Trigonométrie Flashcards
1
Q
Formules d’addition cos, sin, tan
A
cos(a-b)=cosacosb+sinasinb
cos(a+b)=cosacosb-sinasinb
sin(a-b)=sinacosb-sinbcosa
sin(a+b)=sinacosb+sinbcosa
tan(a+b)=(tan(a)+tan(b))/(1-tan(a)tan(b))
tan(a-b)=(tan(a)-tan(b))/(1+tan(a)tan(b))
2
Q
cos(2a)
A
=cos²a-sin²a=2cos²a-1=1-2sin²a
3
Q
sin(2a)
A
=2cosasina
4
Q
tan(2a)
A
2tana/(1-tan²a)
5
Q
Relation entre cos et sin
A
cos(pi/2 - x)=sinx
sin(pi/2 - x)=cosx
cos^2+sin^2=1
6
Q
tan’x
A
=1/cos²x
=1+tan²x
7
Q
arcsin’x
A
=1/sqrt(1-x²)
8
Q
arccos’x
A
= -1/sqrt(1-x²)
9
Q
arccosx+arcsinx
A
=pi/2
10
Q
arctan’x
A
1/(1+x²)
11
Q
limites arctan
A
-pi/2 et pi/2
12
Q
arctanx+arctan(1/x)
A
= pi/2 si x est positif non nul
= -pi/2 si x est négatif non nul
13
Q
ch(x)
A
=(e^x+e^-x)/2
14
Q
sh(x)
A
=(e^x-e^-x)/2
15
Q
ch’
A
sh
16
Q
sh’
A
ch
17
Q
th’
A
1/ch²
=1-th²
18
Q
ch²-sh²
A
1
19
Q
Cotan
A
1/tan
=cos/sin
20
Q
Cotan’
A
-1/sin^2
21
Q
Primitive tan x
A
-ln(cosx)
22
Q
Primitive cotan
A
ln(sinx)
