三角形内角正弦乘积不等式：0 ≤ sinA·sinB·sinC ≤ (√3/2)³
2017-10-13 12:02
本GeoGebra范例演示三角形三个内角A、B、C的正弦值乘积所满足的经典不等式。对于任意三角形，其内角正弦乘积恒满足 0 ≤ sinA·sinB·sinC ≤ (√3/2)³。当三角形为等边三角形（A=B=C=60°）时，乘积取最大值(√3/2)³；当某一内角趋近于0°或180°时，乘积趋近于0。通过动态构造与滑块交互，可直观观察不同角度组合下正弦乘积的变化规律，验证该三角不等式的上下界，并探索等腰三角形等特殊情形下的取值特征。
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