// Numbas version: finer_feedback_settings
{"name": "Converting angles from radians to degrees", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Converting angles from radians to degrees", "tags": [], "metadata": {"description": "<p>Convert from radians to degrees</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Please <g class=\"gr_ gr_3 gr-alert gr_spell gr_inline_cards gr_run_anim ContextualSpelling ins-del multiReplace\" id=\"3\" data-gr-id=\"3\">convert</g> the following angles from radians to degrees.</p>", "advice": "<p>$\\pi$ radians is equal to $180^\\circ$.&nbsp;This means each $\\pi$ we see we can replace it with $180^\\circ$. In other words, to convert from radians to degrees we divide by $\\pi$ and multiply by $180^\\circ$.</p>\n<p></p>\n<p>For example, $\\displaystyle \\frac{2\\pi}{5}=\\frac{2\\pi\\times 180^\\circ}{5\\pi}=\\frac{2\\times 180^\\circ}{5}=72^\\circ$.</p>\n<p></p>\n<p>It is useful to memorise some of the very common angles, for example, $\\displaystyle \\frac{\\pi}{6}=30^\\circ,\\, \\frac{\\pi}{4}=45^\\circ,\\, \\frac{\\pi}{3}=60^\\circ, \\,\\frac{\\pi}{2}=90^\\circ, \\,\\pi=180^\\circ$ and $2\\pi=360^\\circ$.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"ans3": {"name": "ans3", "group": "Ungrouped variables", "definition": "a*180/b", "description": "", "templateType": "anything", "can_override": false}, "ans1": {"name": "ans1", "group": "Ungrouped variables", "definition": "switch(d=6, 30, d=4, 45, d=3, 60, d=2, 90 )", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "random(1,2)", "description": "", "templateType": "anything", "can_override": false}, "ans2": {"name": "ans2", "group": "Ungrouped variables", "definition": "if(m=1,180,360)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90)", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(2,3,4,6)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["d", "ans1", "m", "ans2", "a", "b", "ans3"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\displaystyle\\simplify{{m}*pi}=$&nbsp;[[0]]$^\\circ$</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p><span data-jme-visible=\"m=1\">Recall that $\\pi$ radians is equal to $180^\\circ$. Alternatively, recall that $360^\\circ$ is equal to $2\\pi$ radians and then halve those angles.</span></p>\n<p><span data-jme-visible=\"m=2\">Recall that $2\\pi$ radians is equal to $360^\\circ$. Alternatively, recall that $180^\\circ$ is equal to $\\pi$ radians radians and then double those angles.</span></p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{ans2}", "maxValue": "{ans2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\displaystyle\\simplify{pi/{d}}=$&nbsp;[[0]]$^\\circ$</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Ultimately, it is beneficial to memorise that&nbsp;</p>\n<p style=\"text-align: center;\">$30^\\circ=\\dfrac{\\pi}{6}\\text{ radians}$</p>\n<p style=\"text-align: center;\">$45^\\circ=\\dfrac{\\pi}{4}\\text{ radians}$</p>\n<p style=\"text-align: center;\">$60^\\circ=\\dfrac{\\pi}{3}\\text{ radians}$</p>\n<p style=\"text-align: center;\">$90^\\circ=\\dfrac{\\pi}{2}\\text{ radians}$</p>\n<p style=\"text-align: left;\">Otherwise, recall each $\\pi$ radians is equal to $180^\\circ$. So to convert from radians to degrees we find out how many $\\pi$ radians fit into our angle and then multiply by $180^\\circ$, we can do this in one step by multiplying by $\\dfrac{180^\\circ}{\\pi \\text{ radians}}$:</p>\n<p style=\"text-align: left;\">\\begin{align}\\frac{\\pi}{\\var{d}}\\text{ radians}&amp;=\\frac{\\pi}{\\var{d}} \\times \\dfrac{180^\\circ}{\\pi\\text{ radians}} \\\\ &amp;= \\var{ans1}^\\circ\\end{align}</p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{ans1}", "maxValue": "{ans1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\displaystyle\\simplify{{a}*pi/{b}}=$&nbsp;[[0]]$^\\circ$</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p style=\"text-align: left;\">Recall each $\\pi$ radians is equal to $180^\\circ$. So to convert from radians to degrees we find out how many $\\pi$ radians fit into our angle and then multiply by $180^\\circ$, we can do this in one step by multiplying by $\\dfrac{180^\\circ}{\\pi \\text{ radians}}$:</p>\n<p style=\"text-align: left;\">\\begin{align}\\simplify{{a}*pi/{b}}\\text{ radians}&amp;=\\simplify{{a}*pi/{b}} \\times \\dfrac{180^\\circ}{\\pi\\text{ radians}} \\\\ &amp;= \\var{ans3}^\\circ\\end{align}</p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{ans3}", "maxValue": "{ans3}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "resources": []}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}