goniometrische vergelijkingen + lijn/puntsymmetrie

Question 1

• sin(A)
  iets met π

Answer 1

= sin(A + π)

Question 2

• cos(A)
  iets met π

Answer 2

= cos(A+ π)

Question 3

cos(π+A)

Answer 3

= - cos(A)

Question 4

sin(-A)

Answer 4

= - sin(A)

Question 5

cos(-A)

Answer 5

= cos(A)

Question 6

sin(x) omzetten naar cos

Answer 6

= cos(½π - x)

Question 7

cos(x) omzetten naar sin

Answer 7

= sin(½π - x)

Question 8

sin(A) = sin(B) oplossen

Answer 8

A= B + k * 2π ⅴ A= π - B + k * 2π

Question 9

cos(A) = cos(B) oplossen

Answer 9

A = B + k *2π ⅴ A= - B + k * 2π

Question 10

tan(A) = tan(B) oplossen

Answer 10

A = B + k * 2π

Question 11

cos²(x) + sin²(x) =

Answer 11

1

Question 12

tan(A)

Answer 12

=sin(A)/cos(A)

Question 13

Tan(x) rijtje

Answer 13

x= o => tan(x) = 0
x= ⅙π => tan(x) = ⅓√3
x= ¼π => tan(x) = 1
x= ⅓π => tan(x) = √3
x= ½π => tan(x) KAN NIET
x= o => tan(x) = 0
etc.

Question 14

sin(A + π)

Answer 14

=- sin(A)

Question 15

lijnsymmetrie in de lijn x=a

Answer 15

toon aan: f(a-p) = f(a+p)
aanpak: begin bij links/rechts en werk naar elkaar toe:
f(a-p) =…
f(a+p) =…

Question 16

puntsymmetrie in het punt (a, b)

Answer 16

toon aan: f(a-p) + f(a+p) = 2b
vb. puntsymmetrie in O (0,0)
=> toon aan: f(-p) + f(p) = 0

Question 17

primitiever f(x) = 3 sin²(x)

Answer 17

= 3 * (½ - ½cos(2x))
= 1½ - 1½cos(2x)
=> F(x) = 1½x - 1½ * ½ * sin(2x) +c