// 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": [{"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>\n<p>Note: do <strong>not</strong> add or subtract multiples of $2\\pi$ to your answer, as we are not necessarily talking about the argument of a complex number.&nbsp;</p>\n<p></p>", "preamble": {"js": "", "css": ""}, "extensions": [], "ungrouped_variables": ["easy1", "easyans", "med", "medansden", "a", "b", "ans3", "d"], "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "<p>Convert from degrees to radians</p>"}, "parts": [{"marks": 0, "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showCorrectAnswer": true, "prompt": "<p>$\\var{easy1}^\\circ=$&nbsp;[[0]]</p>", "gaps": [{"vsetrange": [0, 1], "answer": "{easyans}", "checkingtype": "absdiff", "variableReplacements": [], "checkingaccuracy": 0.001, "checkvariablenames": false, "vsetrangepoints": 5, "marks": 1, "scripts": {}, "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showCorrectAnswer": true, "type": "jme", "showpreview": true, "showFeedbackIcon": true}], "type": "gapfill", "showFeedbackIcon": true}, {"marks": 0, "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showCorrectAnswer": true, "prompt": "<p>$\\var{med}^\\circ=$&nbsp;[[0]]</p>", "gaps": [{"vsetrange": [0, 1], "answer": "pi/{medansden}", "checkingtype": "absdiff", "variableReplacements": [], "checkingaccuracy": 0.001, "checkvariablenames": false, "vsetrangepoints": 5, "marks": 1, "scripts": {}, "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showCorrectAnswer": true, "type": "jme", "showpreview": true, "showFeedbackIcon": true}], "type": "gapfill", "showFeedbackIcon": true}, {"marks": 0, "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showCorrectAnswer": true, "prompt": "<p>$\\var{a*b}^\\circ=$&nbsp;[[0]]</p>", "gaps": [{"vsetrange": [0, 1], "answer": "{a*b/180}pi", "checkingtype": "absdiff", "variableReplacements": [], "answersimplification": "fractionNumbers", "checkingaccuracy": 0.001, "checkvariablenames": false, "vsetrangepoints": 5, "marks": 1, "scripts": {}, "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showCorrectAnswer": true, "type": "jme", "showpreview": true, "showFeedbackIcon": true}], "type": "gapfill", "showFeedbackIcon": true}], "name": "Converting angles from degrees to radians", "variables": {"a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..12)", "description": "", "name": "a"}, "b": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90)", "description": "", "name": "b"}, "easyans": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(easy1=180, pi, 2*pi)", "description": "", "name": "easyans"}, "medansden": {"templateType": "anything", "group": "Ungrouped variables", "definition": "switch(med=30, 6, med=45, 4, med=60, 3, med=90, 2)", "description": "", "name": "medansden"}, "ans3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "a*180/b", "description": "", "name": "ans3"}, "easy1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(180,360)", "description": "", "name": "easy1"}, "med": {"templateType": "anything", "group": "Ungrouped variables", "definition": " random(30, 45, 60, 90)", "description": "", "name": "med"}, "d": {"templateType": "anything", "group": "Ungrouped variables", "definition": "gcd(a*b,180)", "description": "", "name": "d"}}, "functions": {}, "tags": [], "variable_groups": [], "rulesets": {}, "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, $\\displaystyle \\var{a*b}^\\circ=\\frac{\\var{a*b}^\\circ}{180^\\circ}\\times \\pi=\\frac{\\var{a*b/d}}{\\var{180/d}}\\pi$.</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>", "variablesTest": {"condition": "", "maxRuns": 100}, "type": "question", "contributors": [{"name": "John Sheekey", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1192/"}]}]}], "contributors": [{"name": "John Sheekey", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1192/"}]}