Chapter 1-Mathematica.nb - IMJ-PRG

N[Pi, 10]
⋯ nombre pi
3.141592654
N[Pi, 1000]
⋯ nombre pi
3.1415926535897932384626433832795028841971693993751058209749445923078164062862!
08998628034825342117067982148086513282306647093844609550582231725359408128481!
11745028410270193852110555964462294895493038196442881097566593344612847564823!
37867831652712019091456485669234603486104543266482133936072602491412737245870!
06606315588174881520920962829254091715364367892590360011330530548820466521384!
14695194151160943305727036575959195309218611738193261179310511854807446237996!
27495673518857527248912279381830119491298336733624406566430860213949463952247!
37190702179860943702770539217176293176752384674818467669405132000568127145263!
56082778577134275778960917363717872146844090122495343014654958537105079227968!
92589235420199561121290219608640344181598136297747713099605187072113499999983!
72978049951059731732816096318595024459455346908302642522308253344685035261931!
18817101000313783875288658753320838142061717766914730359825349042875546873115!
9562863882353787593751957781857780532171226806613001927876611195909216420199
TrigExpand[Sin[a + b]]
élargis fonctio⋯ sinus
Cos[b] Sin[a] + Cos[a] Sin[b]
TrigExpand[Cos[a + b + c]]
élargis fonctio⋯ cosinus
Cos[a] Cos[b] Cos[c] -− Cos[c] Sin[a] Sin[b] -−
Cos[b] Sin[a] Sin[c] -− Cos[a] Sin[b] Sin[c]
TrigFactor[Sin[p] -− Sin[q]]
factorise expr⋯ sinus
2 Cos
sinus
p q
p q
+  Sin -− 
2 2
2 2
TrigFactor[Cos[p] -− Cos[q]]
factorise expr⋯ cosinus
-− 2 Sin
cosinus
p q
p q
-−  Sin + 
2 2
2 2
N[Log[2], 100]
⋯ logarithme
0.6931471805599453094172321214581765680755001343602552541206800094933936219696!
947156058633269964186875
Arg[I]
ar⋯ unité imaginaire
π
2
2
Chapter 1-Mathematica.nb
Arg[1 + I]
argume⋯ unité imaginaire
π
4
Integrate[(Sin[x]) ^ 3, x]
intègre
-−
sinus
3 Cos[x]
1
+
Cos[3 x]
4
12
G[n_, x_] := Integrate[(Cos[x]) ^ n, x]
intègre
cosinus
G[10, x]
63 x 105
15
15 Sin[6 x] 5 Sin[8 x] Sin[10 x]
+
Sin[2 x] +
Sin[4 x] +
+
+
256
512
256
1024
2048
5120
T[n_, x_] := D[G[n, x], x]
dérivée d
T[2, x]
1 1
+ Cos[2 x]
2 2
TrigReduce
1
+
1
Cos[2 x]
2 2 cosinus
réduis fonctions trigo⋯
1
(1 + Cos[2 x])
2
TrigReduce[Expand[{T[1, x], T[2, x], T[3, x], T[4, x], T[5, x], T[6, x], T[7, x]}]]
réduis fonction⋯ développe
1
1
1
(1 + Cos[2 x]),
(3 Cos[x] + Cos[3 x]),
(3 + 4 Cos[2 x] + Cos[4 x]),
2
4
8
1
1
(10 Cos[x] + 5 Cos[3 x] + Cos[5 x]),
(10 + 15 Cos[2 x] + 6 Cos[4 x] + Cos[6 x]),
16
32
1
(35 Cos[x] + 21 Cos[3 x] + 7 Cos[5 x] + Cos[7 x])
64
Cos[x],
TrigExpand[Cos[10 x]]
élargis fonctio⋯ cosinus
Cos[x]10 -− 45 Cos[x]8 Sin[x]2 + 210 Cos[x]6 Sin[x]4 -−
210 Cos[x]4 Sin[x]6 + 45 Cos[x]2 Sin[x]8 -− Sin[x]10
TrigReduceCos[x]10 -− 45 Cos[x]8 Sin[x]2 +
réduis fonctions trigonométriques
210 Cos[x]6 Sin[x]4 -− 210 Cos[x]4 Sin[x]6 + 45 Cos[x]2 Sin[x]8 -− Sin[x]10 
Cos[10 x]
FunctionExpand[Cos[21 ArcCos[x]]] /∕/∕ Expand /∕/∕ TraditionalForm
développe fonctionne⋯ cosinus
21
19
arc cosinus
développe
17
15
apparence traditionnelle
1 048 576 x -− 5 505 024 x + 12 386 304 x -− 15 597 568 x +
12 042 240 x13 -− 5 870 592 x11 + 1 793 792 x9 -− 329 472 x7 + 33 264 x5 -− 1540 x3 + 21 x