// Numbas version: exam_results_page_options {"name": "Trigonometric Equations 2 - Simple (Radians multiple angles0)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"statement": "

Solve the following equations in radians, for $\\theta$ in the range $0\\leq\\theta\\leq2\\pi$.

\n

Give your answers correct to 2 decimal places in ascending order.

", "rulesets": {}, "variable_groups": [{"variables": ["a", "f1", "s1", "s11", "s12"], "name": "Q1"}, {"variables": ["b", "c", "f2", "s2", "s21", "s22"], "name": "Q2"}, {"variables": ["f3", "s31", "s32", "s3"], "name": "Q4"}, {"variables": ["f4", "s4", "s41", "s42"], "name": "Q3"}], "extensions": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

Simple trig equations with radians

"}, "parts": [{"prompt": "

\\[\\var{a}\\sin(\\theta)=\\var{a-1}\\]

\n

$\\sin(\\theta)=$ [[0]]

\n

$\\theta=$ [[1]] or [[2]]

", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "marks": 0, "variableReplacements": [], "gaps": [{"marks": 1, "type": "numberentry", "maxValue": "{f1}+0.01", "variableReplacementStrategy": "originalfirst", "allowFractions": true, "minValue": "{f1}-0.01", "showCorrectAnswer": true, "scripts": {}, "variableReplacements": [], "correctAnswerFraction": true}, {"precisionPartialCredit": "100", "maxValue": "{s11}", "variableReplacementStrategy": "originalfirst", "precisionType": "dp", "showPrecisionHint": false, "precision": "2", "variableReplacements": [], "type": "numberentry", "showCorrectAnswer": true, "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "minValue": "{s11}", "marks": 1, "scripts": {}, "correctAnswerFraction": false, "strictPrecision": true}, {"precisionPartialCredit": "100", "maxValue": "{s12}", "variableReplacementStrategy": "originalfirst", "precisionType": "dp", "showPrecisionHint": false, "precision": "2", "variableReplacements": [], "type": "numberentry", "showCorrectAnswer": true, "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "minValue": "{s12}", "marks": 1, "scripts": {}, "correctAnswerFraction": false, "strictPrecision": true}], "scripts": {}}, {"prompt": "

\\[\\var{b}\\cos(\\theta)=\\var{c}\\]

\n

$\\cos(\\theta)=$ [[0]]

\n

$\\theta=$ [[1]] or [[2]]

", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "marks": 0, "variableReplacements": [], "gaps": [{"marks": 1, "type": "numberentry", "maxValue": "{f2}+0.01", "variableReplacementStrategy": "originalfirst", "allowFractions": true, "minValue": "{f2}-0.01", "showCorrectAnswer": true, "scripts": {}, "variableReplacements": [], "correctAnswerFraction": true}, {"precisionPartialCredit": "100", "maxValue": "{s21}", "variableReplacementStrategy": "originalfirst", "precisionType": "dp", "showPrecisionHint": false, "precision": "2", "variableReplacements": [], "type": "numberentry", "showCorrectAnswer": true, "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "minValue": "{s21}", "marks": 1, "scripts": {}, "correctAnswerFraction": false, "strictPrecision": true}, {"precisionPartialCredit": "100", "maxValue": "{s22}", "variableReplacementStrategy": "originalfirst", "precisionType": "dp", "showPrecisionHint": false, "precision": "2", "variableReplacements": [], "type": "numberentry", "showCorrectAnswer": true, "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "minValue": "{s22}", "marks": 1, "scripts": {}, "correctAnswerFraction": false, "strictPrecision": true}], "scripts": {}}, {"prompt": "

\\[\\var{c+3}\\sin(\\theta)=-\\var{c}\\]

\n

$\\sin(\\theta)=$ [[0]]

\n

$\\theta=$ [[1]] or [[2]]

\n

Discard any solutions out of range.

", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "marks": 0, "variableReplacements": [], "gaps": [{"marks": 1, "type": "numberentry", "maxValue": "{f4}+0.01", "variableReplacementStrategy": "originalfirst", "allowFractions": true, "minValue": "{f4}-0.01", "showCorrectAnswer": true, "scripts": {}, "variableReplacements": [], "correctAnswerFraction": true}, {"precisionPartialCredit": "100", "maxValue": "{s41}", "variableReplacementStrategy": "originalfirst", "precisionType": "dp", "showPrecisionHint": false, "precision": "2", "variableReplacements": [], "type": "numberentry", "showCorrectAnswer": true, "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "minValue": "{s41}", "marks": 1, "scripts": {}, "correctAnswerFraction": false, "strictPrecision": true}, {"precisionPartialCredit": "100", "maxValue": "{s42}", "variableReplacementStrategy": "originalfirst", "precisionType": "dp", "showPrecisionHint": false, "precision": "2", "variableReplacements": [], "type": "numberentry", "showCorrectAnswer": true, "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "minValue": "{s42}", "marks": 1, "scripts": {}, "correctAnswerFraction": false, "strictPrecision": true}], "scripts": {}}, {"prompt": "

\\[\\var{b+1}\\cos(\\theta)=-\\var{b-1}\\]

\n

$\\cos(\\theta)=$ [[0]]

\n

$\\theta=$ [[1]] or [[2]]

", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "marks": 0, "variableReplacements": [], "gaps": [{"marks": 1, "type": "numberentry", "maxValue": "{f3}+0.01", "variableReplacementStrategy": "originalfirst", "allowFractions": true, "minValue": "{f3}-0.01", "showCorrectAnswer": true, "scripts": {}, "variableReplacements": [], "correctAnswerFraction": true}, {"precisionPartialCredit": "100", "maxValue": "{s31}", "variableReplacementStrategy": "originalfirst", "precisionType": "dp", "showPrecisionHint": false, "precision": "2", "variableReplacements": [], "type": "numberentry", "showCorrectAnswer": true, "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "minValue": "{s31}", "marks": 1, "scripts": {}, "correctAnswerFraction": false, "strictPrecision": true}, {"precisionPartialCredit": "100", "maxValue": "{s32}", "variableReplacementStrategy": "originalfirst", "precisionType": "dp", "showPrecisionHint": false, "precision": "2", "variableReplacements": [], "type": "numberentry", "showCorrectAnswer": true, "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "minValue": "{s32}", "marks": 1, "scripts": {}, "correctAnswerFraction": false, "strictPrecision": true}], "scripts": {}}], "variables": {"s32": {"templateType": "anything", "description": "", "name": "s32", "definition": "precround(2*pi-s3,2)", "group": "Q4"}, "c": {"templateType": "anything", "description": "", "name": "c", "definition": "random(2..b-1)", "group": "Q2"}, "s42": {"templateType": "anything", "description": "", "name": "s42", "definition": "precround(2*pi+s4,2)", "group": "Q3"}, "b": {"templateType": "anything", "description": "", "name": "b", "definition": "random(5..12)", "group": "Q2"}, "f2": {"templateType": "anything", "description": "", "name": "f2", "definition": "c/b", "group": "Q2"}, "f3": {"templateType": "anything", "description": "", "name": "f3", "definition": "(1-b)/(b+1)", "group": "Q4"}, "s1": {"templateType": "anything", "description": "", "name": "s1", "definition": "arcsin(f1)", "group": "Q1"}, "a": {"templateType": "anything", "description": "", "name": "a", "definition": "random(3..9)", "group": "Q1"}, "s4": {"templateType": "anything", "description": "", "name": "s4", "definition": "arcsin(f4)", "group": "Q3"}, "s2": {"templateType": "anything", "description": "", "name": "s2", "definition": "arccos(f2)", "group": "Q2"}, "f1": {"templateType": "anything", "description": "", "name": "f1", "definition": "(a-1)/a", "group": "Q1"}, "s22": {"templateType": "anything", "description": "", "name": "s22", "definition": "precround(2*pi-s2,2)", "group": "Q2"}, "s11": {"templateType": "anything", "description": "", "name": "s11", "definition": "precround(s1,2)", "group": "Q1"}, "s41": {"templateType": "anything", "description": "", "name": "s41", "definition": "precround(pi-s4,2)", "group": "Q3"}, "s31": {"templateType": "anything", "description": "", "name": "s31", "definition": "precround(s3,2)", "group": "Q4"}, "s21": {"templateType": "anything", "description": "", "name": "s21", "definition": "precround(s2,2)", "group": "Q2"}, "s12": {"templateType": "anything", "description": "", "name": "s12", "definition": "precround(pi-s1,2)", "group": "Q1"}, "f4": {"templateType": "anything", "description": "", "name": "f4", "definition": "-c/(c+3)", "group": "Q3"}, "s3": {"templateType": "anything", "description": "", "name": "s3", "definition": "arccos(f3)", "group": "Q4"}}, "question_groups": [{"questions": [], "pickQuestions": 0, "name": "", "pickingStrategy": "all-ordered"}], "type": "question", "name": "Trigonometric Equations 2 - Simple (Radians multiple angles0)", "showQuestionGroupNames": false, "functions": {}, "ungrouped_variables": [], "advice": "

Please refer to the advice section of 'Trigonometric Equations 1 - Simple (Degrees)' for help.

\n

To convert from degrees to radians, multiply by $\\frac{\\pi}{180}$.

", "preamble": {"css": "", "js": ""}, "tags": [], "contributors": [{"name": "steve kilgallon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/268/"}]}]}], "contributors": [{"name": "steve kilgallon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/268/"}]}