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 2 years ago
is there a method for proving the following without calculus or arguing by a diagram?
 2 years ago
is there a method for proving the following without calculus or arguing by a diagram?

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eigenschmeigen
 2 years ago
Best ResponseYou've already chosen the best response.0\[\forall x \ge 0 \text{ }\sin(x) \le x \]

hba
 2 years ago
Best ResponseYou've already chosen the best response.0Actually calculus is a very powerful tool to solve problems.So Most of the problems can be solved my Calculus,Therfore,they maybe other ways to solve questions without the use of calculus.

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0yelling, shouting, and just being overall obnoxius tend to be used by kids today to prove their point :)

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.0I don't know if this works lol 1<sinx <1 x < xsinx < x xsinx < x < see this?!

eigenschmeigen
 2 years ago
Best ResponseYou've already chosen the best response.0that works for 1=<x but i dont think it helps particularly for the harder case 0=<x=<1

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1353765596912:dw

eigenschmeigen
 2 years ago
Best ResponseYou've already chosen the best response.0yeah see that's what i meant by arguing from a diagram

eigenschmeigen
 2 years ago
Best ResponseYou've already chosen the best response.0maybe using the cosine rule we can convert the diagram proof into something more formal

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0arent most things proved by being vague and nondescript? or is it just my number theory text that does that?

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1353765811446:dw

eigenschmeigen
 2 years ago
Best ResponseYou've already chosen the best response.0hmm are you using the area of a sector there? doesn't that require calculus?

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.0Yes it doesn't. It just uses compare between to area. And first one compare two line and curve.

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.2from that diagram you can see that: sin(x) = b/c

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.2also, from arc length, we know: cx = s (assuming x is measured in radians)

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.2I am starting the proof off from the basic definition of what sin(x) represents. so you need a diagram.

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.2@eigenschmeigen  what "methods" are you looking for if no diagrams can be used?

hba
 2 years ago
Best ResponseYou've already chosen the best response.0He doesn't want geometry or Calculus.

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0the sine of an angle in a triangle (with the opposite side equal to one,) is the length of the hypotenuse, the hypotenuse is the longest side of a triangle the angle \(x\) is a measure of the arc, the arc is longer than the opposite side

eigenschmeigen
 2 years ago
Best ResponseYou've already chosen the best response.0my 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<x<1 the power series converges to a limit less than x?

eigenschmeigen
 2 years ago
Best ResponseYou've already chosen the best response.0when i stated it without proof my tutor wrote "why?" next to it which means i should have given some form of proof

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.2aren't you contradicting yourself here  the power series is derived using calculus and you stated "no calculus allowed"?

eigenschmeigen
 2 years ago
Best ResponseYou've already chosen the best response.0no, in our course we are _defining_ the functions sin, cos, e^x as their power series, we are not deriving them through the maclauren.

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.0But power series related to advance calcules!

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.0xsinx=x3/3!x5/5!+...>0 for all x>0

eigenschmeigen
 2 years ago
Best ResponseYou've already chosen the best response.0http://www.maths.ox.ac.uk/system/files/coursematerial/2012/2644/22/12MTAnalysisIextsyn13.pdf

eigenschmeigen
 2 years ago
Best ResponseYou've already chosen the best response.0of course i know its related. the way we are doing it (which is perfectly valid) is by defining the functions as the power series and deriving properties from there.

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.0The link you have already suggested was about complex function, and we know there is no comparing in complex number. And also sinZ is not bounded.

eigenschmeigen
 2 years ago
Best ResponseYou've already chosen the best response.0its given as sinz but thats the general case of sinx...

eigenschmeigen
 2 years ago
Best ResponseYou've already chosen the best response.0im fed up. dont worry ill figure it out

CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.0@UnkleRhaukus , did you mean to say, "the sine of an angle in a triangle (with the *hypotenuse* equal to one,) is the length of the *opposite side*, . . . " ?

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0whoops,and yeah @CliffSedge , its kinda hard when you dont draw it

CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.0Yeah, why wouldn't someone want a diagram?

eigenschmeigen
 2 years ago
Best ResponseYou've already chosen the best response.0you cant argue from a diagram in formal mathematics. i cant exactly draw a diagram and hand it in to my analysis tutor
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