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This question is an old question from mathstackexchange.
Let $f_- (n) = \Pi_{i=0}^n ( \sin(i) - \frac{5}{4}) $
And let
$ f_+(m) = \Pi_{i=0}^m ( \sin(i) + \frac{5}{4} ) $
It appears that
$$\sup f_- (n) \inf f_+ (m) = \frac{5}{4} $$
Why is that so ?
Notice
$$\int_0^{2 \pi} \ln(\sin(x) + \frac{5}{4}...
