Sinus et cosinus Flashcards

1
Q

mesure principale

A

On appelle mesure principale d’un angle α, la mesure x qui se trouve dans l’intervalle ]−π;π]

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2
Q

Equations trigonométriques

A

•L’équation cosx = cosa admet les solutions suivantes sur R:

x=a+k2π ou x=−a+k2π avec k∈Z

•L’équation sinx=sina admet les solutions suivantes sur R:

x=a+k2π ou x=π−a+k2π avec k∈Z

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3
Q

sinx > 0

A

x∈ ]0 ;π[

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4
Q

cosx > 0

A

x∈ ]−π2;π2[

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5
Q

définition

A

À tout réel x, on associe un point unique M du cercle unité ou cercle trigonométrique de centre O, dont les coordonnées sont :

M(cosx; sinx)

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6
Q

parité

A
  • La fonction sinus est impaire : ∀x∈R sin(−x) =−sinx

* La fonction cosinus est paire : ∀x∈R cos(−x) =cosx

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7
Q

périodicité

A

f est periodique de periode T si sur un itervalle I:
x+ T appartient à I
f(x+T)=f(x)

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8
Q

sin(π/2−x)

A

sin(π/2−x)=cosx

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9
Q

cos(π/2−x)

A

cos(π/2−x)=sinx

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10
Q

sin′x

A

cosx

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11
Q

cos’x

A

-sinx

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12
Q

x=0

A

cos0=1 sin0=0

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13
Q

x=π/6

A

cosπ/6=racine de 3/2

sinπ/6= 1/2

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14
Q

x=π/4

A

cos et sin: racine de 2/2

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15
Q

x=π/3

A

cosπ/3=1/2

sinπ/3= racine de 3/2

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16
Q

x=π/2

A

cos1/2=0

sin1/2=1

17
Q

x=π

A

cosπ=-1

sinπ=0

18
Q

somme des carrés d’un cos et d’un sin

A

cosx²+sinx²=1

19
Q

sin(π/2+x)

20
Q

cos(π/2+x)

21
Q

cos(a-b)

A

cosa cosb + sina sinb

22
Q

cos(a+b)

A

cosa cosb - sina sinb

23
Q

sin (a-b)

A

cosa sinb - cosb sina

24
Q

sin (a+b)

A

cosa sinb + cosb sina

25
cos2x
= cos²x-sin²x = 2cos²x-1 = 1-2sin²x
26
sin2x
2sinxcosx
27
1 + tan²(x)
1 + tan²(x) = 1/cos2(x)
28
tan(a + b)
tan(a + b) = tan(a) + tan(b)/1 − tan(a) tan(b)
29
tan(a − b)
tan(a − b) = tan(a) − tan(b)/1 + tan(a) tan(b)
30
tan(2a)
tan(2a) = 2 tan(a)/1 − tan²(a)
31
cos²a
cos²(a) = 1 + cos(2a)/2
32
sin²(a)
sin²(a) = 1 − cos(2a)2
33
cos(a) cos(b)
cos(a) cos(b) = 1/2(cos(a − b) + cos(a + b))
34
sin(a) sin(b)
sin(a) sin(b) = 1/2(cos(a − b) − cos(a + b))
35
sin(a) cos(b)
sin(a) cos(b) = 1/2(sin(a − b) + sin(a + b))
36
on pose t = tan (x/2) tan(x) sin(x) cos(x)
tan(x) = 2t/1 − t² sin(x) = 2t/1 + t² cos(x) = 1 − t²/1 + t²