Ok, I split it up like you said. I have [0, pi/4), (pi/4, 5pi/4), and (5pi/4,2pi].
1. On the interval [0,pi/4) cos x is > sin x so this case does not work.
2. On the interval (pi/4, 5pi/4) sinx > cosx, so this is a true statement.
3. On the interval (5pi/4, 2pi] cosx > sin x so this case does...