Trigonometrie Flashcards

1
Q

1 + tan^2(x)

A

1/Cos^2(x)

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2
Q

1 + cotan^2(x)=

A

1/sin^2(x)

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3
Q

Cos (a+b) =

A

Cos a Cos b - Sin a Sin b

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4
Q

Cos (a -b) =

A

Cos a Cos b + Sin a Sin b

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5
Q

Sin (a+b)

A

sinacosb+sinbcosa

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6
Q

Sin (a-b)=

A

sinacosb - sinbcosa

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7
Q

Cos (2a) =

A

= cos2 a − sin2 a

= 2 cos2 a − 1
= 1 − 2 sin2 a

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8
Q

Sin (2a) =

A

= 2 Sin a Cos a

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9
Q

Tan (2a)=

A

= 2 tan a / 1−tan2 a

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10
Q

Tan (a+b) =

A

= tan (a) +Tan (b) / 1−Tan a Tan b

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11
Q

Tan (a -b)=

A

= tana−tanb / 1+tanatanb

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12
Q

Cos a Cos b =

A

=(1/2)(cos(a−b)+cos(a+b))

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13
Q

Sin a Sin b =

A

= (1/2) (cos(a−b)−cos(a+b))

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14
Q

Sin a Cos b =

A

= (1/2)(sin(a+b)+sin(a−b))

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15
Q

cos^2 (a) =

A

1+cos(2a)
___________
2

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16
Q

Sin ^2 (a) =

A

1-cos(2a)
___________
2

17
Q

Cos p + Cos q =

A

2 Cos ((p+q)/2) Cos ((p-q)/2)

18
Q

Cos p - Cos q =

A

-2 Sin ((p+q)/2) sin ((p-q)/2)

19
Q

Sin p + Sin q =

A

2 Sin ((p+q)/2) Cos ((p-q)/2)

20
Q

Sin p - Sin q =

A

2 Sin ((p-q)/2) Cos ((p+q)/2)

21
Q

1 + Cos x =

A

2 Cos ^2 (x/2)

22
Q

1 - Cos (x) =

A

2 Sin ^2 (x/2)

23
Q

Cos (3x) =

A

4 Cos^3(x) -3 Cos (x)

24
Q

Sin (3x) =

A

= 3 Sin (x) - 4 Sin ^3 (x)

25
Q

Cos^2(x) + Sin^2(x) =

A

1

26
Q

Pour tout x de R,

e(ix) =

A

Cos (x) + i Sin (x)

27
Q

e (2ipi/3) =

A

J = -1/2 + i racine3/2

28
Q

Racine 2 e (ipi/4) =

A

1 + i

29
Q

Pour tout x de -1;1

Cos(arcsinx) =

A

Racine de 1 moins x^2

30
Q

Pour tt x de -1;1

Sin(arccos x) =

A

Racine de 1 - x^2

31
Q

Pour tt x de -1;1

Arccos x + arcsin x =

A

Pi/2

32
Q

Pour tt x >0

Arctan x + arctan 1/x =

A

Pi/2

33
Q

Pour tt x

A

-Pi/2

34
Q

Dérivée n-aime du cosinus

A

Cos (x+npi/2)

35
Q

Dérivée n-aime du sinus

A

Sin (x+npi/2)

36
Q

Sur ]-1;1[ sin ( arccos x) =

A

Racine (1-x^2)

37
Q

Sur [-1;1] Cos ( arcsin (x)) =

A

Racine (1-x^2)