Trigonométrie

Question 1

cos(-a)

Answer 1

cos(a)

Question 2

sin(-a)

Answer 2

-sin(a)

Question 3

tan(-a)

Answer 3

-tan(a)

Question 4

cos(a+PI)

Answer 4

-cos(a)

Question 5

sin(a+PI)

Answer 5

-sin(a)

Question 6

tan(a+PI)

Answer 6

tan(a)

Question 7

cos(PI-a)

Answer 7

-cos(a)

Question 8

sin(PI-a)

Answer 8

sin(a)

Question 9

cos(a+PI/2)

Answer 9

-sin(a)

Question 10

sin(a+PI/2)

Answer 10

cos(a)

Question 11

cos(PI/2-a)

Answer 11

sin(a)

Question 12

sin(PI/2-a)

Answer 12

cos(a)

Question 13

cos(a+b)

Answer 13

cos(a)cos(b)-sin(a)sin(b)

Question 14

cos(a-b)

Answer 14

cos(a)cos(b)+sin(a)sin(b)

Question 15

sin(a+b)

Answer 15

sin(a)cos(b)+sin(b)cos(a)

Question 16

sin(a-b)

Answer 16

sin(a)cos(b)-sin(b)cos(a)

Question 17

cos(2a)

Answer 17

cos2(a)-sin2(a)
2cos2(a)-1
1-2sin2(a)

Question 18

sin(2a)

Answer 18

2sin(a)cos(a)

Question 19

cos2(a)

Answer 19

(cos(2a)+1)/2

Question 20

sin2(a)

Answer 20

(1-cos(2a))/2

Question 21

cos(a)cos(b)

Answer 21

1/2(cos(a+b)+cos(a-b))

Question 22

sin(a)cos(b)

Answer 22

1/2(sin(a+b)+sin(a-b))

Question 23

sin(a)sin(b)

Answer 23

1/2(cos(a-b)-cos(a+b))

Question 24

cos(a)+cos(b)

Answer 24

2cos(a+b/2)cos(a-b/2)

Question 25

cos(a)-cos(b)

Answer 25

-2sin(a+b/2)sin(a-b/2)

Question 26

sin(a)+sin(b)

Answer 26

2sin(a+b/2)cos(a-b/2)

Question 27

sin(a)-sin(b)

Answer 27

2cos(a+b/2)sin(a-b/2)

Question 28

Formule d’Euler

Answer 28

cos(x)=(e^ix+e^-ix)/2

sin(x)=(e^ix-e^-ix)/2

Question 29

Formule de Moivre

Answer 29

(cos(a)+isin(a))^n=cos(na)+isin(na)