ADM~~~Trigonometric function

Find the range of x satisfying all the following conditions:
a) x is positive and less than 2(pi)
b) sinx is positive and cosx is negative, and
c) cosx is numerically greater than sinx.
from (b)
sin x is positive at quadrant 1 and 2
cos x is negative at quadrant 2 and 3
So x should be at quadrant 2
from (c)
cosx is numerically greater than sinx
since sin 135=|cos 135|=√2/2
Also |cos x| is increasing and sin x is decreasing in quadrant 2
So the range of x satisfying all the following conditions is
135<x<=180


2007-01-29 23:25:25 補充：
講真朋友sinx is positive and cosx is negativecosx is numerically greater than sinx 根本上就矛盾所以我當(c)個句是指絕對值而言啦

0&lt; x &lt;2pi

sin x&gt;0 and cos x&lt;0
so, combine (a) and (b), pi&gt;x&gt;pi/2

cos^2x&gt;sin^2x, 1&gt;tan^2x
so, combine (a) and (c), pi/4 &gt; x &gt; 0 or 5pi/4 &gt; x &gt;3pi/4 or 2pi &gt; x &gt;7pi/4

Combine all, pi&gt;x&gt;3pi/4