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Intersections Between a Circle and a Trig Equation

Source:

March 3, 2009
trigonometry

Problem Statement

An arbitrary circle can intersect the graph y \equal{} \sin x in <spanclass=′latex−bold′>(A)</span> at most 2 points<spanclass=′latex−bold′>(B)</span> at most 4 points <span class='latex-bold'>(A)</span> \text{ at most 2 points} \qquad <span class='latex-bold'>(B)</span> \text{ at most 4 points} \qquad <spanclass=′latex−bold′>(C)</span> at most 6 points<spanclass=′latex−bold′>(D)</span> at most 8 points <span class='latex-bold'>(C)</span> \text{ at most 6 points} \qquad <span class='latex-bold'>(D)</span> \text{ at most 8 points} \qquad <spanclass=′latex−bold′>(E)</span> more than 16 points <span class='latex-bold'>(E)</span> \text{ more than 16 points}
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