A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 3 years ago
What is the ordered pair of positive intgers (a,b) for which a/b is a reduced fraction and \[x = \frac{a \pi}{b}\] is the least positive solution of the equation: \[(2\cos(8x)−1)(2\cos(4x)−1)(2\cos(2x)−1)(2\cos(x)−1)=1 \]
 3 years ago
What is the ordered pair of positive intgers (a,b) for which a/b is a reduced fraction and \[x = \frac{a \pi}{b}\] is the least positive solution of the equation: \[(2\cos(8x)−1)(2\cos(4x)−1)(2\cos(2x)−1)(2\cos(x)−1)=1 \]

This Question is Closed

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.0From inspection (\(x=0\)) (and therefore \(x=2n\pi\), \(n=0,1,2,...\)) would certainly be a solution to this, but can you confirm that this is not valid since you said "least POSITIVE solution" and I understand that to mean \(x\gt 0\)?

moneybird
 3 years ago
Best ResponseYou've already chosen the best response.1Then other than 0, are there any other possible pairs?

malevolence19
 3 years ago
Best ResponseYou've already chosen the best response.0Well we know for cos(2ax) to be 1 we need that: \[(2m)\frac{a \pi}{b}=2n \pi; n,m \in \mathbb{Z}\] \[a=\frac{bn}{m}; n,m \in \mathbb{Z}\] I'm not sure if you might be looking for a different form.
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.