{"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":"16a33991-3c7e-5b72-a856-71cc1685802f","task_key":"precalculus--test--16a33991-3c7e-5b72-a856-71cc1685802f","task_revision_id":"1","upstream_id":"","short_description":"If $0 \\le \\theta \\le 4 \\pi,$ find all values of $\\theta$ which satisfy","config":"precalculus","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"If $0 \\\\le \\\\theta \\\\le 4 \\\\pi,$ find all values of $\\\\theta$ which satisfy\\n\\\\[\\\\log_{\\\\frac{1}{2} \\\\sin 2 \\\\theta} \\\\sin \\\\theta = \\\\frac{1}{2}.\\\\]Enter all the solutions, separated by commas.\",\"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":[]}