toute la trigonométrie de début d'année

Question 1

sin(-θ)

Answer 1

-sin(θ)

Question 1

cos(-θ)

Answer 1

cos(θ)

Question 2

tan(-θ)

Answer 2

-tan(θ)

Question 3

sin(θ+pi)

Answer 3

-sin(θ)

Question 4

cos(θ+pi)

Answer 4

-cos(θ)

Question 5

tan(θ+pi)

Answer 5

tan(θ)

Question 6

sin(pi-θ)

Answer 6

sin(θ)

Question 7

cos(pi-θ)

Answer 7

-cos(θ)

Question 8

tan(pi-θ)

Answer 8

-tan(θ)

Question 9

sin(θ+pi/2)

Answer 9

cos(θ)

Question 10

cos(θ+pi/2)

Answer 10

-sin(θ)

Question 11

tan(θ+pi/2)

Answer 11

-cotan(θ)

Question 12

sin(pi/2-θ)

Answer 12

cos(θ)

Question 13

cos(pi/2-θ)

Answer 13

sin(θ)

Question 14

tan(pi/2-θ)

Answer 14

cotan(θ)

Question 15

cos(a+b)

Answer 15

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

Question 16

cos(a-b)

Answer 16

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

Question 17

sin(a+b)

Answer 17

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

Question 18

sin(a-b)

Answer 18

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

Question 19

tan(a+b)

Answer 19

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

Question 20

tan(a-b)

Answer 20

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

Question 21

cos(2a)

Answer 21

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

Question 22

sin(2a)

Answer 22

2sin(a)cos(a)

Question 23

cos2(a)

Answer 23

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

Question 24

sin2(a)

Answer 24

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

Question 25

cos(a)cos(b)

Answer 25

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

Question 26

sin(a)sin(b)

Answer 26

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

Question 27

sin(a)cos(b)

Answer 27

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

Question 28

cos(p)+cos(q)

Answer 28

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

Question 29

cos(p)-cos(q)

Answer 29

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

Question 30

sin(p)+sin(q)

Answer 30

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

Question 31

sin(p)-sin(q)

Answer 31

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

Question 32

sin(θ), en fonction de t = tan(θ/2)

Answer 32

(2t)/(1+t^2)

Question 33

cos(θ), en fonction de t = tan(θ/2)

Answer 33

(1-t^2)/(1+t^2)

Question 34

tan(θ), en fonction de t = tan(θ/2)

Answer 34

(2t)/(1-t^2)

Question 35

solutions de sin(x)=sin(θ) pour x

Answer 35

θ+2kpi ou pi-θ+2kpi

Question 36

solutions de cos(x)=cos(θ) pour x

Answer 36

θ+2kpi ou -θ+2kpi

Question 37

solutions de tan(x)=tan(θ) pour x

Answer 37

θ+kpi