On a Trigonometric Inequality and its Applications

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Zhang, Zhi-Hua and Wu, Yu-Dong (2004) On a Trigonometric Inequality and its Applications. Research report collection, 7 (3).


In this paper, we establish the following trigonometric inequality and another two similar inequalities: 8xy cosA(x cosB + y cosC)² ≤ (x² + y²)², where A,B,C are the angles of triangle ABC and x, y ≥ 0, with equality holding if and only if √((x² + y²)/2a) = xb = yc. By its applications, we give some mobile point geometric inequalities.

Item type Article
URI https://vuir.vu.edu.au/id/eprint/18055
Subjects Historical > FOR Classification > 0101 Pure Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords trigonometric inequality, triangle, conjecture, geometric inequality, mobile point
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