Formule Flashcards
(35 cards)
1
Q
tan(2a)
A
2 tan a/1 − tan2 a
2
Q
cos a cos b
A
1/2(cos(a − b) + cos(a + b))
3
Q
sin a sin b
A
1/2(cos(a − b) − cos(a + b))
4
Q
sin a cos b
A
1/2(sin(a + b) + sin(a − b))
5
Q
cos p + cos q
A
2 cos(p + q/2)cos(p − q/2)
6
Q
cos p - cos q
A
-2 sin(p + q/2)sin(p − q/2)
7
Q
sin p + sin q
A
2 sin(p + q/2)cos(p − q/2)
8
Q
sin p - sin q
A
2 cos(p + q/2)sin(p − q/2)
9
Q
[arcsin(u)]′
A
u′/√(1 − u^2)
10
Q
arccos′(u)
A
-u’/√(1 − u^2)
11
Q
[arctan(u)]′
A
u’/(1 + u^2)
12
Q
sin (arccos x)
A
√(1 − x^2)
13
Q
cos(arcsin(x))
A
√(1 − x^2)
14
Q
cos(arctan(x))
A
1/√(1 + x^2)
15
Q
sin(arctan(x))
A
x/√(1 + x^2)
16
Q
arccos (x) + arcsin (x)
A
π/2
17
Q
arccos (x) + arccos (−x)
A
π
18
Q
arctan x + arctan1/x
A
signe (x).π/2
19
Q
d/dx (a^x)
A
(lna)a^x
20
Q
(cos θ + isin θ)^n
A
cos nθ + isin nθ
21
Q
Re z/|z|
A
cosx
22
Q
Imz/|z|
A
sinx
23
Q
Imz/Rez
A
tanx
24
Q
z=a+ib, e^z?
A
e^a(cos b + isin b)
25
Re(exp(a+ib))
exp(a)cosb
26
Im(exp(a+ib))
exp(a)sinb
27
1 + exp(iθ)
2 cos (θ/2)exp(iθ/2)
28
1 - exp(iθ)
-2 isin (θ/2)exp(iθ/2)
29
1 + j + j^2
0
30
n
∑K^2
k=0
n (n + 1) (2n + 1)/6
31
n
∑K^3
k=0
(n (n + 1)/2)^2
32
b^n − a^n
n-1
(b-a)∑a^k.b^n-1-k
k=0
33
card (A\B)
card (A) − card (A ∩ B)
34
(fg)^(n)
n
∑(n,k)f^(k).g^(n-k)
k=0
35
∫u′(x)v(x)dx
u(x)v(x) −∫u(x)v′(x)dx
