{"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":"e775ca9f-aec3-5ca2-9728-5ad36dbd7534","task_key":"precalculus--test--e775ca9f-aec3-5ca2-9728-5ad36dbd7534","task_revision_id":"1","upstream_id":"","short_description":"Let $\\alpha$ and $\\beta$ be angles such that","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Let $\\\\alpha$ and $\\\\beta$ be angles such that\\n\\\\[\\\\frac{\\\\cos \\\\alpha}{\\\\cos \\\\beta} + \\\\frac{\\\\sin \\\\alpha}{\\\\sin \\\\beta} = -1.\\\\]Find all possible values of\\n\\\\[\\\\frac{\\\\cos^3 \\\\beta}{\\\\cos \\\\alpha} + \\\\frac{\\\\sin^3 \\\\beta}{\\\\sin \\\\alpha}.\\\\]Enter all possible values, 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":[]}