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samenvatting getal en ruimte wiskunde B vwo hoofdstuk 12
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  • Course
  • Wiskunde B
  • Level
  • VWO / Gymnasium
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In deze samenvatting staat uitgebreid maar overzichtelijk uitgelegd welke onderwerpen in dit hoofdstuk worden besproken, meestal aangevuld met afbeeldingen en tabellen. Alles over de sinus en cosinus staat hierin

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  • Yes
  • October 4, 2021
  • 4
  • 2020/2021
  • Summary

Subjects

  • parametervoorstelling
  • harmonische functie
  • cirkelbeweging
  • goniometerische fucnties
  • sinus
  • cosinus
  • somformule
  • verdubbelingsformule
  • verschilformule
  • differentiëren
  • integreren
  • primitieve
  • symmetrie

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  • Secondary school
  • VWO / Gymnasium
  • Wiskunde B
  • 6
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Content preview

Wiskunde hoofdstuk 12: Goniometrische formules


Voorkennis:
sinus: Y en cosinus: X

sin ( A ) =C en cos ( A )=C met C=−1 , 0 ,1
Oplossen met de eenheidscirkel

Gevolg door: k + π



−1 1 1 1 1 1
sin ( A ) =C en cos ( A )=C met C= √ 3 ,− √ 2 ,− , , √ 2 , √ 3
2 2 2 2 2 2
Aflezen uit de exacte-waarden-cirkel.

Hierbij: sin ( A ) =C geeft A=B+k∗2 π ∨ A=π−B+k∗2 π .

Hierbij: cos ( A )=C geeft A=B+ k∗2 π ∨ A=−B+ k∗2 π .



sin ( A ) =sin ( B ) en cos ( A )=cos ( B ) .
Hierbij: sin ( A ) =sin ( B ) geeft A=B+k∗2 π ∨ A=π−B+ k∗2 π .

Hierbij: cos ( A )=cos ( B ) geeft A=B+k∗2 π ∨ A=−B+k∗2 π .



Sinusoïde: y=a+b sin ⁡(c ( x−d )) met c>0

 De evenwichtsstand a
 De amplitude |b|
2π
 De periode
c
 Een beginpunt (d,a): bij b>0 gaat de grafiek stijgend door dat punt, met b<0 dalend.

Sinusoïde: y=a+b cos ⁡(c ( x−d ) ) met c>0

 De evenwichtsstand a
 De amplitude |b|
2π
 De periode
c
 Een beginpunt (d,a+b): bij b>0 is dit het hoogste punt, bij b<0 het laagste.

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