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{"name": "Ida Friestad's copy of Trigonometric Equations 7 - Using Identities", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": [], "name": "Ida Friestad's copy of Trigonometric Equations 7 - Using Identities", "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></p>\n<p>You will need to use basic trigonometric identities in this question.</p>\n<p>Please see&nbsp;<a href=\"http://www.purplemath.com/modules/idents.htm\">this link</a>&nbsp;if you do not know what these are.</p>\n<p></p>\n<p>To convert from degrees to radians, multiply by $\\frac{\\pi}{180}$.</p>", "rulesets": {}, "parts": [{"prompt": "<p>$\\sin\\theta-\\sqrt{\\var{a}}\\cos\\theta=0$</p>\n<p>$\\tan\\theta=$&nbsp;[[0]]</p>\n<p></p>\n<p>$\\theta=$&nbsp;[[1]]&nbsp;or&nbsp;[[2]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "sqrt({a})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "allowFractions": false, "variableReplacements": [], "precision": "2", "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, 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[], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "2*cos^2(theta)-cos(theta)-1", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "allowFractions": false, "variableReplacements": [], "precision": "2", "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": 1, "maxValue": "0", "minValue": "0", "type": "numberentry"}, {"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "allowFractions": false, "variableReplacements": [], "precision": "2", "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": 1, "maxValue": "2.0944", "minValue": "2.0944", "type": "numberentry"}, {"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "allowFractions": false, "variableReplacements": [], "precision": "2", "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": 1, "maxValue": "4.1888", "minValue": "4.1888", "type": "numberentry"}, {"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "allowFractions": false, "variableReplacements": [], "precision": "2", "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, 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"variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": 1, "maxValue": "3.6652", "minValue": "3.6652", "type": "numberentry"}, {"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "allowFractions": false, "variableReplacements": [], "precision": "2", "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": 1, "maxValue": "5.7596", "minValue": "5.7596", "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\cos^2\\theta-4\\sin^2\\theta=1$</p>\n<p>$\\theta=$&nbsp;[[0]],&nbsp;[[1]] or&nbsp;[[2]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "allowFractions": false, "variableReplacements": [], "precision": "2", "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": 1, "maxValue": "0", "minValue": "0", "type": "numberentry"}, {"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "allowFractions": false, "variableReplacements": [], "precision": "2", "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": 1, "maxValue": "3.1416", "minValue": "3.1416", "type": "numberentry"}, {"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "allowFractions": false, "variableReplacements": [], "precision": "2", "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": 1, "maxValue": "6.2832", "minValue": "6.2832", "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p><strong>Solve the following equations in <i>radians</i>, for $\\theta$ in the range $0\\leq \\theta\\leq2\\pi$.</strong></p>\n<p>Give your answers rounded to 2 decimal places in ascending order.</p>\n<p>The square root of $a$ is written as sqrt($a$). $\\theta$ is written as theta.</p>", "variable_groups": [{"variables": ["a", "s11", "s12"], "name": "Q1"}, {"variables": ["b", "c", "f2", "s22", "s21", "s23", "s24"], "name": "Q2"}, {"variables": ["f3", "s31", "s32", "s33", "s34"], "name": "Q3"}, {"variables": ["f4", "s4", "s41", "s42", "s43", "s44"], "name": "Q4"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "type": "question", "variables": {"a": {"definition": "random(3..9)", "templateType": "anything", "group": "Q1", "name": "a", "description": ""}, "s22": {"definition": "360-s21", "templateType": "anything", "group": "Q2", "name": "s22", "description": ""}, "f2": {"definition": "c/b", "templateType": "anything", "group": "Q2", "name": "f2", "description": ""}, "f3": {"definition": "(1-b)/(b+1)", "templateType": "anything", "group": "Q3", "name": "f3", "description": ""}, "f4": {"definition": "-c/(c+3)", "templateType": "anything", "group": "Q4", "name": "f4", "description": ""}, "s42": {"definition": "360+s4", "templateType": "anything", "group": "Q4", "name": "s42", "description": ""}, "s12": {"definition": "s11+pi", "templateType": "anything", "group": "Q1", "name": "s12", "description": ""}, "s11": {"definition": "arctan(sqrt(a))", "templateType": "anything", 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