Fonctions Classiques Flashcards
1
Q
cos’(x)
A
-sin(x)
2
Q
arcos’(x)
A
-1/(1-x2)1/2
3
Q
sin’(x)
A
cos(x)
4
Q
arcsin’(x)
A
1/(1-x2)1/2
5
Q
tan’(x)
A
1/cos2(x) = 1 + tan2(x)
6
Q
arctan’(x)
A
1/(1+x2)
7
Q
ch’(x)
A
sh(x)
8
Q
argch(x)
A
ln(x + (x2 -1)1/2))
9
Q
argch’(x)
A
1/(x2-1)1/2
10
Q
sh’(x)
A
ch(x)
11
Q
argsh(x)
A
ln(x+(x2+1)1/2)
12
Q
argsh’(x)
A
1/(1+x2)1/2
13
Q
th’(x)
A
1/ch2(x)
14
Q
argth(x)
A
1/2 x ln((1+x)/(1-x))
15
Q
argth’(x)
A
1/(1-x2)
16
Q
ch2+sh2
A
1
17
Q
Sh(2x)
A
2sh(x)ch(x)
18
Q
ch(2x)
A
ch2+sh2
19
Q
arccos(x) + arcsin(x)
A
π/2
20
Q
arctan(x) + arctan(1/x)
A
+/- π/2 selon le signe de x
21
Q
cos2(x)
A
(1+cos(2x))/2
22
Q
sin2(x)
A
(1-cos(2x))/2
23
Q
t = tan(x/2)
A
cos(x) = (1-t2)/(1+t2)
sin(x) = 2t/(1+t2)
tan(x) = 2t/(1-t2)
24
Q
cos(a+b)
A
cos(a)cos(b)-sin(a)sin(b)
25
cos(a-b)
cos(a)cos(b) + sin(a)sin(b)
26
2cos(a)cos(b)
cos(a+b) + cos (a-b)
27
2sin(a)sin(b)
cos(a-b) - cos(a+b)
28
sin(a+b)
sin(a)cos(b) + sin(b)cos(a)
29
2sin(b)cos(a)
sin(a+b) - sin(a-b)
30
sin(p) + sin(q)
2sin((p+q)/2)cos((p-q)/2)
31
cos(p) + cos(q)
2cos((p+q)/2)cos((p-q)/2)
32
tan(a+b)
( tan(a) +tan(b) ) / (1 - tan(a)tan(b) )
