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{"name": "Trig Identity 6", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Trig Identity 6", "tags": [], "metadata": {"description": "<p>Students need to rewrite a given trig espression in terms of one trig ratio only, Written as a scan solution and upload question, no randomisation.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Using results for double angles and trig identities rewrite the expression \\[5\\cos 2\\theta+ \\cos^2\\theta-3\\] in terms of \\(\\sin\\theta\\) only.</p>", "advice": "<p>\\begin{align}5\\cos 2\\theta+ \\cos^2\\theta-3&amp;=5(1-2\\sin^2\\theta)+\\cos^2\\theta-3\\quad\\text{using identity for }\\cos 2\\theta\\\\&amp;=5(1-2\\sin^2\\theta)+(1-\\sin^2\\theta)-3\\quad\\text{using the Pythagorean identity}\\\\&amp;=5-10\\sin^2\\theta+1-\\sin^2\\theta-3\\\\&amp;=3-11\\sin^2\\theta\\quad\\text{as required}\\end{align}</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}]}]}], "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}]}