Statement I: For any triangle ,

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Statement I: For any triangle ABCABC, sin⁡(A+B+C3)≥sin⁡A+sin⁡B+sin⁡C3\sin\left(\frac{A+B+C}{3}\right)\ge\frac{\sin A+\sin B+\sin C}{3}. Statement II: y=sin⁡xy=\sin x is concave downward for x∈(0,π]x\in(0,\pi].

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