Triangle Sine Product Inequality: 0 ≤ sinA·sinB·sinC ≤ (√3/2)³

2017-10-13 12:02

This GeoGebra example demonstrates the classic trigonometric inequality for the product of sines of the three interior angles A, B, and C of any triangle. The inequality states that 0 ≤ sinA·sinB·sinC ≤ (√3/2)³. The maximum value (√3/2)³ is achieved when the triangle is equilateral (A=B=C=60°), while the product approaches 0 as any angle approaches 0° or 180°. Through dynamic construction and inte

#triangle #trigonometry #inequality #optimization

In collections Interactive 3D Surfaces in GeoGebra

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