2018 AMC 12A Problem #9

Algebra Level 3

Which of the following describes the largest subset of values of y y within the closed interval [ 0 , π ] [0,\pi] for which sin ⁡ ( x + y ) ≤ sin ⁡ ( x ) + sin ⁡ ( y ) \sin(x+y)\leq \sin(x)+\sin(y) for every x x between 0 0 and π , \pi, inclusive?

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0 ≤ y ≤ π 0 \leq y \leq \pi 0 ≤ y ≤ π 2 0 \leq y \leq \dfrac{\pi}{2} 0 ≤ y ≤ π 4 0 \leq y \leq \dfrac{\pi}{4} 0 ≤ y ≤ 3 π 4 0 \leq y \leq \dfrac{3\pi}{4} y = 0 y=0

Steven Yuan by Steven Yuan , 20, USA

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