{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"f23abca6-3213-5dbc-bc0a-f5bbb2619de8","task_key":"precalculus--test--f23abca6-3213-5dbc-bc0a-f5bbb2619de8","task_revision_id":"1","upstream_id":"","short_description":"For a positive integer $n$ and an angle $\\theta,$ $\\cos \\theta$ is irrational,…","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"For a positive integer $n$ and an angle $\\\\theta,$ $\\\\cos \\\\theta$ is irrational, but $\\\\cos 2 \\\\theta,$ $\\\\cos 3 \\\\theta,$ $\\\\dots,$ $\\\\cos n \\\\theta$ are all rational.  Find the largest possible value of $n.$\",\"type\":\"Precalculus\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}