Interview
Application of Compound and Double angles
- Course
- Mathematics
- Institution
- 11
How to apply Compound and Double angles in trig equations
[Show more]
Seller
Follow
Content preview
EQUATIONS USING COMPOUND ANGLE AND DOUBLE ANGLE IDENITIESNB You do not necessarily start by expanding compound and double angles!
In Grade 11, we solved plenty of equations involving compound and double angles –
without any knowledge of compound and double angle identities!
Take a look at this one…..
e.g. Find the general solution to the equation: sin(𝑥 + 300 ) = cos 2𝑥
Solution:
sin(𝑥 + 300 ) = sin(900 − 2𝑥) (Q I or Q II) DO NOT EXPAND WITH AN IDENTITY!
𝑥 + 300 = 900 − 2𝑥 + 𝑛. 3600 , 𝑛 ∈ 𝑍
3𝑥 = 600
𝑥 = 200 + 𝑛. 1200
or
𝑥 + 300 = 1800 − (900 − 2𝑥) + 𝑛. 3600 , 𝑛 ∈ 𝑍
𝑥 + 300 = 900 + 2𝑥 + 𝑛. 3600
−𝑥 = 600 + 𝑛. 3600
𝑥 = −60 + 𝑛. 3600
e.g. Determine the general solution to the equation:
cos A. cos 240 + sin A. sin 240 = 0,715
Here reducing by using a compound angle identity is essential…
Solution:
cos A. cos 240 + sin A. sin 240 = 0,715
cos (A - 240) = 0,715 (Q I or Q IV) compound angle identity
ref = arccos (0,715) = 44,4 0
A - 240 = 44,40 + n.3600 or A - 240 = 3600 - 44,40 + n.3600, n
A = 68,40 + n.3600 A = 339,60 + n.3600
e.g. Determine the general solution to the equation: sin 2𝑥 + 2 sin 𝑥 = 0
Solution:
sin 2x + 2 sin x = 0
Notice that we must expand here because the angles are different sizes (2𝑥 vs 𝑥)
2 sin x. cos x +2 sin x = 0 double angle identity
2 sin x (cos x +1) = 0 factorise
2 sin x = 0 or cos x = -1
sin x = 0 x = 1800 + n.3600 , n
x = 00 + n.1800 , n
(0;1) (360;1)
(90;1)
1
(270;0)
(360;0) (90;0)
(180;0)
(180;-1)
-1 (270;-1)
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 EFT, 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 this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller kalebroodt. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for R70,00. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
52355 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy summaries for 14 years now