MathDB
A Bad Sine

Source: 2018 AMC 12A #9

February 8, 2018
trigonometry

Problem Statement

Which of the following describes the largest subset of values of yy 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 xx between 00 and π\pi, inclusive? <spanclass=latexbold>(A)</span>y=0<spanclass=latexbold>(B)</span>0yπ4<spanclass=latexbold>(C)</span>0yπ2<spanclass=latexbold>(D)</span>0y3π4<spanclass=latexbold>(E)</span>0yπ<span class='latex-bold'>(A) </span> y=0 \qquad <span class='latex-bold'>(B) </span> 0\leq y\leq \frac{\pi}{4} \qquad <span class='latex-bold'>(C) </span> 0\leq y\leq \frac{\pi}{2} \qquad <span class='latex-bold'>(D) </span> 0\leq y\leq \frac{3\pi}{4} \qquad <span class='latex-bold'>(E) </span> 0\leq y\leq \pi