Let c be the Champernowne's constant, or c=0.123456789101112131415161718192021....

Show, without calculator aid, that
sin(c) + cos(c) + tan(c) > 10c

(In reply to re(3): solution by Charlie)

c is small enough that you can get away with the fact that tan(c)>sin(c)
to squeeze in
sin(c) + cos(c) + tan(c) > 2sin(c)+cos(c) > 10c

Next maybe use 1/81 = .012345679012345679...
so 10/81>c and 100/81 > 10c
Actually I'm note sure how to use this since the functions are all increasing but 10c is increasing fastest.

Posted by Jer on 2014-12-13 20:25:35