MathDB

Sin sqrt(x) < sqrt(sin x) for 0 < x < pi/2

Source: All-Russian Olympiad 2006 finals, problem 11.1

May 6, 2006

trigonometryfunctioncalculusderivativeinequalitiesreal analysisreal analysis unsolved

Problem Statement

Prove that

\sin\sqrt{x}<\sqrt{\sin x}

for every real

x

such that

0<x<\frac{\pi}{2}