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Sin и Cos суммы и разности двух аргументов.

sin cos

sin(((()=sin ((cos((sin((cos(

cos(((()=cos((cos((+sin ( (sin(

tg ( ( tg (

tg (((() = 1 ( tg ( ( tg (

tg (((() = ctg ( ( ctg ((+ 1 =

ctg ( ( ctg (

= 1 ( tg ( ( tg (

tg ( ( tg (



sin2x=2sinx cosx

cos 2x = cos2x - sin2x=

= 2cos2x-1=1-2sin2x

tg2x= 2 tgx

1 - tg2x

sin 3x =3sin x - 4 sin3x

cos 3x= 4 cos3 x - 3 cos

: , - x:

sin x= ( 1-cosx

2

cos x= ( 1+cosx

2

NB! ( 0
, (tg, ctg)

tg x=sinx =1-cosx =( 1-cosx

1+cosx sinx 1+cosx

tg x=sinx =1+cosx =(1+cosx

1-cosx sinx 1-cosx

:

sin2 x = 1 cos 2x

2

cos2 x = 1+ cos 2x

2

sin3 x = 3 sin x sin 3x

4

cos3 x = 3 cos x + cos 3x

4

:

2 sinx siny = cos(x-y) cos(x+y)

2 cosx cosy = cos(x-y)+cos(x+y)

2 sinx cosy = sin(x-y) + sin (x+y)

tgx tgy = tgx + tgy

ctgx + ctgy

ctgx ctgy = ctgx + ctgy

tgx + tgy

tgx ctgy = tgx + ctgy

ctgx + tgy

NB! ( 0
, (tg, ctg)

sinx ( siny= 2sin x(y cos x(+ y

2 2

cosx + cosy =2cos x+y cos x-y

2 2

cosx - cosy = - 2sin x+y sin x-y

2 2

tgx ( tgy= sin(x(y)

cosx cosy

tgx + tgy= cos(x-y)

cosx siny

ctgx - ctgy= cos(x+y)

sinx cosy

ctgx(ctgy= sin(y(x)

sinx siny

sin x = 1 x= ( +2(n, n( Z

sin x = 0 x= (n, n( Z

sin x = -1 x= - ( +2(n, n( Z

sin x = a , (a(( 1

x = (-1)karcsin a + (k, k( Z

tg x= a x= arctg a +(n, n( Z



cos=1 x=2(n, n( Z

cosx=0 x= ( +(n, n( Z

cosx=-1 x=( +2(n, n( Z

cosx = a , (a(( 1

x=arccos a + 2(n, n( Z

ctg x = a x=arcctg a + (n, n( Z

:

\f(() sin cos tg ctg

I + + + +

II + ( ( (

III ( ( + +

IY ( + ( +





( (/2 ( ( ( ( ( 3/2 ( ( ( 2( (

sin ( sin ( cos ( (+sin ( cos ( sin (

cos cos ( (+sin ( cos ( ( sin ( cos (

tg tg ( (+ ctg ( ( tg ( (+ ctg ( tg (

ctg ctg ( (+ tg ( ( ctg ( (+ tg ( ctg (





:

\

f\ 0 30(=(

6 45(=(

4 60(=(

3 90(=(

2

180(=( 270(=3(

2

sin 0 (2 / 2 (3 / 2 1 0 1

cos 1 (3 / 2 (2 / 2 0 (1 0

tg 0 (3 / 3 1 (3 ( 0 (

ctg (3 1 (3 / 3 0 ( 0




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