formules

Question 1

cos (α-B)

Answer 1

= cos a * cos b - sin a* sin b

Question 2

cos (a+b)

Answer 2

= cos a * cos b + sin a * sin b

Question 3

bewijs cos (a-b)

Answer 3

We weten AB = IIAIIIIBII* cos AOB
= 11 cos (b-a)
= cos (a-b)
en A. B = cosa. cos ẞ+ sina. sin b
Analytische uitdrukkin van scalair product

Question 4

bewijs cos (a+b)

Answer 4

cos (a+b) = cos (a-(-b))
= cos α. cos (-b)+ sina. sin(-b)
=cosa. cos ẞ-sina. sin ẞ

Question 5

sin (a -B)

Answer 5

= sina. cosẞ- cosa. sinẞ

Question 6

sin(α+ B)

Answer 6

= sina. cos ẞ+cosa. sinB

Question 7

bewijs sin(a-b)

Answer 7

sin(a-B) = cos (90°-(α- В))
= cos ((90° -a)+B)
cosinussen van een som
= cos (90° - a). cos B- sin (90° - α). sin ẞ
= sina. cos B- cos a. sin ẞ

Question 8

bewijs sin(a+b)

Answer 8

sin (a+ B) = sin (-(-B))
sinus van een verschil
= sina. cos(-B) -cosa. sin(-B)
tegengestelde hoeken
= sina. cos B- cosa. sin ẞ

Question 9

sin 2α

Answer 9

= 2 sin acos a

Question 10

cos 2a

Answer 10

= cos² a - sin² a
= 2cos² a-1
= 1-2sin²a

Question 11

tan 2a

Answer 11

= 2tan a/ 1-tan² a

Question 12

sin2a (in tan)

Answer 12

sin2a = 2tan a/1+tan² a

Question 13

cos2a (in tan)

Answer 13

1- tan²a/ 1+tan²a

Question 14

Bewijs sin 2a

Answer 14

= sin(a +α)
= sin a*cos α + cos a *sin a
= 2 sinacos a

Question 15

bewijs cos 2a

Answer 15

= cos (a+ a)
= cos a cos a- sin a sin a
= cos² a - sin² α

Question 16

bewijs tan2a

Answer 16

tan2α = tan (a + a)
enzovo

Question 17

sin a t-formules

Answer 17

2t/1+t²

Question 18

tan a t-formules

Answer 18

2t/1-t²

Question 18

cos a t-formules

Answer 18

1-t²/1+t²

Question 19

sin²a carnot

Answer 19

1- cos 2a/2

Question 20

cos²a carnot

Answer 20

1+ cos 2a/2

Question 21

bewijs sin²a carnot

Answer 21

cos 2a = 1-2sin²a ⇒ sin² α =
1- cos 2α/2

Question 22

bewijs cos²a carnot

Answer 22

cos² α = 2 cos² α -1= cos² a = 1+ cos 2a

Question 23

van som naar product sin

Answer 23

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

Question 24

van som naar product cos

Answer 24

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

Question 25

van verschil naar product sin

Answer 25

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

Question 26

van verschil naar product cos

Answer 26

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