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).
Abstract
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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