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Source: AMC 12 2017A/15

February 8, 2017
AMCAMC 122017 AMC 12A

Problem Statement

Let f(x)=sin⁡x+2cos⁡x+3tan⁡xf(x)=\sin x+2\cos x+3\tan x, using radian measure for the variable xx. In what interval does the smallest positive value of xx for which f(x)=0f(x)=0 lie?
<spanclass=′latex−bold′>(A)</span>(0,1)<spanclass=′latex−bold′>(B)</span>(1,2)<spanclass=′latex−bold′>(C)</span>(2,3)<spanclass=′latex−bold′>(D)</span>(3,4)<spanclass=′latex−bold′>(E)</span>(4,5)<span class='latex-bold'>(A) </span> (0,1) \qquad <span class='latex-bold'>(B) </span> (1,2) \qquad <span class='latex-bold'>(C) </span> (2,3) \qquad <span class='latex-bold'>(D) </span> (3,4) \qquad <span class='latex-bold'>(E) </span> (4,5)
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