Please give me the proof for " absolute value of cos x is less than or equal to absolute value of x? "

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- Jul 4th 2012, 01:15 AMmaddymathprove |cos x| <= |x|
Please give me the proof for " absolute value of cos x is less than or equal to absolute value of x? "

- Jul 4th 2012, 01:21 AMProve ItRe: prove |cos x| <= |x|
- Jul 4th 2012, 06:36 AMHallsofIvyRe: prove |cos x| <= |x|
Have you ever looked at graphs of y= cos(x) and y= |x|?

- Jul 4th 2012, 06:47 AMskeeterRe: prove |cos x| <= |x|
maybe ...

$\displaystyle |\sin{x}| \le |x|$

... ??? - Jul 5th 2012, 06:42 PMmaddymathRe: prove |cos x| <= |x|
thanks guys you gave me confidence actually it were written in a professor's notes but now I'm sure |cos x| =! |x| but |sin x| = |x|

- Jul 6th 2012, 01:14 AMemakarovRe: prove |cos x| <= |x|
- Jul 6th 2012, 01:16 AMProve ItRe: prove |cos x| <= |x|
- Jul 6th 2012, 05:36 AMHallsofIvyRe: prove |cos x| <= |x|
- Jul 6th 2012, 08:37 AMDevenoRe: prove |cos x| <= |x|
sin(x) is approximately x, when |x| is small enough. this is because the 2 curves g(x) = sin(x) and f(x) = x, have "the same slope and value" at the point x = 0.

- Jul 8th 2012, 08:57 AMmaddymathRe: prove |cos x| <= |x|
sin pi/4 =! pi/4

but

sin pi/4 < pi/4 - Jul 8th 2012, 10:20 AMpanda89Re: prove |cos x| <= |x|
Here is a small problem which is related to the given question. prove y=f(x)=x-sinx >=0 for all x>=0

take dy/dx=1-cosx >=0 for all x, y is increasing func, f(x) >= f(0) = 0 for all x>=0

then we can easily extend this solution to solve |sinx| <= |x| - Jul 9th 2012, 10:53 AMmaddymathRe: prove |cos x| <= |x|
I got what I wanted guys thanks

but isn't this amazing see graph in this link graph of sin - Google Search

in this graph sinx does never equal 0,

except only at zero

I was expecting it to be zero at pi, 2pi, 3pi ..... and so on, everywhere on (i-e n(pi)) where n belongs to Z+ - Jul 9th 2012, 11:04 AMemakarovRe: prove |cos x| <= |x|
- Jul 10th 2012, 08:36 AMmaddymathRe: prove |cos x| <= |x|
- Jul 10th 2012, 08:40 AMemakarovRe: prove |cos x| <= |x|