-

-

cos2a=cos2 a-sin2 a=2cos2 a-1=1-2sin2 a

a×sina+b×cosa= x=arctg(b/a)

sin18o = sin36o =


a/sina=2R a2 =b2 +c2 -2bc×cosa

S3 =ab×sina/2=pr=aha /2=

R=abc/4S r=2S/(a+b+c)

(c+d)c=a2

(c+d)d=b2

h2 =cd

(f+h)h=(g+i)i=e2

ad=cb

Ðaob=

=Èab

Ðmpk=

..==..

=½Èmk=½Ðmok

C=2p S=pR2 l=Ra( .)= pRao /180o

ÐAn =180o (n-2)/n S=arn/2=R2 nsin(3600 /n)/2

.: ÐA+ÐC=ÐB+ÐD=3600

ACCD+BCAD=BDAC

.: a+c=b+d S=pr

: S=½d1 d2 sinb=a[..]=½ h(a+c)

c . . =2ab(a+b) c .. =(a-b)/2

.: c..= . , h2 =ab

. .: h=

: S=ah=½d1 d2 =a2 sin(a) r=h/2

: S=ah=absina =½d1 d2 sin(a)

d1 2 +d2 2 =a(a2 +b2 )

. .: [l d.. ]=

: [l d d ]=a/Ö6

: R r


S S V
. PoH S+2So SoH
. Pol S+2So SoH
ϳ nS S+So SoH/3
½Poa S+So SoH/3
nS S+So1 + So2 H(So1 +S o2 +ÖSo1 So2 )/3
. ½(Po1 + Po2 ) a S+So1 + So2 H(So1 +S o2 +ÖSo1 So2 )/3
2pRH 2pr(h+r) pR2 H
pRL rp(L+r) pR2 H/3
. pL(R+r) S+ So1 +So2 ph(R2 +r2 + Rr)/3
L=2pR 4pR2 4pR3 /3

x2 +px+q=0 x1 x2 =q x1 +x2 = - b

f(x)=f(x0 )+f / (x0 )(x-x0 ) -

: xn nxn -1 sinx cosx cosx -sinx

tgx 1/cos2 x ctgx -1/sin2 x

a x a x lna lnx 1/x loga kx k / x loga kx

: cosx sinx sinx -cosx

xn xn +1 /(n+1) a x a x /lna 1/x lnx

..: an =a1 +d(n-1) Sn =(a+an )n/2

...: bn =b1 qn-1 Sn =b1 (1-qn )/(1-q)

: S=b1 /(1-q)

: ab= x1 x2 +y1 y2 +z1 z2

|a|=Öx2 +y2 +z2 a+b=c(xa +xb ;ya +yb )

cos(a^b )=(ab)/|a||b| ab=xa xb +ya yb

a | bab=0 a||bxa /xb =ya /yb

|la|=|l||a|

loga xy =loga x+loga y loga x/y =loga x -loga y

loga x =logb x /logb a