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{"name": "Trigonometric Equations 1 - Simple (Degrees)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": [], "name": "Trigonometric Equations 1 - Simple (Degrees)", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p>Firstly, isolate the trigonometric function on one side of the equation.</p>\n<p>Then perform the appropriate inverse trigonometric function on both sides to find the argument.</p>\n<p>Finally, if the argument is an equation or function of the variable you want to find, manipulate your results accordingly.</p>\n<p>For example, if the solutions for the argument of $\\sin(2x)=a$, where $a$ is a number or function, were found to be $46^\\circ$ and&nbsp;$134^\\circ$ within the given range, further operations would be necessary to&nbsp;find the solutions for $x$.</p>\n<p>Here, the first results would be halved and $x$ would therefore be&nbsp;equal to&nbsp;$23^\\circ$ and&nbsp;$67^\\circ$.</p>", "rulesets": {}, "parts": [{"prompt": "<p>\\[\\var{a}\\sin(x)=\\var{a-1}\\]</p>\n<p>$\\sin(x)=$&nbsp;[[0]]</p>\n<p>$x=$&nbsp;[[1]]$^\\circ$,&nbsp;[[2]]$^\\circ$,&nbsp;[[3]]$^\\circ$ or&nbsp;[[4]]$^\\circ$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{f1}+0.01", "minValue": "{f1}-0.01", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": "100", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{s11}", "minValue": "{s11}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": "100", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{s12}", "minValue": "{s12}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": "100", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{s13}", "minValue": "{s13}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": "100", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{s14}", "minValue": "{s14}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>\\[\\var{b}\\cos(x)=\\var{c}\\]</p>\n<p>$\\cos(x)=$ [[0]]</p>\n<p>$x=$&nbsp;[[1]]$^\\circ$,&nbsp;[[2]]$^\\circ$,&nbsp;[[3]]$^\\circ$ or&nbsp;[[4]]$^\\circ$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{f2}+0.01", "minValue": "{f2}-0.01", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": "100", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{s21}", "minValue": "{s21}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": "100", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{s22}", "minValue": "{s22}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": "100", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{s23}", "minValue": "{s23}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": "100", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{s24}", "minValue": "{s24}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>\\[\\var{b+1}\\cos(x)=-\\var{b-1}\\]</p>\n<p>$\\cos(x)=$&nbsp;[[0]]</p>\n<p>$x=$&nbsp;[[1]]$^\\circ$,&nbsp;[[2]]$^\\circ$,&nbsp;[[3]]$^\\circ$ or&nbsp;[[4]]$^\\circ$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{f3}+0.01", "minValue": "{f3}-0.01", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": "100", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{s31}", "minValue": "{s31}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": "100", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{s32}", "minValue": "{s32}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": "100", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{s33}", "minValue": "{s33}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": "100", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{s34}", "minValue": "{s34}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>\\[\\var{c+3}\\sin(x)=-\\var{c}\\]</p>\n<p>$\\sin(x)=$&nbsp;[[0]]</p>\n<p>$x=$&nbsp;[[1]]$^\\circ$,&nbsp;[[2]]$^\\circ$,&nbsp;[[3]]$^\\circ$ or&nbsp;[[4]]$^\\circ$</p>\n<p>Discard any solutions out of range.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{f4}+0.01", "minValue": "{f4}-0.01", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": "100", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{s41}", "minValue": "{s41}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": "100", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{s42}", "minValue": "{s42}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": "100", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{s43}", "minValue": "{s43}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": "100", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{s44}", "minValue": "{s44}", "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 equations in <em>degrees</em>, for $x$ in the range $0^\\circ\\leq x\\leq720^\\circ$.</strong></p>\n<p>Give your answers correct to the nearest degree in ascending order.</p>", "variable_groups": [{"variables": ["a", "f1", "s11", "s12", "s13", "s14"], "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": ""}, "variables": {"f1": {"definition": "(a-1)/a", "templateType": "anything", "group": "Q1", "name": "f1", "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": ""}, "s22": {"definition": "360-s21", "templateType": "anything", "group": "Q2", "name": "s22", "description": ""}, "s4": {"definition": "round(arcsin(f4)*180/pi)", "templateType": "anything", "group": "Q4", "name": "s4", "description": ""}, "s12": {"definition": "180-s11", "templateType": "anything", "group": "Q1", "name": "s12", "description": ""}, "s42": {"definition": "360+s4", "templateType": "anything", "group": "Q4", "name": "s42", "description": ""}, "s13": {"definition": "360+s11", "templateType": "anything", "group": "Q1", "name": "s13", "description": ""}, "s34": {"definition": "720-s31", "templateType": "anything", "group": "Q3", "name": "s34", "description": ""}, "s11": {"definition": "round(arcsin(f1)*180/pi)", "templateType": "anything", "group": "Q1", "name": 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"group": "Q2", "name": "s23", "description": ""}, "s21": {"definition": "round(arccos(f2)*180/pi)", "templateType": "anything", "group": "Q2", "name": "s21", "description": ""}, "s41": {"definition": "180-s4", "templateType": "anything", "group": "Q4", "name": "s41", "description": ""}, "s24": {"definition": "720-s21", "templateType": "anything", "group": "Q2", "name": "s24", "description": ""}, "s43": {"definition": "540-s4", "templateType": "anything", "group": "Q4", "name": "s43", "description": ""}}, "metadata": {"notes": "", "description": "<p>Simple trig equations with 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": 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