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Sistine
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Homework Statement
I'm trying to prove the following inequality for [tex]0\leq \theta\leq\frac{\pi}{2}[/tex]
[tex] \frac{2}{\pi} \theta \leq\sin\theta[/tex]
Homework Equations
[tex] 0 \leq \theta\leq\frac{\pi}{2} [/tex]
[tex] 0\leq \frac{2}{\pi}\theta\leq 1 [/tex]
The Attempt at a Solution
I've looked at the limit
[tex] \lim_{\theta\to 0}\frac{\sin\theta}{\theta}=1 [/tex]
I've also looked at other inequalities involving [tex]\sin\theta[/tex]
[tex]\sin\theta<\theta[/tex]
I've also tried to take derivatives to see how fast [tex]\sin\theta[/tex] grows in comparison to [tex]\theta[/tex], but I have not managed to prove the inequality.