In $ \left( 0, \dfrac{\pi}{4} \right) $, which is greater?
sin(tan(x)) or x

Question

In $ \left( 0, \dfrac{\pi}{4} \right) $, which is greater? 
sin(tan(x)) or x

anonymous · Answer

what is x again?  does x have to be somewhere between 0 and pi/4 ?

geerky42 · Answer

Just linear function, y = x. I'm asking which function are greater in between 0 and pi/4

geerky42 · Answer

Just linear function, y = x. I'm asking which function are greater in between 0 and pi/4

anonymous · Answer

well i guess..
if you could prove they are both increasing on that interval

which y = x is doing obviously

y = sin(tan x)..  tan x is certainly increasing from 0 to 1
so sin(0) = 0 up to sin(1) = 
sin(x) is increasing on the interval from 0 to pi/2, so certainly increasing on the interval 0 to 1

so both functions are increasing

maybe integrate both and see which one is greater?

anonymous · Answer

i dont see how this would prove that one is always greater than the other though unless we can determine they do not intersect

anonymous · Answer

analytically not sure how to prove this.  a computer algebra system will verify that the points of intersection are x = 0 and x = about 1.. 

so we are sure that both functions are increasing on the interval (0, pi/4) and only intersect at x = 0.  so one of them is always larger than the other on that interval.

just not sure how to integrate sin tan x