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{"name": "Trigonometric Equations 6 - Complex (Radians)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"variableReplacementStrategy": "originalfirst", "gaps": [{"variableReplacementStrategy": "originalfirst", "scripts": {}, "correctAnswerFraction": true, "showPrecisionHint": false, "maxValue": "{f}+0.01", "variableReplacements": [], "type": "numberentry", "allowFractions": true, "showCorrectAnswer": true, "minValue": "{f}-0.01", "marks": 1}], "scripts": {}, "showCorrectAnswer": true, "type": "gapfill", "marks": 0, "variableReplacements": [], "prompt": "<p>$\\cos(3\\theta+\\var{d})=$ [[0]]</p>"}, {"variableReplacementStrategy": "originalfirst", "gaps": [{"variableReplacementStrategy": "originalfirst", "scripts": {}, "correctAnswerFraction": false, "showPrecisionHint": false, "maxValue": 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"{a4}-0.01", "marks": 1}], "scripts": {}, "showCorrectAnswer": true, "type": "gapfill", "marks": 0, "variableReplacements": [], "prompt": "<p>$3\\theta+\\var{d}=$ [[0]]&nbsp;,&nbsp;[[1]], [[2]] or [[3]]</p>"}, {"variableReplacementStrategy": "originalfirst", "gaps": [{"variableReplacementStrategy": "originalfirst", "scripts": {}, "correctAnswerFraction": false, "showPrecisionHint": false, "maxValue": "{b1}+0.01", "variableReplacements": [], "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "minValue": "{b1}-0.01", "marks": 1}, {"variableReplacementStrategy": "originalfirst", "scripts": {}, "correctAnswerFraction": false, "showPrecisionHint": false, "maxValue": "{b2}+0.01", "variableReplacements": [], "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "minValue": "{b2}-0.01", "marks": 1}, {"variableReplacementStrategy": "originalfirst", "scripts": {}, "correctAnswerFraction": false, "showPrecisionHint": false, "maxValue": "{b3}+0.01", "variableReplacements": [], "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "minValue": "{b3}-0.01", "marks": 1}, {"variableReplacementStrategy": "originalfirst", "scripts": {}, "correctAnswerFraction": false, "showPrecisionHint": false, "maxValue": "{b4}+0.01", "variableReplacements": [], "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "minValue": "{b4}-0.01", "marks": 1}], "scripts": {}, "showCorrectAnswer": true, "type": "gapfill", "marks": 0, "variableReplacements": [], "prompt": "<p>$3\\theta=$ [[0]]&nbsp;,&nbsp;[[1]], [[2]] or [[3]]</p>"}, {"variableReplacementStrategy": "originalfirst", "gaps": [{"precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerFraction": false, "maxValue": "{c1}+0.01", "showCorrectAnswer": true, "marks": 1, "strictPrecision": true, "precisionType": "dp", "variableReplacementStrategy": "originalfirst", "precision": "2", "precisionPartialCredit": "100", "showPrecisionHint": false, "variableReplacements": [], "type": "numberentry", "allowFractions": false, "scripts": {}, "minValue": "{c1}-0.01"}, {"precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerFraction": false, "maxValue": "{c2}+0.01", "showCorrectAnswer": true, "marks": 1, "strictPrecision": true, "precisionType": "dp", "variableReplacementStrategy": "originalfirst", "precision": "2", "precisionPartialCredit": "100", "showPrecisionHint": false, "variableReplacements": [], "type": "numberentry", "allowFractions": false, "scripts": {}, "minValue": "{c2}-0.01"}, {"precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerFraction": false, "maxValue": "{c3}+0.01", "showCorrectAnswer": true, "marks": 1, "strictPrecision": true, "precisionType": "dp", "variableReplacementStrategy": "originalfirst", "precision": "2", "precisionPartialCredit": "100", "showPrecisionHint": false, "variableReplacements": [], "type": "numberentry", "allowFractions": false, "scripts": {}, "minValue": "{c3}-0.01"}], "scripts": {}, "showCorrectAnswer": true, "type": "gapfill", "marks": 0, "variableReplacements": [], "prompt": "<p>$\\theta=$ [[0]]&nbsp;,&nbsp;[[1]] or&nbsp;[[2]]</p>\n<p>(Discard any solutions not in range.)</p>"}], "name": "Trigonometric Equations 6 - Complex (Radians)", "metadata": {"notes": "", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>More difficult trigonometric&nbsp;equations with radians</p>"}, "statement": "<p><strong>Solve the following equations in <em>radians</em>, for $\\theta$ in the range $0\\leq\\theta\\leq\\pi$:</strong></p>\n<p>\\[\\var{b}\\cos(3\\theta+\\var{d})=\\var{c}\\]</p>\n<p>Give your final answers correct to 2 decimal places in ascending order.</p>", "functions": {}, "ungrouped_variables": ["a1", "a2", "a3", "a4", "b", "b1", "b2", "b3", "b4", "c", "c1", "c2", "c3", "c4", "d", "f", "p"], "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"c1": {"templateType": "anything", "name": "c1", "description": "", "group": "Ungrouped variables", "definition": "b1/3"}, "b2": {"templateType": "anything", "name": "b2", "description": "", "group": "Ungrouped variables", "definition": "a2-d"}, "c": {"templateType": "anything", "name": "c", "description": "", "group": "Ungrouped variables", "definition": "random(2..b-1)"}, "c2": {"templateType": "anything", "name": "c2", "description": "", "group": "Ungrouped variables", "definition": "b2/3"}, "p": {"templateType": "anything", "name": "p", "description": "", "group": "Ungrouped variables", "definition": "arccos(f)"}, "d": {"templateType": "anything", "name": "d", "description": "", "group": "Ungrouped variables", "definition": "random(0.1..p-0.1 #0.1)"}, "a1": {"templateType": "anything", "name": "a1", "description": "", "group": "Ungrouped variables", "definition": "p"}, "b3": {"templateType": "anything", "name": "b3", "description": "", "group": "Ungrouped variables", "definition": "a3-d"}, "b": {"templateType": "anything", "name": "b", "description": "", "group": "Ungrouped variables", "definition": "random(5..12)"}, "b4": {"templateType": "anything", "name": "b4", "description": "", "group": "Ungrouped variables", "definition": "a4-d"}, "c3": {"templateType": "anything", "name": "c3", "description": "", "group": "Ungrouped variables", "definition": "b3/3"}, "a2": {"templateType": "anything", "name": "a2", "description": "", "group": "Ungrouped variables", "definition": "2*pi-p"}, "a4": {"templateType": "anything", "name": "a4", "description": "", "group": "Ungrouped variables", "definition": "4*pi-p"}, "f": {"templateType": "anything", "name": "f", "description": "", "group": "Ungrouped variables", "definition": "c/b"}, "c4": {"templateType": "anything", "name": "c4", "description": "", "group": "Ungrouped variables", "definition": "b4/3"}, "a3": {"templateType": "anything", "name": "a3", "description": "", "group": "Ungrouped variables", "definition": "2*pi+p"}, "b1": {"templateType": "anything", "name": "b1", "description": "", "group": "Ungrouped variables", "definition": "a1-d"}}, "preamble": {"js": "", "css": ""}, "tags": [], "variable_groups": [], "type": "question", "advice": "<p>Please refer to the advice section of&nbsp;<em>'Trigonometric Equations 1 - Simple (Degrees)'</em> for help.</p>\n<p>To convert from degrees to radians, multiply by $\\frac{\\pi}{180}$.</p>", "question_groups": [{"pickQuestions": 0, "name": "", "pickingStrategy": "all-ordered", "questions": []}], "showQuestionGroupNames": false, "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/"}]}