Trigonometrie clasa a IX-a

Semnele functiilor trigonometrice şi monotonia pe cadrane:
x I II III IV
sinx + + − −
cosx + − − +
tgx + − + −
ctgx + − + −
Identităţi fundamentale
⎛π
⎞ ⎛π
⎞
sin ⎜ -x ⎟=cosx cos⎜ -x ⎟=sinx
⎝2 ⎠ ⎝2
⎠
⎛π
⎞ ⎛π
⎞
tg⎜ -x ⎟=ctgx ctg ⎜ -x ⎟=tgx
⎝2 ⎠ ⎝2
⎠
2 2
sin x+cos x=1
tgx ⋅ctgx=1
( ) ( )
( ) ( )
( ) ( )
sin arcsinx =x arcsin sinx =x
cos arccosx =x arccos cosx =x
tg arctgx =x arctg tgx =x
π
π
arcsinx+arccosx= arctgx+arcctgx=
2 2
Reducerea la primul cadran
II →I III →I IV →I
( π ) ( π) ( π )
( π ) ( π) ( π )
( π ), ( π) , ( 2π
)
( π ), ( π) , ( 2π
)
sin x= sin − x , sin x=−sin x− , sin x=−sin 2 −x
cos x=−cos − x , cos x=−cos x− , cos x=
cos 2 -x
tgx =−tg − x tgx = tg x − tgx =−tg −x
ctgx =−ctg − x ctgx = ctg x − ctgx =−ctg −x
Formule paritate
sin − x =−sin
x
cos
( )
( x)
( )
( )
T R A I A N
− = cos x
tg − x =−tgx
ctg − x =−ctgx
Formule periodicitate
arcsin
arccos
x I II III IV
sinx
cosx
tgx
ctgx
( x)
( x)
( )
( )
− =−arcsinx
− = π −arccos
x
arctg − x =−arctgx
arcctg − x = π −arcctgx
2