i 6 o M. L’Huilier on an elementary Manner 
terme des seconds membres est — i.s.Az*. Done ; 1 = 1.2. A; 
Prenant successivement les differences troisiemes et qua- 
triemes ; on obtient 
2 4 sin. 4 — z cos. gz = A iv (4 4 ...i 4 ) Bz 4 -f- A iv (4 6 ...i 6 ) C z 6 -f- A iT 
(4 8 ...! 8 ) Dz 8 + A”( 4 i 0 ...i 10 ) Ez'°.... 
2 4 sin. 4 i% cos. 4% = A iv (s 4 ...2 4 ) Bz* -f- A iv (5*.. .2 6 ) C z 6 -f A iv 
(5 8 ...2 8 )D% 8 + A-( 5 io ...2 10 ) Ez'° . . . 
2 4 sin. 4 |-2: cos. 5% = A iv (6 4 ...3 4 ) B z 4 + A iv (6 6 ...3 6 ) C z 6 -j- A fT 
(6 , ... 3 8 )D* > + A"(6 “.. S “)E*"... i 
D’ ou Ton a de meme ; i.= i. 2...4B; et B — — ? ^ . 
Soient prises successivement les differences cinquiemes et 
sixiemes ; on obtient 
— 2 6 sin. 6 — z cos. 4 z — A vi (6 6 ....i 6 ) Cz 6 + A vi (6 8 ....i 8 ) Dz 8 -f 
A vi (6 ,0 ....i l °) Ez 10 -f . . . 
— 2 6 sin. 6 |-%cos. 52: = A vi (7 6 ...2 6 ) Cz 6 + A vi (7 s -- 28 ) D2 8 -j- 
A vi (7 I0 ....2 , °) Ez'° + ... 
— 2 6 sin 6 y % cos. 6z = A vi (8 6 ...3 6 ) C% 6 -j- A vi (8 8 .. 3 s ) D2 8 -f 
A vi (8 I3 ....3 ,0 )E^ IO + .... 
D'ou Ton obtient — 1 = 1.2... 6C; et C = — 
On obtient successivement D = -j- ~- 
E == — — — 
Et partant ; cos. z=i — 7^ s* + % 4 — 77- j -f 
— ~ * s — % 10 4 - ...... . 
1.2...8 1. 2. ..10 1 
§ 14. Puisque sin. z = z — ■— s 1 + z ! — z’+ 
1.2. .9 
et 
cos. 3=1 — 4 - — ■ ■ — z* — • — ^ 
1.2 ' 1.2. .4 1.2...C 
1.2. .4 
