The discussion revolves around proving the inequality \(0 \leq \frac{2x}{\pi} \leq \sin x\) for the interval \(0 \leq x \leq \frac{\pi}{2}\). Participants express confusion about how to approach this proof and note the context of its relevance to Jordan's lemma.
The discussion is ongoing, with participants exploring different interpretations of the inequality and suggesting various approaches to tackle the proof. There is no explicit consensus on a single method, but some guidance has been offered regarding potential strategies.
Participants note the importance of the specified interval for \(x\) and the relevance of proper formatting for mathematical expressions in the discussion.
This isn't true in general. If ##x > \pi/2##, the expression in the middle is larger than 1.binbagsss said:Homework Statement
Homework Equations
The Attempt at a Solution
Hi
How do I go about showing ##0 \leq \frac{2x}{\pi} \leq sin x ##?
binbagsss said:I am completely stuck where to start.
Many thanks.
(I see it is a step in the proof of Jordan's lemma, but I'm not interested in this, and the proofs I find do not explain this actual step, ta).
Mark44 said:This isn't true in general. If ##x > \pi/2##, the expression in the middle is larger than 1.
BTW, surround your TeX expressions with either ## (inline) or $$ (standalone) at beginning and end. A single $ character doesn't do anything.
I edited your earlier post to fix this.
binbagsss said:I am completely stuck where to start.
Many thanks.