Trigonometric approach

Algebra Level 2

What is the maximum value of sinA+sinB+sinC if A+B+C=225˚?
Round off to nearest decimal place


The answer is 2.9.

Naman Kapoor by Naman Kapoor , 22, India

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1 solution

We can use this identity

s i n A + s i n B + s i n C 3 ≥ s i n ( A + B + C 3 ) \dfrac{sinA + sinB + sinC}{3} \geq sin(\dfrac{A+B+C}{3}) .

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Jensen's inequality is only true for positive reals. However, when x ∈ ( π , 5 π 4 ] x \in \left(\pi,\dfrac{5\pi}{4}\right] gives the value of sin ⁡ x \sin x as negative.

Rishik Jain - 4 years, 11 months ago

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