# MAT - Paper 2010 - Q3

> Source: https://ollybritton.com/notes/maths/problems/mat/2010/q3/ · Updated: 2021-08-04 · Tags: mat, school, maths

## 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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