FOI

IMULES TRIGONOMÉTRIQUES.

sin' a ■+- cos' a = i .

sina

col a =

cosa

C0Béca= -T-sina

sina ** cosa

séca =

cosa

séc*a = I H-.tang«a, coséc'a = i -h cot*a,

sina= '^ — * langa = . ,- /

dbv/i-^Ung«a it:/i-sin«a

sin cos

lang* a =

sin(— ^) =-— sinar, 8in(ir — .r)= sin.r, Cos(— x) =- COSX, COS(« - .ir) = — COS.r,

in il ^a\ ^. cosar, sin (ic h- .r)= - sina-, ,g Z'!! H- .r\ = — sin or, COS(ir -i- .r) = — cosj;

sin (a ± P)= sin a cos P ± sin? cosa, cos(ad= P)= cosacosprp sina sin p,

. / -*-ftN tangaihtangP .

lang(a±P)= ,^ ^„g^tang|i'

sina-^sinp= 2^in |(a -f- p)C08i(a -- ?), sin a — sin p = acos i (a h- p) sin i (a — ?), cosa -+- cosp = 2C0S ^ (a -i- p) cos } (a — ?), cosa — cos? = — 2sin H« -^ P) sin i (« — ?);

FORMULES TRIGONOMÉTRIQUES. 5oi

tanga ± tangp = — ^^ Ç ,

1 i .û 8in(a±Û) cotait cotfl=-T-^ — :-^:

'^ sinasinp

sin (a H- P) sin (a ~ 3) = gin* a — sin« p, cos(a-*- p)cos(a — P)= cos*a — sin* p ;

sina + sinp tang j ( « -4- P ) sina — sinp ~ langea — P)'

i-H sina = 2C0S*

sinaa = asinacosa, C0S2a= cos'a — sin*a, 2 tanga

ii-iy

tanga a =

I — tang* a

! * , — cosa sinf a = zt4/ ,

^, X 1 4- cosa

tang}a =

sina I — cosa

i + cosa sma

sina = asin , a cos { a.

cosa = cos» i a — - sin* { a = i — 2 sin* | a,

atangla

tanga = ^^ , >

^ I — tang«^«

cot» i a — - 1

cota= î— r ;

sina sin P = f cos(a— P)— |cos(a -4- p), COSaCOSp =-5C0S(a — P)-h f C08(a-4- p ;

a -+- p -H Y = iî,

sina -4- sin p -H sin Y = 4 cos I a cos J p cos | y.

5o2 FORMULES USUELLES.

Résolution de l'équation du second degré . x^-h px-h 9 = 0,

4 ' / ^ ' ^ sin<p'

\ v/^langfo,

/ v^^cot ï?î

^ a lang<p

i - \^—^ lang I «p,

^± £tangçv/-i.

Résolution de l'équation du troisième degré.

4 /?» -h 97 9* < o racines réelles et inégales,

^ / — p 1 .rj = a 4/ -ô^ ces J <p,

4 /?»-4- 27ç*> o; une racine réelle et deux racines imaginaires ;

/) < o, sina»}^ = —

FORML'LKS TRIGONOXËTRIQL'ES. 5o3

Jv/f)'

lang?p = ? tang4^, •^1 = — 2 4/4 colacp.

Formules relatives aux triangles, / A -i- B H- C = T,

( sinA ~" sinB ~~ sinC^

S = \ ab sinC.

i a -*- b -h c = ipj ( S= \//;(/? — aj(/> — />)(/? — 6-); R = rayon du cercle circonscrit,

Formule fondamentale de la Trigonométrie sphérique, cosû = cos/^cosc-4- sin/-»sinccosA.

Différentielles usuelles,

d.a.v = ad.c^

d.x"^ = mx"«-* dx^

d,xf =xdx-\-xdf^

, X Y dx — X dr d— = ' ^ ,

,1 dx ^

5o4 FORMULES USUELLES.

d\oe'x= -^> rflogx = -^log<?,

d,a* =a' log'a dj: = a^ •=-— dx, log<?

i/sinx = cosx cLr, d cosx = — sin j: cLr,

tf Ungx= — —-,

atoix = r-r- ;

, (ix

^arcsm^ =

aarccosj: = -y

a arc langx = ,

aarccolx =

i-f-x«* rf log sin j: = col x dx, dlog cosr = — iang.r rfx,

d\osidJigix= ~. — ;

Intégrales usuelles.

jc« rfx = h const..

J log' a log a

I e^ dx = e^,

I e^xdx =xe*— e*:

FORMULES TRIGONOMÉTRIQUES. 5o5

r dx ^ r — dx

/-> ^^— = log'(.r -h /a + x«),

/dx . r—dx

, =arc8inx ou /-;=== arc cosj:,

/dx J i 'fLiîlf

rt* — X* ~ aa ^ a — x'

/ dx^i-hx^ = i[log'(a:-f- /i 4-x*)-+-a:v/i -f-x*],

/ dx^i—x^ = j(arcsinj:-f-x /i — or*),

/ — 7== = arc 8in - > j x/x»— I ^

/ \ogxdx =x\ogx — xlog^;

/ sinx dx = — cosx -h const., / cosxdx = sinx, / tangx dx — — log' cosx, / coixdx = log'sinx, / sinxcosxdx = |8in*x;

/^ =-log'tangi(^-x).

/dx sinxcosx ~~ ® ^^'

r dx