(12C) Trigonometric Functions

[Gerson W. Barbosa]

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.