sin(x) & cos(x) for x = 10²² in radians

[Albert Chan]

(10-03-2023 12:56 AM)Albert Chan Wrote:  I wonder how big is [HP71B] lookup table to get this good ...

I should just try it! No table, just many digits of pi.

>sin(1e22)
-.852200849762
>sin(1e33)
-5.11830428837E-2

Using rpn.exe, HP71B stored 32 digits of pi (note, next digit of pi is 0)
Note, "pi =-31" means digits=31, but only for pi, global digits (default=36) unaffected.

C:\> rpn
pi ?
3.14159265358979323846264338327950288

1e22 pi =-31 2x % sin ?12
-0.852200850595
1e22 pi =-32 2x % sin ?12
-0.852200849762
1e22 sin ?12
-0.852200849767

1e33 pi =-31 2x % sin ?12
0.899003019303
1e33 pi =-32 2x % sin ?12
-0.0511830428837
1e33 sin ?12
0.762302394953

For comparison, Free42 Decimal "stored" thousands of digits of pi

(10-24-2021 12:46 PM)Albert Chan Wrote:  min(|cos(x)|) for integer x (also, for real x)

2344813655066356855719930664718056e1381 COS ABS → 1.030557387629248882465543827418861e-37

C:\>spigot --printf "%.34g" cos(2344813655066356855719930664718056e1381)
1.030557387629248882465543827418861e-37