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Simple cosine...

Source: AMC 12 2006A, Problem 15

February 5, 2006
trigonometryAMC

Problem Statement

Suppose \cos x \equal{} 0 and \cos (x \plus{} z) \equal{} 1/2. What is the smallest possible positive value of z z? <spanclass=′latex−bold′>(A)</span>π6<spanclass=′latex−bold′>(B)</span>π3<spanclass=′latex−bold′>(C)</span>π2<spanclass=′latex−bold′>(D)</span>5π6<spanclass=′latex−bold′>(E)</span>7π6 <span class='latex-bold'>(A) </span> \frac {\pi}{6}\qquad <span class='latex-bold'>(B) </span> \frac {\pi}{3}\qquad <span class='latex-bold'>(C) </span> \frac {\pi}{2}\qquad <span class='latex-bold'>(D) </span> \frac {5\pi}{6}\qquad <span class='latex-bold'>(E) </span> \frac {7\pi}{6}
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