// Numbas version: finer_feedback_settings
{"name": "Converting angles from degrees to radians", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Converting angles from degrees to radians", "metadata": {"description": "<p>Convert from degrees to radians</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "advice": "<p>$180^\\circ$&nbsp;is equal to $\\pi$ radians. This means for each $180^\\circ$ we can replace it with $\\pi$ radians. To determine how many $180^\\circ$s are <g class=\"gr_ gr_8 gr-alert gr_gramm gr_inline_cards gr_run_anim Grammar multiReplace\" id=\"8\" data-gr-id=\"8\">in</g> an angle, we divide the angle by $180^\\circ$. In other words,&nbsp;to convert from degrees to radians we divide by $180^\\circ$ and multiply by $\\pi$ radians.</p>\n<p></p>\n<p>For example, $\\displaystyle 72^\\circ=\\frac{72^\\circ}{180^\\circ}\\times \\pi=\\frac{2\\pi}{5}$.</p>\n<p></p>\n<p>It is useful to memorise some of the very common angles, for example, $30^\\circ=\\displaystyle \\frac{\\pi}{6},\\, 45^\\circ=\\frac{\\pi}{4},\\, 60^\\circ=\\frac{\\pi}{3}, \\,90^\\circ=\\frac{\\pi}{2}, \\,180^\\circ=\\pi$ and $360^\\circ=2\\pi$.</p>", "statement": "<p>Please <g class=\"gr_ gr_6 gr-alert gr_spell gr_inline_cards gr_run_anim ContextualSpelling ins-del multiReplace\" id=\"6\" data-gr-id=\"6\">convert</g> the following angles from degrees to radians.</p>\n<p><strong>Note:</strong> to enter the value $\\pi$ simply type pi. For example, $\\frac{3\\pi}{2}$ could be entered as 3*pi/2 or even as 3pi/2</p>", "functions": {}, "ungrouped_variables": ["easy1", "easyans", "med", "medansden", "a", "b", "ans3"], "parts": [{"showFeedbackIcon": true, "scripts": {}, "marks": 0, "gaps": [{"showFeedbackIcon": true, "showpreview": true, "checkingtype": "absdiff", "checkingaccuracy": 0.001, "answer": "{easyans}", "expectedvariablenames": [], "checkvariablenames": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "marks": 1, "vsetrangepoints": 5, "type": "jme", "showCorrectAnswer": true, "vsetrange": [0, 1]}], "type": "gapfill", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "prompt": "<p>$\\var{easy1}^\\circ=$&nbsp;[[0]]</p>"}, {"showFeedbackIcon": true, "scripts": {}, "marks": 0, "gaps": [{"showFeedbackIcon": true, "showpreview": true, "checkingtype": "absdiff", "checkingaccuracy": 0.001, "answer": "pi/{medansden}", "expectedvariablenames": [], "checkvariablenames": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "marks": 1, "vsetrangepoints": 5, "type": "jme", "showCorrectAnswer": true, "vsetrange": [0, 1]}], "type": "gapfill", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "prompt": "<p>$\\var{med}^\\circ=$&nbsp;[[0]]</p>"}, {"showFeedbackIcon": true, "scripts": {}, "marks": 0, "gaps": [{"showFeedbackIcon": true, "showpreview": true, "checkingtype": "absdiff", "checkingaccuracy": 0.001, "answer": "{a*b/180}pi", "expectedvariablenames": [], "checkvariablenames": false, "answersimplification": "fractionNumbers", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "marks": 1, "vsetrangepoints": 5, "type": "jme", "showCorrectAnswer": true, "vsetrange": [0, 1]}], "type": "gapfill", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "prompt": "<p>$\\var{a*b}^\\circ=$&nbsp;[[0]]</p>"}], "variables": {"ans3": {"name": "ans3", "definition": "a*180/b", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "med": {"name": "med", "definition": " random(30, 45, 60, 90)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "easy1": {"name": "easy1", "definition": "random(180,360)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "easyans": {"name": "easyans", "definition": "if(easy1=180, pi, 2*pi)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "a": {"name": "a", "definition": "random(2..12)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "medansden": {"name": "medansden", "definition": "switch(med=30, 6, med=45, 4, med=60, 3, med=90, 2)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "b": {"name": "b", "definition": "random(2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}}, "preamble": {"js": "", "css": ""}, "rulesets": {}, "tags": [], "variable_groups": [], "extensions": [], "variablesTest": {"condition": "", "maxRuns": 100}, "type": "question", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}