 00 64- 36 ENTER 97- 34 x≷y
32- 36 ENTER 65- 20 × 98- 34 x≷y
33- 20 × 66- 36 ENTER 99- 30 −
Constants
R0: 1.745329252e-02
R1: -8.86096144e-07
R2: 1.3495798e-11
R3: -9.7284-17
R4: 0.199991241
R5: 0.14251795
R6: -0.0616468
These should be stored manually:
1.745329252 EEX CHS 2 STO 0
8.86096144 CHS EEX CHS 7 STO 1
1.3495798 EEX CHS 11 STO 2
9.7284 CHS EEX CHS 17 STO 3
.199991241 STO 4
.14251795 STO 5
.0616468 CHS STO 6
Take care not pressing Σ+ as this will change the contents of registers R1 through R6.
Usage
Angles in DEGREES
-90 =< x =< 90
R/S --> cos(x)
R/S x≷y --> sin(x)
R/S ÷ --> tan(x)
GTO 32 R/S --> asin(x) 0 =< x < 1
GTO 38 R/S --> acos(x) 0 < x <= 1
GTO 44 R/S --> atan(x) 1e-50 < x < 1e50, x=0
(On the HP-12C Platinum, GTO 032, GTO 038 and GTO 044, respectively)
RCL 0 ÷ --> Rad->Deg
RCL 0 × --> Deg->Rad
Examples:
30 R/S --> 0.866025404 ; cos(30 deg)
x≷y --> 0.500000000 ; sin(30 deg)
x≷y ÷ --> 0.577350270 ; tan(30 deg)
0.5 GTO 32 R/S --> 29.99999998 ; asin(0.5) = 30 deg
0.5 GTO 38 R/S --> 60.00000002 ; acos(0.5) = 60 deg
1 GTO 44 R/S --> 44.99999997 ; atan(1) = 45 deg
RCL 0 180 × --> 3.141592654 ; π
3 ÷ --> 1.047197551 ; π÷3
RCL 0 ÷ --> 59.99999999 ; π÷3 rad = 60 deg
R/S --> 0.500000001 ; cos(π÷3 rad) = 1÷2
x≷y --> 0.866025403 ; sin(π÷3 rad) = 1÷2×√3
x≷y ÷ --> 1.732050804 ; tan(π÷3 rad) = √3
5 1/x GTO 44 R/S --> 11.30993251 ; atan(1÷5) = 11.30993251 deg
RCL 0 × --> 0.197395561 ; atan(1÷5) = 0.197395561 rad
16 × STO FV --> 3.158328968
239 1/x GTO 44 R/S --> 0.239725192 ; atan(1÷239) = 0.239725192 deg
RCL 0 × --> 0.004183994 ; atan(1÷239) = 0.004183994 rad
4 × CHS RCL FV + --> 3.141592992 (3.141592652 on the HP-12C Platinum) ; π = 16×atan(1÷5) - 4×atan(1÷239)
Accuracy comparison with the HP-15C and the HP-35:
Sin(x):
x (deg) HP-12C HP-12C Platinum HP-15C (1982) HP-35 (1972)
------------------------------------------------------------------------
0.000000 0.000000000E+00 0.000000000E+00 0.000000000E+00 0.000000000E+00
0.000010 1.745329252E-07 1.745329252E-07 1.745329252E-07 1.745000000E-07
0.000110 1.919862177E-06 1.919862177E-06 1.919862177E-06 1.919800000E-06
0.022000 3.839724258E-04 3.839724261E-04 3.839724260E-04 3.839723931E-04
3.330000 5.808674960E-02 5.808674961E-02 5.808674960E-02 5.808674961E-02
14.44000 2.493660251E-01 2.493660252E-01 2.493660251E-01 2.493660250E-01
25.55000 4.312985869E-01 4.312985871E-01 4.312985870E-01 4.312985871E-01
36.66000 5.970652564E-01 5.970652564E-01 5.970652564E-01 5.970652561E-01
47.77000 7.404527823E-01 7.404527827E-01 7.404527827E-01 7.404527828E-01
58.88000 8.560867284E-01 8.560867283E-01 8.560867283E-01 8.560867285E-01
69.99000 9.396329131E-01 9.396329128E-01 9.396329127E-01 9.396329127E-01
81.11000 9.879868530E-01 9.879868529E-01 9.879868528E-01 9.879868527E-01
88.88000 9.998089502E-01 9.998089500E-01 9.998089500E-01 9.998089499E-01
89.99000 9.999999850E-01 9.999999848E-01 9.999999848E-01 9.999999848E-01
89.99900 1.000000000E+00 9.999999998E-01 9.999999998E-01 9.999999998E-01
90.00000 1.000000000E+00 1.000000000E+00 1.000000000E+00 1.000000000E+00
Tan(x):
x (deg) HP-12C HP-12C Platinum HP-15C (1982) HP-35 (1972)
------------------------------------------------------------------------
0.000000 0.000000000E+00 0.000000000E+00 0.000000000E+00 0.000000000E+00
0.000010 1.745329252E-07 1.745329252E-07 1.745329252E-07 1.745000000E-07
0.000110 1.919862177E-06 1.919862177E-06 1.919862177E-06 1.919800000E-06
0.022000 3.839724258E-04 3.839724544E-04 3.839724543E-04 3.839724542E-04
3.330000 5.818499267E-02 5.818499268E-02 5.818499267E-02 5.818499266E-02
14.44000 2.575006491E-01 2.575006492E-01 2.575006491E-01 2.575006490E-01
25.55000 4.780471796E-01 4.780471799E-01 4.780471798E-01 4.780471798E-01
36.66000 7.442915883E-01 7.442915884E-01 7.442915883E-01 7.442915880E-01
47.77000 1.101686576E+00 1.101686577E+00 1.101686578E+00 1.101686578E+00
58.88000 1.656411391E+00 1.656411391E+00 1.656411391E+00 1.656411391E+00
69.99000 2.745986127E+00 2.745986120E+00 2.745986117E+00 2.745986119E+00
81.11000 6.393166511E+00 6.393166491E+00 6.393166451E+00 6.393166426E+00
88.88000 5.115045162E+01 5.115043114E+01 5.115042993E+01 5.115042860E+01
89.99000 5.773502604E+04 5.728989416E+04 5.729577951E+05 5.729655162E+04
89.99900 Error 0 5.735393346E+05 5.729577951E+05 5.730193057E+05
90.00000 Error 0 Error 0 9.999999999E+99 9.999999999E+99
ArcTan(x):
x HP-12C HP-12C Platinum HP-15C (1982) HP-35 (1972)
-----------------------------------------------------------------------
0.00000 0.000000000E+00 0.000000000E+00 0.000000000E+00 0.000000000E+00
0.00011 6.302535741E-03 6.302535739E-03 6.302535721E-03 6.302535688E-03
0.15500 8.810733019E+00 8.810732983E+00 8.810732986E+00 8.810732984E+00
0.26795 1.500004317E+01 1.500004315E+01 1.500004317E+01 1.500004317E+01
0.41421 2.249982576E+01 2.249982574E+01 2.249982578E+01 2.249982579E+01
0.57735 2.999998843E+01 2.999998845E+01 2.999998843E+01 2.999998843E+01
0.77700 3.784720679E+01 3.784720675E+01 3.784720677E+01 3.784720676E+01
0.88800 4.160507644E+01 4.160507646E+01 4.160507646E+01 4.160507646E+01
1.00000 4.499999997E+01 4.499999999E+01 4.500000000E+01 4.500000000E+01
1.22200 5.070548705E+01 5.070548704E+01 5.070548702E+01 5.070548702E+01
1.48880 5.611145719E+01 5.611145720E+01 5.611145723E+01 5.611145722E+01
2.11100 6.465265739E+01 6.465265738E+01 6.465265735E+01 6.465265735E+01
4.88800 7.843782363E+01 7.843782359E+01 7.843782359E+01 7.843782360E+01
7.55500 8.246000676E+01 8.246000683E+01 8.246000683E+01 8.246000679E+01
99.9990 8.942705958E+01 8.942705557E+01 8.942705557E+01 8.942705555E+01
7777.77 8.999266614E+01 8.999263291E+01 8.999263339E+01 8.999263337E+01
1.0E+05 9.000000000E+01 8.999942704E+01 8.999942704E+01 8.999942704E+01
Edited to change subject line.