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{"name": "Trigonometric Equations 3 - Intermediate (Degrees)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"b": {"templateType": "anything", "name": "b", "description": "", "definition": "random(10..p-5)", "group": "Ungrouped variables"}, "a4": {"templateType": "anything", "name": "a4", "description": "", "definition": "720-p", "group": "Ungrouped variables"}, "a1": {"templateType": "anything", "name": "a1", "description": "", "definition": "p", "group": "Ungrouped variables"}, "p": {"templateType": "anything", "name": "p", "description": "", "definition": "arccos(f)*180/pi", "group": "Ungrouped variables"}, "a": {"templateType": "anything", "name": "a", "description": "", "definition": "random(3..9)", "group": "Ungrouped variables"}, "a2": {"templateType": "anything", "name": "a2", "description": "", "definition": "360-p", "group": "Ungrouped variables"}, "a3": {"templateType": "anything", "name": "a3", "description": "", "definition": "360+p", "group": "Ungrouped variables"}, "b3": {"templateType": "anything", "name": "b3", "description": "", "definition": "a3+b", "group": "Ungrouped variables"}, "b4": {"templateType": "anything", "name": "b4", "description": "", "definition": "a4+b", "group": "Ungrouped variables"}, "f": {"templateType": "anything", "name": "f", "description": "", "definition": "(a-2)/(a+1)", "group": "Ungrouped variables"}, "b2": {"templateType": "anything", "name": "b2", "description": "", "definition": "a2+b", "group": "Ungrouped variables"}, "b1": {"templateType": "anything", "name": "b1", "description": "", "definition": "a1+b", "group": "Ungrouped variables"}}, "statement": "<p><strong>Solve the following equation in <em>degrees</em>, for $x$ in the range $0^\\circ\\leq x\\leq720^\\circ$.</strong></p>\n<p>\\[\\var{a+1}\\cos(x-\\var{b})=\\var{a-2}\\]</p>\n<p>Give your final answers correct to the nearest degree in ascending order.</p>", "name": "Trigonometric Equations 3 - Intermediate (Degrees)", "parts": [{"marks": 0, "showCorrectAnswer": true, "scripts": {}, "type": "gapfill", "prompt": "<p>$\\cos(x-\\var{b})=$ [[0]]</p>", "gaps": [{"showPrecisionHint": false, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "maxValue": "{f}+0.01", "allowFractions": true, "variableReplacements": [], "correctAnswerFraction": true, "minValue": "{f}-0.01", "variableReplacementStrategy": "originalfirst"}], "variableReplacementStrategy": "originalfirst", "variableReplacements": []}, {"marks": 0, "showCorrectAnswer": true, "scripts": {}, "type": "gapfill", "prompt": "<p>$x-\\var{b}=$ [[0]]$^\\circ$, [[1]]$^\\circ$, [[2]]$^\\circ$ or [[3]]$^\\circ$</p>", "gaps": [{"showPrecisionHint": false, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "maxValue": "{a1}+0.5", "allowFractions": false, "variableReplacements": [], "correctAnswerFraction": false, "minValue": "{a1}-0.5", "variableReplacementStrategy": "originalfirst"}, {"showPrecisionHint": false, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "maxValue": "{a2}+0.5", "allowFractions": false, "variableReplacements": [], "correctAnswerFraction": false, "minValue": "{a2}-0.5", "variableReplacementStrategy": "originalfirst"}, {"showPrecisionHint": false, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "maxValue": "{a3}+0.5", "allowFractions": false, "variableReplacements": [], "correctAnswerFraction": false, "minValue": "{a3}-0.5", "variableReplacementStrategy": "originalfirst"}, {"showPrecisionHint": false, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "maxValue": "{a4}+0.5", "allowFractions": false, "variableReplacements": [], "correctAnswerFraction": false, "minValue": "{a4}-0.5", "variableReplacementStrategy": "originalfirst"}], "variableReplacementStrategy": "originalfirst", "variableReplacements": []}, {"marks": 0, "showCorrectAnswer": true, "scripts": {}, "type": "gapfill", "prompt": "<p>$x=$ [[0]]$^\\circ$, [[1]]$^\\circ$, [[2]]$^\\circ$ or [[3]]$^\\circ$</p>", "gaps": [{"showPrecisionHint": false, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "maxValue": "{b1}+0.5", "allowFractions": false, "variableReplacements": [], "correctAnswerFraction": false, "minValue": "{b1}-0.5", "variableReplacementStrategy": "originalfirst"}, {"showPrecisionHint": false, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "maxValue": "{b2}+0.5", "allowFractions": false, "variableReplacements": [], "correctAnswerFraction": false, "minValue": "{b2}-0.5", "variableReplacementStrategy": "originalfirst"}, {"showPrecisionHint": false, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "maxValue": "{b3}+0.5", "allowFractions": false, "variableReplacements": [], "correctAnswerFraction": false, "minValue": "{b3}-0.5", "variableReplacementStrategy": "originalfirst"}, {"showPrecisionHint": false, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "maxValue": "{b4}+0.5", "allowFractions": false, "variableReplacements": [], "correctAnswerFraction": false, "minValue": "{b4}-0.5", "variableReplacementStrategy": "originalfirst"}], "variableReplacementStrategy": "originalfirst", "variableReplacements": []}], "functions": {}, "rulesets": {}, "variable_groups": [], "preamble": {"css": "", "js": ""}, "tags": [], "question_groups": [{"name": "", "pickQuestions": 0, "questions": [], "pickingStrategy": "all-ordered"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "ungrouped_variables": ["a", "a1", "a2", "a3", "a4", "b", "b1", "b2", "b3", "b4", "f", "p"], "advice": "<p>Please refer to the advice section of&nbsp;<em>'Trigonometric Equations 1 - Simple (Degrees)'</em> for help.</p>", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Trigonometric equations with degrees</p>", "notes": ""}, "showQuestionGroupNames": false, "type": "question", "contributors": [{"name": "Katie Lester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/586/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Katie Lester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/586/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}