// Numbas version: exam_results_page_options
{"name": "Write as a single trigonometric ratio", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"vsetrangepoints": 5, "answer": "10cos(x+0.64)", "vsetrange": [0, "5"], "marks": "8", "showpreview": true, "checkingtype": "reldiff", "type": "jme", "variableReplacementStrategy": "originalfirst", "checkvariablenames": false, "showFeedbackIcon": true, "expectedvariablenames": [], "scripts": {}, "prompt": "<p>You should find the exact value of $R$ and write $a$ correct to two decimal places.&nbsp;</p>", "variableReplacements": [], "checkingaccuracy": 0.001, "showCorrectAnswer": true}, {"mustBeReduced": false, "allowFractions": false, "precisionPartialCredit": 0, "marks": 1, "precision": "3", "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "prompt": "<p>State the Maximum possible value of $A$</p>", "variableReplacements": [], "showPrecisionHint": true, "showCorrectAnswer": true, "maxValue": "10", "type": "numberentry", "correctAnswerFraction": false, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "mustBeReducedPC": 0, "scripts": {}, "precisionType": "sigfig", "minValue": "10"}], "advice": "<p>R\\cos(x+a) = R\\cos{x}\\cos{a}-R\\sin{x}\\sin{a}&nbsp;</p>\n<p>R\\cos{a}=8&nbsp;and R\\sin{a}=6&nbsp;</p>\n<p>R^2=100 \\Rightarrow R=10&nbsp;</p>\n<p>\\tan{a}=\\frac{3}{2} \\Rightarrow a=0.6435...</p>\n<p>A=10\\cos(x+0.64)&nbsp;</p>\n<p>max(A)=10</p>", "statement": "<p>Express $$8\\cos{x}-6\\sin{x}$$ in the form $$R\\cos{x+a}$$ where $R\\in \\mathbb{R}$ and $-\\pi&lt;a&lt;\\pi$.</p>", "variablesTest": {"maxRuns": 100, "condition": ""}, "functions": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Addition Formulas in Trigonometry. <g class=\"gr_ gr_38 gr-alert gr_gramm gr_inline_cards gr_run_anim Grammar only-ins doubleReplace replaceWithoutSep\" id=\"38\" data-gr-id=\"38\">Range</g> of Sinusoidal&nbsp;functions.&nbsp;</p>"}, "preamble": {"js": "", "css": ""}, "rulesets": {}, "variable_groups": [], "ungrouped_variables": [], "name": "Write as a single trigonometric ratio", "variables": {}, "tags": [], "extensions": [], "type": "question", "contributors": [{"name": "Theodora Ntoka", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2287/"}]}]}], "contributors": [{"name": "Theodora Ntoka", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2287/"}]}