Fonctions circulaires et hyperboliques

Question 1

cos²(x)+sin²(x)

Answer 1

1

Question 2

tan(x)

Answer 2

sin(x)/cos(x)

Question 3

coordonnées polaires (C,O) -> (x,y) ?

Answer 3

x = C cos(O)
y = C sin(O)

Question 4

Coordonnées cartésienne -> (C,O)

Answer 4

C = √(x² + y²)
tan(O) = y/x

Question 5

Domaine de définition de tan ?

Answer 5

D = R / {π/2 + kπ , k € Z}
ou
D = U ] -π/2 + kπ ; π/2 + kπ [

Question 6

cos(a+b)

Answer 6

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

Retenir : coco - sisi

Question 7

sin(a+b)

Answer 7

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

Retenir : sico + cosi

Question 8

tan(a+b)

Answer 8

(tan(a)+tan(b))/(1-tan(a)tan(b))

Question 9

formule de duplication :

cos(2a)

Answer 9

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

Question 10

formule de duplication :

sin(2a)

Answer 10

2sin(a)cos(a)

Question 11

formule de duplication :

tan(2a)

Answer 11

(2tan(a))/(1-tan²(a)

Question 12

sin(-x)

Answer 12

-sin(x)

Question 13

Période de sin ?

Answer 13

sin est 2π-periodique

Question 14

cos(-x)

Answer 14

cos(x)

Question 15

Période de cos ?

Answer 15

2π-periodique

Question 16

tan(-x)

Answer 16

-tan(x)

Question 17

Période de tan ?

Answer 17

tan est π-periodique

Question 18

tan′(x)

Answer 18

1/cos²
OU
1 + tan²

Question 19

lim sin(x)/x
x->0

Answer 19

1 = sin′(0)

Question 20

lim (cos(x)-1)/x
x->0

Answer 20

0 = cos′(0)

Question 21

lim tan(x)/x
x->0

Answer 21

1 = tan′(0)

Question 22

sh(x)

Answer 22

(exp(x)-exp(-x))/2

Question 23

ch(x)

Answer 23

(exp(x)+exp(-x))/2

Question 24

th(x)

Answer 24

sh(x)/ch(x)

Question 25

sh(-x)

Answer 25

-sh(x)

Question 26

ch(-x)

Answer 26

ch(x)

Question 27

th(-x)

Answer 27

-th(x)

Question 28

sh′

Answer 28

ch

Question 29

ch′

Answer 29

sh

Question 30

th′

Answer 30

1/ch²
OU
1 - th²

Question 31

ch² - sh²

Answer 31

1