Formulaire de trigonométrie - Pagesperso

Formulaire de trigonométrie
sin2x + cos2x = 1
tanx =
1 + tan2x =
1
cos2x
π
6
1
2
π
4
π
3
π
2
angle
–x
π–x
π+x
π
–x
2
π
+x
2
2
2
3
2
1
sinus
– sinx
sinx
– sinx
cosx
cosx
1
3
2
2
2
1
2
0
cosinus
cosx
– cosx
– cosx
sinx
– sinx
0
3
3
1
non
définie
tangente
– tanx
– tanx
tanx
1
tanx
–
angle
0
sinus
0
cosinus
tangente
sinx = sina
cosx = cosa
tanx = tana
3
⇔
| x = a + 2kπ
ou
| x = π – a + 2kπ
⇔
| x = a + 2kπ
ou
| x = – a + 2kπ
⇔
 x = a + kπ
π

 x ≠ 2 + kπ
(k ∈ ZZ)
(k ∈ ZZ)
(k ∈ ZZ)
tana + tanb
tan(a + b) =
1 – tana.tanb
tana – tanb
tan(a – b) =
1 + tana.tanb
cos(a + b) = cosa.cosb – sina.sinb
cos(a – b) = cosa.cosb + sina.sinb
sin(a + b) = sina.cosb + sinb.cosa
sin(a – b) = sina.cosb – sinb.cosa
1 + cos(2x)
2
x
Si t = tan 
2
 
alors
cos(2x) = cos2x – sin2x
sin(2x) = 2sinx.cosx
2tanx
tan(2x) =
1 – tan2x
p + q
p – q
sinp + sinq = 2sin 
.cos 2 
 2 


p – q
p + q
sinp – sinq = 2sin 
.cos 2 
2




p + q
p – q


cosp + cosq = 2cos 
.cos 2 
 2 


p + q p – q

cosp – cosq = –2sin 
.sin

 2   2 
1
sina.sinb = [cos(a – b) – cos(a + b)]
2
1
cosa.cosb = [cos(a + b) + cos(a – b)]
2
1
sina.cosb = [sin(a + b) + sin(a – b)]
2
cos2x =
sinx
cosx
sin2x =
2t
sinx =
1 + t2
1 – cos(2x)
2
1 – t2
cosx =
1 + t2
tanx =
2t
1 – t2
1
tanx