```
Starting find y=sin(x)
degrees = 0                               sin= 0
degrees = 1.666666666666667E-002          sin= 2.90888204563416E-004
degrees = 3.333333333333333E-002          sin= 5.817763845130503E-004
degrees = 5E-002                          sin= 8.726645152351237E-004
degrees = 6.666666666666667E-002          sin= 1.163552572115861E-003
degrees = 8.333333333333333E-002          sin= 1.454440530541492E-003
degrees = .1                              sin= 1.745328365898257E-003
degrees = .1166666666666667               sin= 2.036216053572405E-003
end phase
now lets do the differences
these are the differences
0   0
1   2.90888204563416E-004
2  -2.461378160751454E-011
3  -2.461377938490009E-011
4   3.903127820947816E-018
5   2.222614453595284E-018
6   1.192622389734055E-018
7  -5.908901840045999E-018
end of differences
output phase
deg= 0  min=  0   0                                     0 %
deg= 0  min=  1   2.90888204563416E-004                 0 %
deg= 0  min=  2   5.817763845130503E-004                0 %
deg= 0  min=  3   8.726645152351237E-004                0 %
deg= 0  min=  4   1.163552572115861E-003                0 %
deg= 0  min=  5   1.454440530541492E-003                0 %
deg= 0  min=  6   1.745328365898257E-003                0 %
deg= 0  min=  7   2.036216053572405E-003                0 %
deg= 0  min=  8   2.327103568950181E-003               -8.013514145037932E-013 %
deg= 0  min=  9   2.617990887417797E-003               -4.555487169439004E-012 %
deg= 0  min=  10   2.908877984361382E-003              -1.599721868474539E-011 %
deg= 0  min=  11   3.199764835166904E-003              -4.385920104629872E-011 %
deg= 0  min=  12   3.490651415220055E-003              -1.023743117094746E-010 %
deg= 0  min=  13   3.781537699906096E-003              -2.134034948382844E-010 %
deg= 0  min=  14   4.072423664609659E-003              -4.086314115496764E-010 %
deg= 0  min=  15   4.363309284714498E-003              -7.321063753157995E-010 %
deg= 0  min=  16   4.654194535603172E-003              -1.243029862214597E-009 %
deg= 0  min=  17   4.945079392656678E-003              -2.018982244908217E-009 %
deg= 0  min=  18   5.235963831254005E-003              -3.159282592210244E-009 %
deg= 0  min=  19   5.526847826771618E-003              -4.788668554006746E-009 %
deg= 0  min=  20   5.817731354582853E-003              -7.061303582694516E-009 %
deg= 0  min=  21   6.108614390057233E-003              -1.016510178247107E-008 %
deg= 0  min=  22   6.399496908559686E-003              -1.432622867379694E-008 %
deg= 0  min=  23   6.690378885449664E-003              -1.981407438199977E-008 %
deg= 0  min=  24   6.981260296080156E-003              -2.694626329415169E-008 %
deg= 0  min=  25   7.272141115796597E-003              -3.609426249117628E-008 %
deg= 0  min=  26   7.563021319935649E-003              -4.76889804930851E-008 %
deg= 0  min=  27   7.853900883823864E-003              -6.222686685407741E-008 %
deg= 0  min=  28   8.144779782776222E-003              -8.027622767350201E-008 %
deg= 0  min=  29   8.435657992094531E-003              -1.024838077436427E-007 %
deg= 0  min=  30   8.726535487065685E-003              -1.295816765314829E-007 %
deg= 0  min=  31   9.017412242959776E-003              -1.62394416737934E-007 %
deg= 0  min=  32   9.308288235028056E-003              -2.018466797209647E-007 %
deg= 0  min=  33   9.599163438500737E-003              -2.489708492692324E-007 %
deg= 0  min=  34   9.890037828584631E-003              -3.049151422427371E-007 %
deg= 0  min=  35   1.018091138046062E-002              -3.709519905757564E-007 %
deg= 0  min=  36   1.047178406928094E-002              -4.48486567129049E-007 %
deg= 0  min=  37   1.076265587016629E-002              -5.390659117409735E-007 %
deg= 0  min=  38   1.105352675820278E-002              -6.443879034956438E-007 %
deg= 0  min=  39   1.134439670843861E-002              -7.663110243223041E-007 %
deg= 0  min=  40   1.163526569588064E-002              -9.068639107422114E-007 %
deg= 0  min=  41   1.192613369549071E-002              -1.068255660875252E-006 %
deg= 0  min=  42   1.22170006821817E-002               -1.25288607509996E-006 %
deg= 0  min=  43   1.250786663081352E-002              -1.463356354351802E-006 %
deg= 0  min=  44   1.279873151618867E-002              -1.702480129071941E-006 %
deg= 0  min=  45   1.308959531304777E-002              -1.973294621626334E-006 %
deg= 0  min=  46   1.33804579960647E-002               -2.279072258997505E-006 %
deg= 0  min=  47   1.367131953984162E-002              -2.623332414948361E-006 %
deg= 0  min=  48   1.396217991890366E-002              -3.009853685243057E-006 %
deg= 0  min=  49   1.425303910769337E-002              -3.442686084293869E-006 %
deg= 0  min=  50   1.454389708056496E-002              -3.926163961484711E-006 %
deg= 0  min=  51   1.483475381177821E-002              -4.464918895285043E-006 %
deg= 0  min=  52   1.512560927549217E-002              -5.06389293518272E-006 %
deg= 0  min=  53   1.541646344575854E-002              -5.728352269315846E-006 %
deg= 0  min=  54   1.570731629651476E-002              -6.463901041783286E-006 %
deg= 0  min=  55   1.599816780157688E-002              -7.276495517491217E-006 %
deg= 0  min=  56   1.628901793463206E-002              -8.172458487240824E-006 %
deg= 0  min=  57   1.657986666923079E-002              -9.158494071929686E-006 %
deg= 0  min=  58   1.687071397877883E-002              -1.024170275435612E-005 %
deg= 0  min=  59   1.716155983652883E-002              -1.14295965611286E-005 %
deg= 1  min=  0   1.74524042155716E-002                -1.273011491396074E-005 %
--- 59 lines not printed, for brevity
deg= 2  min=  0   3.489914957719134E-002               -9.946427352625191E-004 %
--- 59 lines not printed, for brevity
deg= 3  min=  0   5.232963007563719E-002               -1.208761195785654E-002 %
--- 59 lines not printed, for brevity
deg= 4  min=  0   6.970754448108735E-002               -7.014297083790016E-002 %
--- 59 lines not printed, for brevity
deg= 5  min=  0   8.691794621368323E-002               -.2728409241613025 %
--- 59 lines not printed, for brevity
deg= 6  min=  0   .1036655524838898                    -.8255270926073792 %
--- 59 lines not printed, for brevity
deg= 7  min=  0   .1193077715591997                    -2.101900095931789 %
--- 59 lines not printed, for brevity
deg= 8  min=  0   .1326059070137257                    -4.718723590286469 %
--- 59 lines not printed, for brevity
deg= 9  min=  0   .1413779978172258                    -9.624776240407625 %
--- 59 lines not printed, for brevity
deg= 10  min= 0   .1420367531201071                    -18.20429386103437 %
--- 59 lines not printed, for brevity
deg= 11  min= 0   .1289960405909524                    -32.39519953637728 %
--- 59 lines not printed, for brevity
deg= 12  min= 0   9.392938716311662E-002               -54.82246005807762 %

**********
[ the rest of the printout deleted to save your eyes,
the results do not get better - "trust me" ]

******* the TurboBASIC program to obtain the above is ***************

print "hello, I am 0-0-sin"
print
print "regular diff equations
print "7th order, 1 minute per step
print
DIM stepval#(40)
DIM w#(40)
Pi# = 3.1415926535897
OPEN "0-0-sin.txt" for OUTPUT as #2

print #2, "Starting find y=sin(x)
for x# = 0 to 7
degrees# = x#/60
print "degrees =" degrees#, "sin=" stepval#(x#)
print #2, "degrees =" degrees#, "sin=" stepval#(x#)
next x#
print #2,"end phase

print #2,"now lets do the differences
for n% = 0 to  7
w#(n%) = stepval#(0)
' print #2, " ** n="n%; " w="w#(n%)
for i% = 0 to (7-n%)
'  print #2, "      n=";n%; " i=";i%, stepval#(i%+1);" - "stepval#(i%);
stepval#(i%) = stepval#(i%+1) - stepval#(i%)
' print #2, "=";stepval#(i%)
next i%
next n%

' the  differences are now in w#()
print #2,"these are the differences
for n% = 0 to 7
print n% " " w#(n%)
print #2, n% " " w#(n%)
next n%
print #2,"end of differences

print #2, "output phase
n% = 0
for deg# = 0 to 45
for min# = 0 to 59
degrees# = deg# + (min#/60)
if (s# <> 0) then
e# = ((w#(0)-s#)*100)/s#
else
e# = 0
end if
if (min# = 0) or (deg# = 0) then
print     " deg=",deg#;" min=",min#;" "; w#(0),  e#;"%"
print #2, " deg=";deg#;" min=",min#;" "; w#(0),  e#;"%"
supress% = 0  ' disable supression
elseif (supress% = 0) then
print #2, "        --- 59 lines not printed, for brevity"
supress% = 1
end if
for i% = 0 to 7
w#(i%) = w#(i%) + w#(i%+1)
next i%
next min#
next deg#
print "cheers"
print #2, "cheers"

```