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\[\forall x \ge 0 \text{ }\sin(x) \le x \]

lol ^

I don't know if this works lol
-1

that works for 1=

|dw:1353765596912:dw|

yeah see that's what i meant by arguing from a diagram

maybe using the cosine rule we can convert the diagram proof into something more formal

haha

|dw:1353765811446:dw|

hmm are you using the area of a sector there? doesn't that require calculus?

Yes it doesn't. It just uses compare between to area.
And first one compare two line and curve.

|dw:1353766410319:dw|

from that diagram you can see that:
sin(x) = b/c

also, from arc length, we know:
cx = s (assuming x is measured in radians)

so x = s/c

but s > d

and d > b

therefore sin(x) <= x

@eigenschmeigen - what "methods" are you looking for if no diagrams can be used?

lol

He doesn't want geometry or Calculus.

my situation is that im using this fact as part of a solution to a problem on my analysis sheet, last time i thought i could state it without giveing a proof (at the top of the sheet it said we may assume basic properties of trig functions)
in the course we have only defined sinx in terms of its power series. should i just show that for 0

But power series related to advance calcules!

x-sinx=x3/3!-x5/5!+-...>0 for all x>0

http://www.maths.ox.ac.uk/system/files/coursematerial/2012/2644/22/12MT-AnalysisI-extsyn13.pdf

its given as sinz but thats the general case of sinx...

im fed up. dont worry ill figure it out

whoops,and yeah @CliffSedge ,
its kinda hard when you dont draw it

Yeah, why wouldn't someone want a diagram?