MAT - Paper 2010 - Q3

Flashcards

You want $$x\cos x < \sin x < x$$ and you have $$sin x < x < tan x$$ How can you convert between the two (long)??

If you multiply by $\cos x$ you get

$$ \sin x \cos x < x\cos x < \tan x \cos x $$

The $x\cos x$ is right there in the middle, and $\tan x \cos x$ is $\sin x$, so you have:

$$ \sin x \cos x < x\cos x < \sin x $$

You know from the original inequality that $\sin x < x$, so you now have:

$$ x\cos x < \sin x < x $$

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date: 2021-08-04 14:15
summary: lets do some stuff with inequalities and trig functions because we hate fun
tags:
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- '@?mat'
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title: MAT - Paper 2010 - Q3