// 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": [{"variable_groups": [], "functions": {}, "tags": [], "ungrouped_variables": ["d", "ans1", "m", "ans2", "a", "b", "ans3"], "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>", "variablesTest": {"condition": "", "maxRuns": 100}, "preamble": {"css": "", "js": ""}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "<p>Convert from radians to degrees</p>"}, "parts": [{"variableReplacementStrategy": "originalfirst", "marks": 0, "prompt": "<p>$\\displaystyle\\simplify{{m}*pi}=$&nbsp;[[0]]$^\\circ$</p>", "type": "gapfill", "gaps": [{"variableReplacementStrategy": "originalfirst", "scripts": {}, "marks": 1, "correctAnswerStyle": "plain", "showCorrectAnswer": true, "correctAnswerFraction": false, "mustBeReducedPC": 0, "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "maxValue": "{ans2}", "showFeedbackIcon": true, "minValue": "{ans2}", "variableReplacements": [], "mustBeReduced": false}], "showFeedbackIcon": true, "showCorrectAnswer": true, "variableReplacements": [], "scripts": {}}, {"variableReplacementStrategy": "originalfirst", "marks": 0, "prompt": "<p>$\\displaystyle\\simplify{pi/{d}}=$&nbsp;[[0]]$^\\circ$</p>", "type": "gapfill", "gaps": [{"variableReplacementStrategy": "originalfirst", "scripts": {}, "marks": 1, "correctAnswerStyle": "plain", "showCorrectAnswer": true, "correctAnswerFraction": false, "mustBeReducedPC": 0, "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "maxValue": "{ans1}", "showFeedbackIcon": true, "minValue": "{ans1}", "variableReplacements": [], "mustBeReduced": false}], "showFeedbackIcon": true, "showCorrectAnswer": true, "variableReplacements": [], "scripts": {}}, {"variableReplacementStrategy": "originalfirst", "marks": 0, "prompt": "<p>$\\displaystyle\\simplify{{a}*pi/{b}}=$&nbsp;[[0]]$^\\circ$</p>", "type": "gapfill", "gaps": [{"variableReplacementStrategy": "originalfirst", "scripts": {}, "marks": 1, "correctAnswerStyle": "plain", "showCorrectAnswer": true, "correctAnswerFraction": false, "mustBeReducedPC": 0, "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "maxValue": "{ans3}", "showFeedbackIcon": true, "minValue": "{ans3}", "variableReplacements": [], "mustBeReduced": false}], "showFeedbackIcon": true, "showCorrectAnswer": true, "variableReplacements": [], "scripts": {}}], "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>", "type": "question", "variables": {"b": {"group": "Ungrouped variables", "description": "", "definition": "random(2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90)", "name": "b", "templateType": "anything"}, "d": {"group": "Ungrouped variables", "description": "", "definition": "random(2,3,4,6)", "name": "d", "templateType": "anything"}, "m": {"group": "Ungrouped variables", "description": "", "definition": "random(1,2)", "name": "m", "templateType": "anything"}, "ans1": {"group": "Ungrouped variables", "description": "", "definition": "switch(d=6, 30, d=4, 45, d=3, 60, d=2, 90 )", "name": "ans1", "templateType": "anything"}, "ans2": {"group": "Ungrouped variables", "description": "", "definition": "if(m=1,180,360)", "name": "ans2", "templateType": "anything"}, "ans3": {"group": "Ungrouped variables", "description": "", "definition": "a*180/b", "name": "ans3", "templateType": "anything"}, "a": {"group": "Ungrouped variables", "description": "", "definition": "random(2..12)", "name": "a", "templateType": "anything"}}, "rulesets": {}, "extensions": [], "name": "Converting angles from radians to degrees", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}