// Numbas version: finer_feedback_settings
{"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": [{"functions": {}, "ungrouped_variables": ["a1", "a2", "a3", "a4", "b", "b1", "b2", "b3", "b4", "c", "c1", "c2", "c3", "c4", "d", "f", "p"], "name": "Trigonometric Equations 6 - Complex (Radians)", "tags": [], "preamble": {"css": "", "js": ""}, "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>", "rulesets": {}, "parts": [{"prompt": "<p>$\\cos(3\\theta+\\var{d})=$ [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{f}+0.01", "minValue": "{f}-0.01", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$3\\theta+\\var{d}=$ [[0]]&nbsp;,&nbsp;[[1]], [[2]] or [[3]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{a1}+0.01", "minValue": "{a1}-0.01", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{a2}+0.01", "minValue": "{a2}-0.01", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{a3}+0.01", "minValue": "{a3}-0.01", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{a4}+0.01", "minValue": "{a4}-0.01", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$3\\theta=$ [[0]]&nbsp;,&nbsp;[[1]], [[2]] or [[3]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{b1}+0.01", "minValue": "{b1}-0.01", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{b2}+0.01", "minValue": "{b2}-0.01", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{b3}+0.01", "minValue": "{b3}-0.01", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{b4}+0.01", "minValue": "{b4}-0.01", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\theta=$ [[0]]&nbsp;,&nbsp;[[1]] or&nbsp;[[2]]</p>\n<p>(Discard any solutions not in range.)</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{c1}+0.01", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "100", "scripts": {}, "marks": 1, "minValue": "{c1}-0.01", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{c2}+0.01", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "100", "scripts": {}, "marks": 1, "minValue": "{c2}-0.01", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{c3}+0.01", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "100", "scripts": {}, "marks": 1, "minValue": "{c3}-0.01", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "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>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a1": {"definition": "p", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "c": {"definition": "random(2..b-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(5..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(0.1..p-0.1 #0.1)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "a4": {"definition": "4*pi-p", "templateType": "anything", "group": "Ungrouped variables", "name": "a4", "description": ""}, "f": {"definition": "c/b", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "b4": {"definition": "a4-d", "templateType": "anything", "group": "Ungrouped variables", "name": "b4", "description": ""}, "p": {"definition": "arccos(f)", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "a3": {"definition": "2*pi+p", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "2*pi-p", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "b1": {"definition": "a1-d", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "b2": {"definition": "a2-d", "templateType": "anything", "group": "Ungrouped variables", "name": "b2", "description": ""}, "b3": {"definition": "a3-d", "templateType": "anything", "group": "Ungrouped variables", "name": "b3", "description": ""}, "c3": {"definition": "b3/3", "templateType": "anything", "group": "Ungrouped variables", "name": "c3", "description": ""}, "c2": {"definition": "b2/3", "templateType": "anything", "group": "Ungrouped variables", "name": "c2", "description": ""}, "c1": {"definition": "b1/3", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "description": ""}, "c4": {"definition": "b4/3", "templateType": "anything", "group": "Ungrouped variables", "name": "c4", "description": ""}}, "metadata": {"notes": "", "description": "<p>More difficult trigonometric&nbsp;equations with radians</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/"}]}