RELATIONS GÉNÉRALES

sin 2 a4-cos 2 a=i.

tanga

__ sina "~ cosa"

cota

__ COSa^

"" sina

tanga

cota = i .

COS a

séca = i.

sinacoséca = i.

séc 2

a = i 4- tang 2 a.

coséc'i

2 = 1 + cot 2 a.

tanga

sina

\/i -+- tang 2 a

cosa

v/i +- tang 2 a

tanga

~~ cota

sma

v/i — sin 2 a

l/i — cos 2 a

cosa

sin (a4-£) = sinacos&4-cosa sinô.

gin ( a — £ ) = sina cosft — cosa sin b.

^,os (a -f- b ) = cosa cos 6 — sina sin 6.

cos(a — b) = cosa cos ô 4- sin a sin 6.

sinacos&==isin(a4-&)-+-ïSin(a — 6).

cosa èinb = |sin (a-+- b) — | sin (a — 6).

cosa cos& = jcos (a — b) 4-icos (a4- 6) .

sinasin& = £cos(a — b) — |cos(a4-£).

8ina-4-sinô = 2Sin^(a-h^)cos|(a — b).

sina — sinfc = 2COs£ (a-\-b) sin J (a — b],

cosb 4- cosa = acosi (a+ 6) cosj (a — b).

cost — cosa = a sin^ (a-4- ô) sini (a — ft).

sina 4- Sin b __ tang \ {a 4- b)

sina — sin6 "" tang|(a — b)'

cos&4-cosa cotj-(a4-fr)

~~ tangua — £)'

cosfc — cosa . .. . ..

-r-r= tangi(«i:d).

sinb ° *

cos fc — cosa' sînadbsinô

cos#4-cosa sina:

tanga zbtangft tang(a±^) = —-———,

sin45°=cos45°= v/ïtang45°=cot45°= i.

sin3o° = cos6o°=±.

cos 3o° = sin 6o° = ■? t/3 • tang3o°=cot6o°= v/ïsin 1 8° = cos 72°= | (y/5 — i) .

cos 1 8° = sin 72°= | V i o 4- 2^5 .

sin 36° = cos 54°= } V^io— 2y/5.

<sos36°=r sin 5^°= \{\/l 4- 1).

sm 2 a = asinacosa.

cos2a = 2 cos 2 a — i

= cos 2 a — sin 2 a

= i — 2 sin 2 a.

. atanea

tang2a = *

i — tang 2 a

cot2a =

cota — tanga cot 2 a — i

2 cota = £cotd— J tanga.

cos a ± sin a = y^2 sin (45° ± a)

= v/2 cos (45° ={=«)• cosa-|-sina i4-tanga

i =f tanga tang b cota cote q= i

COt£ :

«*(«*») = ■ eot6±cota -

. . , sin(a±fc) tang«=btangft = - 55i ^^ F -

., 4 sin(azbft) cotfc d= cota = — r-J — r-~sina sin b

* , A * cos(aqzft)

cota ± tango = — ~ r- *

* sina cos 6

cosa =fc sin 6 = 2sin [45°— J (a q= *)] cos[45°— i (a=fc £)]

sin 2 a— sin 2 £ = cos 2 £ — cos* a = sin (a -4-6) sin (a — b).

cos s a — sin 2 6 = cos 2 ô — sin 2 a = cos(a +b) cos(a — b).

cosa — sina

-tanga

1 4- sin 2a i — sin2a = tang(45°+a) = cot(45°— a).

i 4- cosa i —cosa i 4- sina î — sina

tangua = cosa =

sina =

sin3a = cos3a =

= 2C0S 2 ja.

= 2sin 2 |a = sinv.a.

= 2sin 2 (45°4-ia) = 2C0S 2 (45°- **),

= 2Sin 2 (45°— ia) = 2COS 2 (45°4-{a)

= cosv.a.

sina i — cosa

tang3a =

COtia i + cosa sma

i — tang 2 j a

i + tang'jV

i — tang 2 (45° — \a)

^tang 2 ^ -^)* 3 sina — 4sin'a = sina ( 4cos 2 a — i ).

4cos*a — 3cosa = cosa (i — 4sin 2 a).

3 tanga — tang 3 a

cot3a =

sin(/*4cos(/i-h

i — 3 tang 2 a cota — 3 tanga

3 — tang 2 a i)a = 2 cos a. sin «a — sin(/ii) a = 2COsa.cos/sa — cos(// -

ENTRE LES FONCTIONS dRCULAIRES.