How to Establish the Inequality xcosx < sinx < x Using the Unit Circle?

[theperthvan]

This was an exam question I had at the end of 2005 in my uni entrance exams.
Can you do it?

Establish the inequality

$$xcosx < sinx < x$$ where $$0<x<pi/2$$ using the unit circle.

is the tex working?

 

[Werg22]

This is a classic. Here:

http://www.csun.edu/~ac53971/courses/math350/xtra_sine.pdf"

The first part of the proof is what you are looking for.

Edit: Is it a challenge? If so then most people here will be able to do it, this is a very known proof.

 

[theperthvan]

That was quick!

Yes, that's it. Cheers,