// Numbas version: exam_results_page_options
{"name": "Converting angles from degrees to radians [L7 Random]", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["easy1", "easyans", "med", "medansden", "a", "b", "ans3", "d"], "extensions": [], "rulesets": {}, "preamble": {"css": "", "js": ""}, "parts": [{"showCorrectAnswer": true, "unitTests": [], "marks": 0, "gaps": [{"checkVariableNames": false, "showCorrectAnswer": true, "expectedVariableNames": [], "showFeedbackIcon": true, "unitTests": [], "showPreview": true, "marks": 1, "vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customMarkingAlgorithm": "", "checkingType": "absdiff", "scripts": {}, "failureRate": 1, "vsetRangePoints": 5, "checkingAccuracy": 0.001, "answer": "{easyans}", "variableReplacementStrategy": "originalfirst", "type": "jme"}], "scripts": {}, "variableReplacements": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "<p>$\\var{easy1}^\\circ=$&nbsp;[[0]]</p>", "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "type": "gapfill"}, {"showCorrectAnswer": true, "unitTests": [], "marks": 0, "gaps": [{"checkVariableNames": false, "showCorrectAnswer": true, "expectedVariableNames": [], "showFeedbackIcon": true, "unitTests": [], "showPreview": true, "marks": 1, "vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customMarkingAlgorithm": "", "checkingType": "absdiff", "scripts": {}, "failureRate": 1, "vsetRangePoints": 5, "checkingAccuracy": 0.001, "answer": "pi/{medansden}", "variableReplacementStrategy": "originalfirst", "type": "jme"}], "scripts": {}, "variableReplacements": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "<p>$\\var{med}^\\circ=$&nbsp;[[0]]</p>", "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "type": "gapfill"}, {"showCorrectAnswer": true, "unitTests": [], "marks": 0, "gaps": [{"checkVariableNames": false, "showCorrectAnswer": true, "expectedVariableNames": [], "answerSimplification": "fractionNumbers", "showFeedbackIcon": true, "unitTests": [], "showPreview": true, "marks": 1, "vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customMarkingAlgorithm": "", "checkingType": "absdiff", "scripts": {}, "failureRate": 1, "vsetRangePoints": 5, "checkingAccuracy": 0.001, "answer": "{a*b/180}pi", "variableReplacementStrategy": "originalfirst", "type": "jme"}], "scripts": {}, "variableReplacements": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "<p>$\\var{a*b}^\\circ=$&nbsp;[[0]]</p>", "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "type": "gapfill"}], "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>", "tags": ["L7"], "variable_groups": [], "metadata": {"description": "<p>Convert from degrees to radians</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "variables": {"easyans": {"definition": "if(easy1=180, pi, 2*pi)", "name": "easyans", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "easy1": {"definition": "random(180,360)", "name": "easy1", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "b": {"definition": "random(2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90)", "name": "b", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "d": {"definition": "gcd(a*b,180)", "name": "d", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "a": {"definition": "random(2..12)", "name": "a", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "medansden": {"definition": "switch(med=30, 6, med=45, 4, med=60, 3, med=90, 2)", "name": "medansden", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "ans3": {"definition": "a*180/b", "name": "ans3", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "med": {"definition": " random(30, 45, 60, 90)", "name": "med", "description": "", "templateType": "anything", "group": "Ungrouped variables"}}, "statement": "<p>Please convert 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>", "name": "Converting angles from degrees to radians [L7 Random]", "functions": {}, "type": "question", "contributors": [{"name": "John Sheekey", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1192/"}, {"name": "Matthew James Sykes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2582/"}]}]}], "contributors": [{"name": "John Sheekey", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1192/"}, {"name": "Matthew James Sykes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2582/"}]}