🚀 go-pugleaf

In article <1992Nov22.030801.4773@dartvax.dartmouth.edu>, J.Theodore.Schuerzinger@dartmouth.edu (J. Theodore Schuerzinger) writes:
=> Show that (sin x)^(sin x) < (cos x)^(cos x) when 0 < x < pi/4.
=
=Simple math.  Remember that (sin x)^2+(cos x)^2=1.  An identity from my
=trig class back in high school.  Setting sin x equal to cos x, we get
=(sin x)^2=1/2.  The answer to this is x=pi/4.  And since sin x
=increases from 0 to 1 as x increases from 0 to pi/2, it's obvious that
=cos x will be greater than sin x.  As neither is negative in this
=range, (cos x)^2 will be greater than (sin x)^2 from 0<x<pi/4.  I
=haven't taken any math since freshman year of college, but this was
=easy!          

And wrong.  Fine; you've proven that sin(x)^2 < cos(x)^2 for 0<x<pi/4. The
problem, however, was to show that
	sin(x)^sin(x) < cos(x)^cos(x)
Not the same thing at all.
--------------------------------------------------------------------------------
Carl J Lydick | INTERnet: CARL@SOL1.GPS.CALTECH.EDU | NSI/HEPnet: SOL1::CARL

Disclaimer:  Hey, I understand VAXen and VMS.  That's what I get paid for.  My
understanding of astronomy is purely at the amateur level (or below).  So
unless what I'm saying is directly related to VAX/VMS, don't hold me or my
organization responsible for it.  If it IS related to VAX/VMS, you can try to
hold me responsible for it, but my organization had nothing to do with it.