{"status": "success", "data": {"description_md": "Suppose $\\cos x=0$ and $\\cos (x+z)=1/2$. What is the smallest possible positive value of $z$?\n\n$\\mathrm{(A) \\ } \\frac{\\pi}{6}\\qquad \\mathrm{(B) \\ } \\frac{\\pi}{3}\\qquad \\mathrm{(C) \\ } \\frac{\\pi}{2}\\qquad \\mathrm{(D) \\ } \\frac{5\\pi}{6}\\qquad \\mathrm{(E) \\ }  \\frac{7\\pi}{6}$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Suppose  <span class=\"katex--inline\">\\cos x=0</span>  and  <span class=\"katex--inline\">\\cos (x+z)=1/2</span> . What is the smallest possible positive value of  <span class=\"katex--inline\">z</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } \\frac{\\pi}{6}\\qquad \\mathrm{(B) \\ } \\frac{\\pi}{3}\\qquad \\mathrm{(C) \\ } \\frac{\\pi}{2}\\qquad \\mathrm{(D) \\ } \\frac{5\\pi}{6}\\qquad \\mathrm{(E) \\ }  \\frac{7\\pi}{6}</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2006 AMC 12A Problem 15", "can_next": true, "can_prev": true, "nxt": "/problem/06_amc12A_p16", "prev": "/problem/06_amc12A_p14"}}