mini challenge: find the smallest cosine of an integer

[Albert Chan]

If calculator had 12-digits precision, and we would like to search x of 14 digits:

pi/2/100 ≈ (x/100) / (2k+1)

Pick (pi/2/100) convergents with odd denominator, then numerator = x/100
Note: To get x of 14 digits, numerator must be 12 digits.

c:\> spigot -d20 -C pi/2/100 | tail -5
1324880093/84344486322
8539351431/543631996417
9864231524/627976482739
205823981911/13103161651197
833160159168/53040623087527

HP50g:
833160159168E2 COS       → -2.94461252684E-14 (red part should be 2017582)