Dit document is een samenvatting van 'Module 2 - BEWIJS bijzondere hoeken', uit het boek 'NANDO 4D' voor het vak Wiskunde in het GO! Onderwijs in de doorstroomfinaliteit/ASO.
Bewijs
Gevraagd:
Goniometrische getallen van een hoek van 45°.
Oplossing:
Teken in de goniometrische cirkel een representant voor  = 45°.
ΔOPA is rechthoekig in P en gelijkbenig want de basishoeken Ô en  zijn gelijk aan 45°.
Dus: |OP| = |PA|
cos 45° = sin 45° (1)
We noteren de hoofdformule:
cos² 45° + sin² 45° = 1 -> (1)
2 cos² 45° = 1
1
cos² 45° =
2
1 √2
cos 45° = √2 = 2
(45° ∈ I, dus cos 45° > 0)
Besluit:
√2
sin 45° = cos 45° = 2
√2
sin 45°
tan 45° = = 2 =1
cos 45° √2
2
1
cot 45° = tan 45° = 1
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller thibauttaminiau. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $5.39. You're not tied to anything after your purchase.