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