Formule Matematica Bacalaureat BAC - Trigonometrie
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Transcript of Formule Matematica Bacalaureat BAC - Trigonometrie
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7/28/2019 Formule Matematica Bacalaureat BAC - Trigonometrie
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Formule de trigonometrie
[ ]
[ ]
2 2
2 2
2 2
sin cos 1
sin : 1,1
sin( ) sin
cos : 1,1
cos( ) cos
sin cos2
cos sin2
( )
( )
sin 2 2sin cos sin 2sin cos2 2
cos2 cos sin
1 cos2cos2 2cos 1 cos
2
cos2
x x
x x
x x
x x
x x
tg x tgx
ctg x ctgx
x xx x x x
x x x
xx x x
+ =
=
=
=
=
=
=
= =
=
+= =
( )
( )
2 2
2
2
1 cos21 2sin sin
2
sin 3 sin (3 4sin )
cos3 cos (4cos 3)
sin( ) sin cos sin cos
sin( ) sin cos sin cos
cos( ) cos cos sin sin
cos( ) cos cos sin sin
1
xx x x
x x x
x x x
a b a b b a
a b a b b a
a b a b a b
a b a b a b
tga tgbtg a btga tgb
tgatg a b
= =
=
=
+ = +
=
+ =
= +
++ =
=1
sin
cos
cos
sin
tgb
tga tgb
xtgx
x
xctgx
x
+
=
=
formula fundamental a trigonometriei
funcia sin este impar
funcia cos este par
Formule pentru transformarea sumelor in pr
sin sin 2sin cos2 2
sin sin 2sin cos
2 2
cos cos 2cos cos2 2
cos cos 2sin sin2 2
p q p qp q
p q p qp q
p q p qp q
p q p qp q
+ + =
+ =
+ + =
+ =
Formule pentru transformarea produselor in
sin( ) sin( )sin cos
2cos( ) cos( )cos cos
2
cos( ) cos( )sin sin
2
x y x yx y
x y xx y
y
x y xx y
+ + =
+ + =
+ =
y
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7/28/2019 Formule Matematica Bacalaureat BAC - Trigonometrie
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3
2
3
2
33
1 3
33
3 1
tgx tg xtg x
tg x
ctg x ctgxctg x
ctg x
=
=
2
2
2
2
2
2sin
1
1cos
1
2
1
1
2
tx
t
tx
t
ttgx
t
tctgx
t
= +
=
+ = =
unde2
xt tg=
2
2
2
2
2
2sin2
1
1cos21
22
1
12
2
tgxx
tg x
tg xxtg x
tgxtg x
tg x
tg xctg x
tgx
= +
= + =
=
Ecuaii trigonometrice fundamentale
1)Ecuaia sinx a= are soluii daci numai dac [ ]1,1a .In acest caz soluiile sunt
{ }( 1) arcsin /kx a k + k .2)Ecuaia cosx b= are soluii daci numai dac [ ]1,1b . In acest caz soluiile sunt
{ }arccos 2 /x b k k + .
3)Ecuaia are soluii .tgx c= c
Soluiile sunt { }arc /x tgc k k + .
4)Ecuaia are soluii .ctgx d = d
Soluiile sunt { }arc /x ctgd k k + .
[ ]2
2
sin(arcsin )
sin(arccos ) 11.1
cos(arccos )
cos(arcsin ) 1
x x
x xx
x x
x x
=
=
= =
