Well, my first thoughts were to consider the range of each function.
Both sin(x) and cos(x) are periodic with a range of [-1, 1].
sin(x) is monotonically increasing on the interval [-1, 1] for x, and
so the range of sin(cos(x)) is [sin(-1), sin(1)] ~= [-0.841, 0.841].
Also the average value of this function is thus 0.
cos(x) on the interval [-1, 1] however has a max of 1 at x=0, and
decreases to cos(1) ~= 0.540 at x = +/-1. So cos(sin(x)) has a range of
[0.540, 1], and thus the average value is positive.
Based on these observations, I would say that cos(sin(x)) is greater than sin(cos(x)).
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Posted by Viet
on 2005-08-12 20:18:10 |
Thoughts
