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Inequality (Posted on 2015-02-11) Difficulty: 2 of 5
Show that (sin x)^(sin x) < (cos x)^(cos x) when 0 < x < pi/4

No Solution Yet Submitted by Danish Ahmed Khan    
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re: Trigonometric solution | Comment 3 of 5 |
(In reply to Trigonometric solution by Steve Herman)

Having sin(x)<cos(x) in itself doesn't show (sin(x))^(sin(x)) < (cos(x))^(cos(x)). It depends on some relationship between the sine function and the cosine function.

For example .1 < .5, but .1^.1 > .5^.5 (it's   .7943282347242815 vs   .7071067811865476).

  Posted by Charlie on 2015-02-12 08:57:31
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