{"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":"15bb2fa5-a9ba-59a4-916d-969af46eee71","task_key":"precalculus--test--15bb2fa5-a9ba-59a4-916d-969af46eee71","task_revision_id":"1","upstream_id":"","short_description":"The point $P$ on the sphere of radius 3 and centered at the origin has spherical…","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"The point $P$ on the sphere of radius 3 and centered at the origin has spherical coordinate $\\\\left( 3, \\\\frac{3 \\\\pi}{8}, \\\\frac{\\\\pi}{5} \\\\right).$  Find the spherical coordinates of the point diametrically opposite $P.$  Enter your answer in the form $(\\\\rho,\\\\theta,\\\\phi),$ where $\\\\rho > 0,$ $0 \\\\le \\\\theta < 2 \\\\pi,$ and $0 \\\\le \\\\phi \\\\le \\\\pi.$\",\"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":[]}