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{"name": "Trigonometric Equations 5 - Complex (Degrees)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "a1", "a2", "a3", "a4", "b", "b1", "b2", "b3", "b4", "f1", "p", "c1", "c2", "c3", "c4"], "name": "Trigonometric Equations 5 - Complex (Degrees)", "tags": [], "advice": "<p>Please refer to the advice section of&nbsp;<em>'Trigonometric Equations 1 - Simple (Degrees)'</em> for help.</p>", "rulesets": {}, "parts": [{"prompt": "<p>$\\sin(2x+\\var{b})=$ [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{f1}+0.01", "minValue": "{f1}-0.01", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, 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"minValue": "{a3}-0.5", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{a4}+0.5", "minValue": "{a4}-0.5", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$2x=$ [[0]]$^\\circ$, [[1]]$^\\circ$, [[2]]$^\\circ$ or [[3]]$^\\circ$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{b1}+0.5", "minValue": "{b1}-0.5", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{b2}+0.5", "minValue": "{b2}-0.5", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{b3}+0.5", "minValue": "{b3}-0.5", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{b4}+0.5", "minValue": "{b4}-0.5", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$x=$ [[0]]$^\\circ$, [[1]]$^\\circ$, [[2]]$^\\circ$ or [[3]]$^\\circ$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"integerPartialCredit": "100", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{c1}+0.5", "minValue": "{c1}-0.5", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": "100", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{c2}+0.5", "minValue": "{c2}-0.5", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": "100", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{c3}+0.5", "minValue": "{c3}-0.5", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": "100", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{c4}+0.5", "minValue": "{c4}-0.5", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p><strong>Solve the following equation in <em>degrees</em>, for $x$ in the range $0^\\circ\\leq x\\leq360^\\circ$.</strong></p>\n<p>\\[\\var{a-1}\\sin(2x+\\var{b})=\\var{a-2}\\]</p>\n<p>Give your final answers correct to the nearest degree in ascending order.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(3..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "f1": {"definition": "(a-2)/(a-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "f1", "description": ""}, "b": {"definition": "random(10..p-5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "a4": {"definition": "540-p", "templateType": "anything", "group": "Ungrouped variables", "name": "a4", "description": ""}, "a1": {"definition": "p", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "p": {"definition": "arcsin(f1)*180/pi", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "a3": {"definition": "360+p", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "180-p", "templateType": "anything", "group": "Ungrouped 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"name": "c4", "description": ""}}, "metadata": {"notes": "", "description": "<p>More difficult trigonometric&nbsp;equations with&nbsp;degrees</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Katie Lester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/586/"}]}]}], "contributors": [{"name": "Katie Lester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/586/"}]}